Data frame of GWAS results where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

Significance level for the threshold. The default is 0.05. You can also assign vector of sinificance levels.

Three methods are offered:

"BH": Benjamini-Hochberg method. To control FDR, use this method.

"Bonf": Bonferroni method. To perform simple correction of multiple testing, use this method.

"Sidak": Sidak method.

You can also assign two of them by 'method = c("BH", "Bonf")'

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance matrices and its design matrices of random effects. You can use more than one kernel matrix. For example, ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D)) (A for additive, D for dominance) Please set names of lists "Z" and "K"!

A list of matrices representing covariance structure between paired random effects. If there are L random effects in the model, the list should contain L lists each consisting of L lists. Each \{i, j\} element of the list includes a matrix K_{ij} representing covariance structure between i-th and j-th random effects. See examples for details.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Perform trace for the optimzation if traceInside >= 1, and this argument shows the frequency of reports.

Maximum number of iterations allowed. Defaults are different depending on 'optimizer'.

If n >= n.thres, perform EMM1.cpp. Else perform EMM2.cpp.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If TRUE, the fitting values of y is returned.

If TRUE, BLUP ('u'; u) will be returned.

If TRUE, the function also computes each BLUP corresponding to different kernels (when solving multi-kernel mixed-effects model). It takes additional time compared to the one with 'return.u.each = FALSE'.

If TRUE, H ^ {-1} = (Var[y] / \sum _{l=1} ^ {L} \sigma _ {l} ^ 2) ^ {-1} will be computed. It also returns V ^ {-1} = (Var[y]) ^ {-1}.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance matrices and its design matrices of random effects. You can use more than one kernel matrix. For example, ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D)) (A for additive, D for dominance) Please set names of lists "Z" and "K"!

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Perform trace for the optimzation if traceInside >= 1, and this argument shows the frequency of reports.

If n >= n.thres, perform EMM1.cpp. Else perform EMM2.cpp.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If TRUE, the fitting values of y is returned.

If TRUE, BLUP ('u'; u) will be returned.

If TRUE, the function also computes each BLUP corresponding to different kernels (when solving multi-kernel mixed-effects model). It takes additional time compared to the one with 'return.u.each = FALSE'.

If TRUE, H ^ {-1} = (Var[y] / \sum _{l=1} ^ {L} \sigma _ {l} ^ 2) ^ {-1} will be computed. It also returns V ^ {-1} = (Var[y]) ^ {-1}.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance matrices and its design matrices of random effects. You can use more than one kernel matrix. For example, ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D)) (A for additive, D for dominance) Please set names of lists "Z" and "K"!

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Package name to be used in this function. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. (‘n.core' will be replaced by 1 for 'package = ’gaston'')

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package = ’RAINBOWR''.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If TRUE, the fitting values of y is returned.

When using the "gaston" package with missing values or using the "MM4LMM" package (with/without missings), computing BLUP will take some time in addition to solving the mixed-effects model. You can choose whether BLUP ('u'; u) will be returned or not.

If TRUE, the function also computes each BLUP corresponding to different kernels (when solving multi-kernel mixed-effects model). It takes additional time compared to the one with 'return.u.each = FALSE' when using packages other than 'RAINBOWR'.

If TRUE, H ^ {-1} = (Var[y] / \sum _{l=1} ^ {L} \sigma _ {l} ^ 2) ^ {-1} will be computed. It also returns V ^ {-1} = (Var[y]) ^ {-1}. It will take some time in addition to solving the mixed-effects model when using packages other than 'RAINBOWR'.

When you use the package other than 'RAINBOWR' and the ratio of variance components is out of the range of 'var.ratio.range', the function will solve the mixed-effects model again with 'RAINBOWR' package, if 'recheck.RAINBOWR = TRUE'.

The range of variance components to check that the results by the package other than RAINBOWR is correct or not when 'recheck.RAINBOWR = TRUE'.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A list of design matrices (Z; n \times m matrix) for Ws. For example, Zs0 = list(A.part = Z.A.part, D.part = Z.D.part)

A list of low rank matrices (W; m \times k matrix). This forms linear kernel K = W \Gamma W'. For example, Ws0 = list(A.part = W.A, D.part = W.D)

A list of matrices for weighting SNPs (Gamma; k \times k matrix). This forms linear kernel K = W \Gamma W'. For example, if there is no weighting, Gammas0 = lapply(Ws0, function(x) diag(ncol(x)))

If each Gamma is the diagonal matrix, please set this argument TRUE. The calculationtime can be saved.

If you repeat this function and when X0 is fixed during iterations, please set this argument TRUE.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

Lower and upper bounds for weights.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Perform trace for the optimzation if traceInside >= 1, and this argument shows the frequency of reports.

If n >= n.thres, perform EMM1.cpp. Else perform EMM2.cpp.

The method of spectral decomposition. In this function, "eigen" : eigen decomposition and "cholesky" : cholesky and singular value decomposition are offered. If this argument is NULL, either method will be chosen accorsing to the dimension of Z and X.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If TRUE, the fitting values of y is returned.

If TRUE, BLUP ('u'; u) will be returned.

If TRUE, the function also computes each BLUP corresponding to different kernels (when solving multi-kernel mixed-effects model). It takes additional time compared to the one with 'return.u.each = FALSE'.

If TRUE, H ^ {-1} = (Var[y] / \sum _{l=1} ^ {L} \sigma _ {l} ^ 2) ^ {-1} will be computed. It also returns V ^ {-1} = (Var[y]) ^ {-1}.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance matrices and its design matrices of random effects. You can use more than one kernel matrix. For example, ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D)) (A for additive, D for dominance) Please set names of lists "Z" and "K"!

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Package name to be used in this function. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores (only for 'MM4LMM').

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If TRUE, the fitting values of y is returned.

When using the "gaston" package with missing values or using the "MM4LMM" package (with/without missings), computing BLUP will take some time in addition to solving the mixed-effects model. You can choose whether BLUP ('u'; u) will be returned or not.

If TRUE, the function also computes each BLUP corresponding to different kernels (when solving multi-kernel mixed-effects model). It takes additional time compared to the one with 'return.u.each = FALSE'.

If TRUE, H ^ {-1} = (Var[y] / \sum _{l=1} ^ {L} \sigma _ {l} ^ 2) ^ {-1} will be computed. It also returns V ^ {-1} = (Var[y]) ^ {-1}. It will take some time in addition to solving the mixed-effects model.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

If n >= n.thres, perform EMM1.cpp. Else perform EMM2.cpp.

If TRUE, EMM2.cpp is performed when the estimation by EMM1.cpp may not be accurate.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The number of initial values you set. If this number is large, the estimation will be more accurate, but computational cost will be large. We recommend setting this value 3 <= lam.len <= 6.

The range of the initial parameters. For example, if lam.len = 5 and init.range = c(1e-06, 1e02), corresponding initial heritabilities will be calculated as seq(1e-06, 1 - 1e-02, length = 5), and then initial lambdas will be set.

The initial parameter if lam.len = 1.

The convergence parameter. If the diffrence of log-likelihood by updating the parameter "lambda" is smaller than this conv.param, the iteration steps will be stopped.

Sometimes algorithms won't converge for some initial parameters. So if the iteration steps reache to this argument, you can stop the calculation even if algorithm doesn't converge.

Lower and Upper bounds of the parameter lambda. If the updated parameter goes out of this range, the parameter is reset to the value in this range.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Perform trace for the optimzation if traceInside >= 1, and this argument shows the frequency of reports.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If this argument is TRUE, warning messages will be shown when estimation is not accurate.

If you want to plot log-likelihood, please set plot.l = TRUE. We don't recommend plot.l = TRUE when lam.len >= 2.

If TRUE, standard errors are calculated.

If TRUE, the function returns the inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u. This is useful for GWAS.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The number of initial values you set. If this number is large, the estimation will be more accurate, but computational cost will be large. We recommend setting this value 3 <= lam.len <= 6.

The range of the initial parameters. For example, if lam.len = 5 and init.range = c(1e-06, 1e02), corresponding initial heritabilities will be calculated as seq(1e-06, 1 - 1e-02, length = 5), and then initial lambdas will be set.

The initial parameter if lam.len = 1.

The convergence parameter. If the diffrence of log-likelihood by updating the parameter "lambda" is smaller than this conv.param, the iteration steps will be stopped.

Sometimes algorithms won't converge for some initial parameters. So if the iteration steps reache to this argument, you can stop the calculation even if algorithm doesn't converge.

Lower and Upper bounds of the parameter 1 / lambda. If the updated parameter goes out of this range, the parameter is reset to the value in this range.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

If this argument is TRUE, warning messages will be shown when estimation is not accurate.

If you want to plot log-likelihood, please set plot.l = TRUE. We don't recommend plot.l = TRUE when lam.len >= 2.

If TRUE, standard errors are calculated.

If TRUE, the function returns the inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u. This is useful for GWAS.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Perform trace for the optimzation if traceInside >= 1, and this argument shows the frequency of reports.

You can choose which method you will use, "REML" or "ML". If REML = TRUE, you will perform "REML", and if REML = FALSE, you will perform "ML".

Lower and Upper bounds of the parameter lambda. If the updated parameter goes out of this range, the parameter is reset to the value in this range.

If TRUE, standard errors are calculated.

If TRUE, the function returns the inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u. This is useful for GWAS.

A n \times m original marker genotype matrix.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is removed from the original marker genotype data.

Specifies the maximum heterozygous rate (HE). If a marker has a HE more than max.HE, it is removed from the original marker genotype data.

Specifies the maximum missing rate (MS). If a marker has a MS more than max.MS, it is removed from the original marker genotype data.

If TRUE, MAF will be returned.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

RGWAS supports two methods to test effects of each SNP-set.

"LR"

Likelihood-ratio test, relatively slow, but accurate (default).

"score"

Score test, much faster than LR, but sometimes overestimate -log10(p).

If this argument is TRUE, dominance effect is included in the model, and additive x dominance and dominance x dominance are also tested as epistatic effects. When you use inbred lines, please set this argument FALSE.

As default, the function also tests the self-interactions among the same SNP-sets. If you want to avoid this, please set 'skip.self.int = TRUE'.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Genotype map for 'gene.set' (list of haplotype blocks). This is a data.frame with the haplotype block (SNP-set, or gene-set) names in the first column. The second and third columns contain the chromosome and map position for each block. The forth column contains the cumulative map position for each block, which can be computed by cumsumPos function. If this argument is NULL, the map will be constructed by genesetmap function after the SNP-set GWAS. It will take some time, so you can reduce the computational time by assigning this argument beforehand.

If TRUE, draw 3d plot

If TRUE, draw 2d plot

The title of 3d plot. If this argument is NULL, trait name is set as the title.

The title of 2d plot. If this argument is NULL, trait name is set as the title.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

RGWAS supports two methods to test effects of each SNP-set.

"LR"

Likelihood-ratio test, relatively slow, but accurate (default).

"score"

Score test, much faster than LR, but sometimes overestimate -log10(p).

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

So local genomic relation matrix is regarded as kernel.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Genotype map for 'gene.set' (list of haplotype blocks). This is a data.frame with the haplotype block (SNP-set, or gene-set) names in the first column. The second and third columns contain the chromosome and map position for each block. The forth column contains the cumulative map position for each block, which can be computed by cumsumPos function. If this argument is NULL, the map will be constructed by genesetmap function after the SNP-set GWAS. It will take some time, so you can reduce the computational time by assigning this argument beforehand.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If TRUE, draw qq plot.

If TRUE, draw manhattan plot.

If this argument = 1, the default manhattan plot will be drawn. If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn. Also, this plot's color is changed by all chromosomes.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

The title of qq plot. If this argument is NULL, trait name is set as the title.

The title of manhattan plot. If this argument is NULL, trait name is set as the title.

If saveName is not NULL and this argument is TRUE, then you can add lines or dots to manhattan plots. However, you should also write "dev.off()" after adding something.

When return.EMM.res = TRUE, the results of equation of mixed models are included in the result of RGWAS.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

If thres = TRUE, the threshold of the manhattan plot is included in the result of RGWAS. When return.EMM.res or thres is TRUE, the results will be "list" class.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

A n \times n Gram (kernel) matrix which may indicate some interaction with SNP-sets to be tested.

Whether or not including 'iteraction.kernel' itself into the null and alternative models.

Whether or not including the interaction term between 'iteraction.kernel' and the genetic background (= kinship matrix) into the null and alternative models. By setting this TRUE, you can avoid the false positives caused by epistastis between polygenes, especially you set kinship matrix as 'interaction.kernel'.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

RGWAS supports only one method to test effects of each SNP-set.

"LR"

Likelihood-ratio test, relatively slow, but accurate (default).

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

So local genomic relation matrix is regarded as kernel.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Genotype map for 'gene.set' (list of haplotype blocks). This is a data.frame with the haplotype block (SNP-set, or gene-set) names in the first column. The second and third columns contain the chromosome and map position for each block. The forth column contains the cumulative map position for each block, which can be computed by cumsumPos function. If this argument is NULL, the map will be constructed by genesetmap function after the SNP-set GWAS. It will take some time, so you can reduce the computational time by assigning this argument beforehand.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If TRUE, draw qq plot.

If TRUE, draw manhattan plot.

If this argument = 1, the default manhattan plot will be drawn. If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn. Also, this plot's color is changed by all chromosomes.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

The title of qq plot. If this argument is NULL, trait name is set as the title.

The title of manhattan plot. If this argument is NULL, trait name is set as the title.

If saveName is not NULL and this argument is TRUE, then you can add lines or dots to manhattan plots. However, you should also write "dev.off()" after adding something.

When return.EMM.res = TRUE, the results of equation of mixed models are included in the result of RGWAS.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

If thres = TRUE, the threshold of the manhattan plot is included in the result of RGWAS. When return.EMM.res or thres is TRUE, the results will be "list" class.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If TRUE, draw qq plot.

If TRUE, draw manhattan plot.

If this argument = 1, the default manhattan plot will be drawn. If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn. Also, this plot's color is changed by all chromosomes.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

The title of qq plot. If this argument is NULL, trait name is set as the title.

The title of manhattan plot. If this argument is NULL, trait name is set as the title.

If saveName is not NULL and this argument is TRUE, then you can add lines or dots to manhattan plots. However, you should also write "dev.off()" after adding something.

When return.EMM.res = TRUE, the results of equation of mixed models are included in the result of RGWAS.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package.MM = ’RAINBOWR''.

If thres = TRUE, the threshold of the manhattan plot is included in the result of RGWAS. When return.EMM.res or thres is TRUE, the results will be "list" class.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

A m \times q matrix. Interaction between each SNP and this matrix will also be tested. For example, principal components of genomic relationship matrix can be used as this matrix to test the interaction between SNPs and the genetic background. Or you can test the interaction with some environmental factors by inputting some omics data that represent the environment. (Test inluding GxE effects.)

Method to compute 'interaction.with.SNPs' when 'interaction.with.SNPs' is NULL. We offer the following four different methods:

"PCA": Principal component analysis for genomic relationship matrix ('K' in 'ZETA') using 'prcomp' function

"LDA": Linear discriminant analysis with independent variables as genomic relationship matrix ('K' in 'ZETA') and dependent variables as some group information ('interaction.group') using 'lda' function

"GROUP": Dummy variables for some group information ('interaction.group')

"DAPC": Perform LDA to the principal components of PCAfor genomic relationship matrix ('K' in 'ZETA') using 'dapc' function in 'adgenet' package. See Jombart et al., 2010 and dapc for more details.

Number of elements (variables) that are included in the model as interaction term for 'interaction.with.SNPs'. If 'interaction.with.SNPs = NULL' and 'n.interaction.element = 0', then the standard SNP-based GWAS will be performed by 'RGWAS.normal' function.

When you use "LDA", "GROUP", or "DAPC", the information on groups (e.g., subgroups for the population) will be required. You can set a vector of group names (or clustering ids) for each genotype as this argument. This vector should be factor.

When 'interaction.group = NULL', 'interaction.group' will be automatically determined by using k-medoids method ('pam' function in 'cluster' package). You should specify the number of groups by this argument to decide 'interaction.group'.

The method to perform clustering when 'interaction.group = NULL'. We offer the following two methods "find.clusters" and "pam". "find.clusters" performs 'adegenet::find.clusters' functions to conduct successive K-means clustering, "pam" performs 'cluster::pam' functions to conduct k-medoids clustering. See find.clusters and pam for more details.

Number of principal components to be used for 'adegenet::find.clusters' or 'adegenet::dapc' functions.

Method for how to test SNPs and the interactions between SNPs and the genetic background. We offer three methods as follows:

"simultaneous": All effects (including SNP efects) are tested simultanously.

"snpSeparate": SNP effects are tested as one effect, and the other interaction effects are simulateneously.

"oneByOne": All efects are tested separately, one by one.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If TRUE, draw qq plot.

If TRUE, draw manhattan plot.

If this argument = 1, the default manhattan plot will be drawn. If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn. Also, this plot's color is changed by all chromosomes.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

The title of qq plot. If this argument is NULL, trait name is set as the title.

The title of manhattan plot. If this argument is NULL, trait name is set as the title.

If saveName is not NULL and this argument is TRUE, then you can add lines or dots to manhattan plots. However, you should also write "dev.off()" after adding something.

When return.EMM.res = TRUE, the results of equation of mixed models are included in the result of RGWAS.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package.MM = ’RAINBOWR''.

If thres = TRUE, the threshold of the manhattan plot is included in the result of RGWAS. When return.EMM.res or thres is TRUE, the results will be "list" class.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

This argument determines how many SNPs (around the SNP detected by normal GWAS) you will recalculate -log10(p).

This argument determines how many genes (around the genes detected by normal GWAS) you will recalculate -log10(p). This argument is valid only when you assign "gene.set" argument.

This argument determines how many SNPs are detected by normal GWAS. For example, when kernel.percent = 0.1, SNPs whose value of -log10(p) is in the top 0.1 percent are chosen as candidate for recalculation by SNP-set GWAS.

If you have already performed normal GWAS and have the result, you can skip performing normal GWAS.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

RGWAS supports two methods to test effects of each SNP-set for 1st GWAS.

"normal"

Normal GWAS (default).

"score"

Score test, much faster than LR, but sometimes overestimate -log10(p).

RGWAS supports two methods to test effects of each SNP-set for 2nd GWAS.

"LR"

Likelihood-ratio test, relatively slow, but accurate (default).

"score"

Score test, much faster than LR, but sometimes overestimate -log10(p).

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

So local genomic relation matrix is regarded as kernel.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test for 1st GWAS. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". you can assign only one test effect for the 1st GWAS!

Effect of each marker to test for 2nd GWAS. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Genotype map for 'gene.set' (list of haplotype blocks). This is a data.frame with the haplotype block (SNP-set, or gene-set) names in the first column. The second and third columns contain the chromosome and map position for each block. The forth column contains the cumulative map position for each block, which can be computed by cumsumPos function. If this argument is NULL, the map will be constructed by genesetmap function after the SNP-set GWAS. It will take some time, so you can reduce the computational time by assigning this argument beforehand.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If TRUE, draw qq plot for normal GWAS.

If TRUE, draw manhattan plot for normal GWAS.

If TRUE, draw qq plot for SNP-set GWAS.

If TRUE, draw manhattan plot for SNP-set GWAS.

If this argument = 1, the default manhattan plot will be drawn. If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn. Also, this plot's color is changed by all chromosomes.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

Color of the points of manhattan plot which are added after the reestimation by SNP-set method. You should substitute this argument as color vector whose length is 2. plot.col3[1] for odd chromosomes and plot.col3[2] for even chromosomes.

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

The title of qq plot for normal GWAS. If this argument is NULL, trait name is set as the title.

The title of manhattan plot for normal GWAS. If this argument is NULL, trait name is set as the title.

The title of qq plot for SNP-set GWAS. If this argument is NULL, trait name is set as the title.

The title of manhattan plot for SNP-set GWAS. If this argument is NULL, trait name is set as the title.

If saveName is not NULL and this argument is TRUE, then you can add lines or dots to manhattan plots. However, you should also write "dev.off()" after adding something.

When return.EMM.res = TRUE, the results of equation of mixed models are included in the result of RGWAS.

If thres = TRUE, the threshold of the manhattan plot is included in the result of RGWAS. When return.EMM.res or thres is TRUE, the results will be "list" class.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A n \times 1 vector or a n \times p _ 1 matrix. You can insert continuous values, such as other traits or genotype score for special markers. This argument is regarded as one of the fixed effects.

A n \times p _ 2 dataframe. You should assign a factor vector for each column. Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.

You can use structure matrix calculated by structure analysis when there are population structure. You should not use this argument with n.PC > 0.

Number of principal components to include as fixed effects. Default is 0 (equals K model).

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

This argument determines how many SNPs (around the SNP detected by normal GWAS) you will check epistasis.

This argument determines how many SNPs are detected by normal GWAS. For example, when epistasis.percent = 0.1, SNPs whose value of -log10(p) is in the top 0.1 percent are chosen as candidate for checking epistasis.

It takes a lot of time to check epistasis, so you can decide the maximum number of SNPs to check epistasis.

Because there are less SNPs that can be tested in epistasis than in kernel-based GWAS, you can select which SNPs you want to test. If you use this argument, please set the number where SNPs to be tested are located in your data (so not position). In the default setting, your_check = NULL and epistasis between SNPs detected by GWAS will be tested.

If you have already performed regular GWAS and have the result, you can skip performing normal GWAS.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

RGWAS supports two methods to test effects of each SNP-set.

"LR"

Likelihood-ratio test, relatively slow, but accurate (default).

"score"

Score test, much faster than LR, but sometimes overestimate -log10(p).

If this argument is TRUE, dominance effect is included in the model, and additive x dominance and dominance x dominance are also tested as epistatic effects. When you use inbred lines, please set this argument FALSE.

As default, the function also tests the self-interactions among the same SNP-sets. If you want to avoid this, please set 'skip.self.int = TRUE'.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Genotype map for 'gene.set' (list of haplotype blocks). This is a data.frame with the haplotype block (SNP-set, or gene-set) names in the first column. The second and third columns contain the chromosome and map position for each block. The forth column contains the cumulative map position for each block, which can be computed by cumsumPos function. If this argument is NULL, the map will be constructed by genesetmap function after the SNP-set GWAS. It will take some time, so you can reduce the computational time by assigning this argument beforehand.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If TRUE, draw qq plot for normal GWAS.

If TRUE, draw manhattan plot for normal GWAS.

If TRUE, draw 3d plot

If TRUE, draw 2d plot

If this argument = 1, the default manhattan plot will be drawn. If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn. Also, this plot's color is changed by all chromosomes.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

The title of qq plot for normal GWAS. If this argument is NULL, trait name is set as the title.

The title of manhattan plot for normal GWAS. If this argument is NULL, trait name is set as the title.

The title of 3d plot. If this argument is NULL, trait name is set as the title.

The title of 2d plot. If this argument is NULL, trait name is set as the title.

As default, RAINBOWR checks the type of input data and modifies it into the correct format. However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure by setting 'skip.check = TRUE'.

If this argument is TRUE, messages for the current steps will be shown.

If this argument is TRUE, welcome message will be shown.

When count is TRUE, you can know how far RGWAS has ended with percent display.

When time is TRUE, you can know how much time it took to perform RGWAS.

Data frame of GWAS results where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

A N (lines) x M (markers) marker genotype data (matrix), coded as [-1, 0, 1] = [aa, Aa, AA].

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.

A vector of causal markers. You should assign where those causal markers are positioned in our marker genotype, rather than physical position of those causal markers.

If you have information of gene (or haplotype block), and if you used it to perform kernel-based GWAS, you should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "x" argument.

We will calculate the mean of -log10(p) values of top 'n.top.false.block' blocks to evaluate the inflation level of results. The default is 10.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

If 'the -log10(p) value for each marker' exceeds ('the inflation level' + 'inflator.plus'), that marker is regarded as significant.

SNPs within the extent of LD are regareded as one set. This LD_length determines the size of LD block, and 2 x LD_length (b.p.) will be the size of LD block.

SNPs within the extent of LD are regareded as one set. This cor.thres also determines the size of LD block, and the region with square of correlation coefficients >= cor.thres is regareded as one LD block. More precisely, the regions which satisfies both LD_length and cor.thres condition is rearded as one LD block.

If you peform SNP-set analysis with slinding window, we can consider the effect of window size by this argument.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

If this argunent is TRUE, ROC (Reciever Operating Characteristic) curve will be drawn with AUC (Area Under the Curve).

Your data. 'vector', 'matrix', 'array' (whose dimensions <= 4), 'data.frame' are supported format. If other formatted data is assigned, str(data) will be returned.

From head. If this argument is TRUE, first part (row) of data will be shown (like head() function). If FALSE, last part (row) of your data will be shown (like tail() function).

From left. If this argument is TRUE, first part (column) of data will be shown (like head() function). If FALSE, last part (column) of your data will be shown (like tail() function).

The number of rows shown in console.

The number of columns shown in console.

The start point for the direction of row.

The start point for the direction of column.

The number of dimensions other than row and column shown in console. This argument is effective only your data is array (whose dimensions >= 3).

When rown = 1 or coln = 1, the dimension will be reduced if this argument is TRUE.

If you want to assign the result to a variable, please set this agument TRUE.

If TRUE, print the first part of data.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance matrices and its design matrices of random effects. You can use only one kernel matrix for this function. For example, ZETA = list(A = list(Z = Z.A, K = K.A)) (A for additive) Please set names of lists "Z" and "K"!

The information on group memberships (e.g., subgroups for the population) will be required. You can set a vector of group names (or clustering ids) for each genotype as this argument. This vector should be factor.

When 'subpopInfo = NULL', 'subpopInfo' will be automatically determined by using find.clusters function. You should specify the number of groups by this argument to decide 'subpopInfo'.

Number of principal components to be used for 'adegenet::find.clusters'. This argument is used inly when 'subpopInfo' is 'NULL'.

Whether or not including the genome-wide epistastic effects into the model to adjust ZETA.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A N \times M matrix of marker genotype

Method to calculate genomic relationship matrix (GRM). We offer the following methods; "addNOIA", "domNOIA", "A.mat", "linear", "gaussian", "exponential", "correlation". For NOIA methods, please refer to Vitezica et al. 2017.

Sub-population names corresponding to each individual. By utilizing 'subpop' argument, you can consider the difference of allele frequencies between sub-populations when computing the genomic relationship matrix. This argument is only valid when NOIA methods are selected.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If this argument is TRUE, we will return W matrix instead of GRM. Here, W satisfies GRM = W W ^ {T}. W corresponds to H matix in Vitezica et al. 2017.

Probability of being homozygous for the reference allele for each marker. If NULL (default), it will be calculated from genoMat.

Probability of being heterozygous for the reference and alternative alleles for each marker If NULL (default), it will be calculated from genoMat.

Split marker genotype data into subsets consisting of 'batchSize' SNPs, and compute GRM. If NULL, all the markers will be used for the computation at a time. We recommend using this argument when the total number of markers is too large.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is only valid 'batchSize' is not 'NULL'.

File name of the haplotype block list generated by PLINK (See reference). The file names must contain ".blocks.det" in the tail.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.

You can specify the header of block names for the returned data.frame.

As default, blocks including only one SNP will be discarded from the returned data. If you want to include them when creating haplotype-block list for RAINBOWR, please set 'imputeOneSNP = TRUE'.

When naming blocks, whether or not inserting zeros to the name of blocks. For example, if there are 1,000 blocks in total, the function will name the block 1 as "block_1" when 'insertZeros = FALSE' and "block_0001" when 'insertZeros = TRUE'.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

When count is TRUE, you can know how far RGWAS has ended with percent display.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.

A vector of genotype (line; accesion; variety) names which correpond to phenotypic values.

A vector of genotype (line; accesion; variety) names for marker genotype data (duplication is not recommended).

A n \times M matrix representing the marker genotype that belongs to the haplotype block of interest. If this argument is NULL, this argument will automatically be determined by 'geno',

You can use the results (data.frame) of haplotype-based (SNP-set) GWAS by 'RGWAS.multisnp' function.

Haplotype blocks (or gene sets, SNP-sets) with top 'nTopRes' p-values by 'gwasRes' will be used.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

You can specify the haplotype block (or gene set, SNP-set) of interest by the marker index in 'geno'.

You can specify the haplotype block (or gene set, SNP-set) of interest by the marker position in 'geno'. Please assign the chromosome number to this argument.

You can specify the haplotype block (or gene set, SNP-set) of interest by the marker position in 'geno'. Please assign the position in the chromosome to this argument.

You can specify the haplotype block (or gene set, SNP-set) of interest by the name of haplotype block in 'geno'.

Number of haplotypes. If not defined, this is automatically defined by the data. If defined, k-medoids clustering is performed to define haplotypes.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

If TRUE, chi-square test for the relationship between haplotypes & subpopulations will be performed.

The threshold for the chi-square test.

If TRUE, the function will return the plot of haplotype network.

You can assign the distance matrix of the block of interest. If NULL, the distance matrix will be computed in this function.

You can choose the method to calculate distance between accessions. This argument corresponds to the 'method' argument in the 'dist' function.

If TRUE, the evolution distance will be used instead of the pure distance. The 'distMat' will be converted to the distance matrix by the evolution distance when you use 'complementHaplo = "phylo"'.

how to complement unobserved haplotypes. When 'complementHaplo = "all"', all possible haplotypes will be complemented from the observed haplotypes. When 'complementHaplo = "never"', unobserved haplotypes will not be complemented. When 'complementHaplo = "phylo"', unobserved haplotypes will be complemented as nodes of phylogenetic tree. When 'complementHaplo = "TCS"', unobserved haplotypes will be complemented by TCS methods (Clement et al., 2002).

The information of subpopulations. This argument should be a vector of factor.

If 'subpopInfo' argument is NULL, this function estimates subpopulation information from marker genotype. You can choose the grouping method from 'kmeans', 'kmedoids', and 'hclust'.

The number of groups (or subpopulations) grouped by 'groupingMethod'. If this argument is 0, the subpopulation information will not be estimated.

If 'groupingMethod' = 'kmeans', the clustering will be performed multiple times. This argument specifies the number of classification performed by the function.

The number of iterations for RMST (randomized minimum spanning tree).

Either one of 'mst' (minimum spanning tree), 'msn' (minimum spanning network), and 'rmst' (randomized minimum spanning tree). 'rmst' is recommended.

This argument will be valid only when you use 'complementHaplo = "all"' or 'complementHaplo = "TCS"'. This argument specifies whether the plant is autogamous or not. If autogamous = TRUE, complemented haplotype will consist of only homozygous sites ([-1, 1]). If FALSE, complemented haplotype will consist of both homozygous & heterozygous sites ([-1, 0, 1]).

Equal to the argument 'prob' in 'haplotypes::parsimnet' function:

A numeric vector of length one in the range [0.01, 0.99] giving the probability of parsimony as defined in Templeton et al. (1992). In order to set maximum connection steps to Inf (to connect all the haplotypes in a single network), set the probability to NULL.

The maximum number of haplotypes. If the number of total (complemented + original) haplotypes are larger than 'nMaxHaplo', we will only show the results only for the original haplotypes to reduce the computational time.

In the function, similarlity matrix between accessions will be computed from marker genotype to estimate genotypic values. This argument specifies the method to compute similarity matrix: If this argument is 'addNOIA' (or one of other options in 'methodGRM' in 'calcGRM'), then the 'addNOIA' (or corresponding) option in the 'calcGRM' function will be used, and if this argument is 'diffusion', the diffusion kernel based on Laplacian matrix will be computed from network. You can assign more than one kernelTypes for this argument; for example, kernelTypes = c("addNOIA", "diffusion").

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation in optimizing hyperparameters for estimating haplotype effects. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

Optimized hyper parameter for constructing kernel when estimating haplotype effects. If hOpt = "optimized", hyper parameter will be optimized in the function. If hOpt is numeric, that value will be directly used in the function.

Optimized hyper parameter for constructing kernel when estimating complemented haplotype effects. If hOpt2 = "optimized", hyper parameter will be optimized in the function. If hOpt2 is numeric, that value will be directly used in the function.

Max number of iterations for optimization algorithm.

The median of off-diagonal of distance matrix multiplied by rangeHStart will be used as the initial values for optimization of hyper parameters.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

This argument specifies how to save the plot of phylogenetic tree. The function offers 'png', 'pdf', 'jpg', and 'tiff'.

We will show the MDS (multi-dimensional scaling) plot, and this argument is a vector of two integers specifying that will define which MDS dimension will be plotted. The first and second integers correspond to the horizontal and vertical axes, respectively.

A vector of two integers or characters specifying the colors of connection between nodes for the original and complemented haplotypes, respectively.

A vector of two characters specifying the line types of connection between nodes for the original and complemented haplotypes, respectively.

A vector of two integers specifying the line widths of connection between nodes for the original and complemented haplotypes, respectively.

A vector of two integers specifying the plot types for the positive and negative genotypic values respectively.

A vector of two integers or characters specifying color of complemented haplotypes for the positive and negative genotypic values respectively.

A vector of integers or characters specifying color of original haplotypes for the positive and negative genotypic values respectively. The length of the vector should equal to the number of subpopulations.

A numeric specifying the maximum point size of the plot.

A numeric specifying the minimum point size of the plot.

If TRUE, the function will return the ggplot version of haplotype network. It offers the precise information on subgroups for each haplotype.

A numeric specifying the maximum point size of the plot for the ggplot version of haplotype network, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

A numeric specifying the minimum point size of the plot for the ggplot version of haplotype network, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

alpha (parameter that indicates the opacity of a geom) for original haplotype with positive / negative effects. alpha for complemented haplotype will be same as the alpha for original haplotype with negative effects.

If this argument is TRUE, messages for the current steps will be shown.

A n \times M matrix representing the marker genotype that belongs to the haplotype block of interest. If this argument is NULL, this argument will automatically be determined by 'geno',

You can use the results (data.frame) of haplotype-based (SNP-set) GWAS by 'RGWAS.multisnp' function.

Haplotype blocks (or gene sets, SNP-sets) with top 'nTopRes' p-values by 'gwasRes' will be used.

If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

You can specify the haplotype block (or gene set, SNP-set) of interest by the marker index in 'geno'.

You can specify the haplotype block (or gene set, SNP-set) of interest by the marker position in 'geno'. Please assign the chromosome number to this argument.

You can specify the haplotype block (or gene set, SNP-set) of interest by the marker position in 'geno'. Please assign the position in the chromosome to this argument.

You can specify the haplotype block (or gene set, SNP-set) of interest by the name of haplotype block in 'geno'.

Number of haplotypes. If not defined, this is automatically defined by the data. If defined, k-medoids clustering is performed to define haplotypes.

Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. Columns 4 and higher contain the marker scores for each line, coded as [-1, 0, 1] = [aa, Aa, AA].

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

If TRUE, chi-square test for the relationship between haplotypes & subpopulations will be performed.

The threshold for the chi-square test.

If TRUE, the function will return the plot of phylogenetic tree.

You can assign the distance matrix of the block of interest. If NULL, the distance matrix will be computed in this function.

You can choose the method to calculate distance between accessions. This argument corresponds to the 'method' argument in the 'dist' function.

If TRUE, the evolution distance will be used instead of the pure distance. The 'distMat' will be converted to the distance matrix by the evolution distance.

The information of subpopulations. This argument should be a vector of factor.

If 'subpopInfo' argument is NULL, this function estimates subpopulation information from marker genotype. You can choose the grouping method from 'kmeans', 'kmedoids', and 'hclust'.

The number of groups (or subpopulations) grouped by 'groupingMethod'. If this argument is 0, the subpopulation information will not be estimated.

If 'groupingMethod' = 'kmeans', the clustering will be performed multiple times. This argument specifies the number of classification performed by the function.

In the function, similarlity matrix between accessions will be computed from marker genotype to estimate genotypic values. This argument specifies the method to compute similarity matrix: If this argument is 'addNOIA' (or one of other options in 'methodGRM' in 'calcGRM'), then the 'addNOIA' (or corresponding) option in the 'calcGRM' function will be used, and if this argument is 'phylo', the gaussian kernel based on phylogenetic distance will be computed from phylogenetic tree. You can assign more than one kernelTypes for this argument; for example, kernelTypes = c("addNOIA", "phylo").

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation in optimizing hyperparameters for estimating haplotype effects. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

Optimized hyper parameter for constructing kernel when estimating haplotype effects. If hOpt = "optimized", hyper parameter will be optimized in the function. If hOpt = "tuned", hyper parameter will be replaced by the median of off-diagonal of distance matrix. If hOpt is numeric, that value will be directly used in the function.

Optimized hyper parameter for constructing kernel when estimating haplotype effects of nodes. If hOpt2 = "optimized", hyper parameter will be optimized in the function. If hOpt2 = "tuned", hyper parameter will be replaced by the median of off-diagonal of distance matrix. If hOpt2 is numeric, that value will be directly used in the function.

Max number of iterations for optimization algorithm.

The median of off-diagonal of distance matrix multiplied by rangeHStart will be used as the initial values for optimization of hyper parameters.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

This argument specifies how to save the plot of phylogenetic tree. The function offers 'png', 'pdf', 'jpg', and 'tiff'.

A vector of two integers specifying the plot types for the positive and negative genotypic values respectively.

A vector of two integers or chracters specifying color of nodes for the positive and negative genotypic values respectively.

A vector of integers or chracters specifying color of tips for the positive and negative genotypic values respectively. The length of the vector should equal to the number of subpopulations.

A numeric specifying the maximum point size of the plot.

A numeric specifying the minimum point size of the plot.

If TRUE, the edge branch of phylogenetic tree wiil be colored.

If TRUE, lavels for tips will be shown.

If TRUE, the function will return the ggplot version of phylogenetic tree. It offers the precise information on subgroups for each haplotype.

A numeric specifying the maximum point size of the plot for ggtree, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

A numeric specifying the minimum point size of the plot for ggtree, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

alpha (parameter that indicates the opacity of a geom) for tip with positive / negative effects. alpha for node will be same as the alpha for tip with negative effects.

If this argument is TRUE, messages for the current step_s will be shown.

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.

Gene information with the format of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "map" argument.

If this argument is TRUE, cumulative position will be returned.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n.sample x n.mark genotype matrix. Markers with fixed effects (QTNs) are chosen from sample.sets. If sample.sets = NULL, sample.sets = x.

If you want to fix QTN postitions, please set the number where SNPs to be fixed are located in your data (so not position). If candidate = NULL, QTNs were randomly sampled from sample.sets or x.

A n.mark x 1 vector. Cumulative position (over chromosomes) of each marker.

If you don't want to match the sampling population and the genotype data to QTN effects, then use this argument as the latter.

A list of covariance (relationship) matrix (K: m \times m) and its design matrix (Z: n \times m) of random effects. Please set names of list "Z" and "K"! You can use more than one kernel matrix. For example,

ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))

Z.A, Z.D

Design matrix (n \times m) for the random effects. So, in many cases, you can use the identity matrix.

K.A, K.D

Different kernels which express some relationships between lines.

For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.

A genotype matrix to calculate additive relationship matrix when Z.ETA = NULL. If Z.ETA = NULL & x2 = NULL, calcGRM(x) will be calculated as kernel matrix.

The number of QTNs

The weights for each QTN by their standard deviations. Negative value is also allowed.

Additive of dominance for each marker effect. This argument should be the same length as num.qtn.

The proportion of effects of QTNs to polygenetic effects.

If there are multiple kernels, this argument determines the weights of each kernel effect.

If polygene = FALSE, pseudo phenotypes with only QTN effects will be generated.

The wide-sense heritability for generating phenotypes. 0 <= h2 < 1

If TRUE, this function will generate phenotypes to match the genomic heritability and "h2".

If seed is not NULL, some fixed phenotypic values will be generated according to set.seed(seed)

If TRUE, boxplot for generated phenotypic values will be drawn.

When drawing any plot, you can save plots in png format. In saveAt, you should substitute the name you want to save. When saveAt = NULL, the plot is not saved.

If there is subpopulation structure, you can draw boxpots divide by subpopulations. n.sample x n.subpop matrix. Please indicate the subpopulation information by (0, 1) for each element. (0 means that line doen't belong to that subpopulation, and 1 means that line belongs to that subpopulation)

If FALSE, only returns generated phenotypic values. If TRUE, this function will return other information such as positions of candidate QTNs.

If TRUE, this function will generate different environment effects every time.

Square matrix.

A n \times p matrix which you want to change into full-rank matrix.

Data frame of GWAS results where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

Significance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

The maximum value for the vertical axis of manhattan plot. If NULL, automatically determined.

A numerical value giving the amount by which plotting text and symbols should be magnified relative to the default.

The font size of the labels.

The line width for the threshold.

This argument determines the color of the manhattan plot. You should substitute this argument as color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes.

The font size of the x axis.

The font size of the y axis.

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

Data frame of GWAS results where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

The marker numbers whose -log10(p)s are corrected by kernel methods.

A numerical value giving the amount by which plotting text and symbols should be magnified relative to the default.

This argument determines the color of the manhattan plot. You should substitute this argument as a color vector whose length is 2. plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes.

Color of -log10(p) corrected by kernel methods. plot.col3[1] for odd chromosomes and plot.col3[2] for even chromosomes

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

Data frame of GWAS results where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

Siginifincance level for the threshold. The default is 0.05.

Method for detemining threshold of significance. "BH" and "Bonferroni are offered.

A numerical value giving the amount by which plotting text and symbols should be magnified relative to the default.

Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1 (so plot.col2 = 1 means color starts from red.)

This argument determines the type of the manhattan plot. See the help page of "plot".

This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".

Cumulative position (over chromosomes) of each marker

The line width for the threshold.

The font size of the labels.

The font size of the axes.

List of results of RGWAS.epistasis / RGWAS.twostep.epi. If the output of 'RGWAS.epistasis' is 'res', 'input' corresponds to 'res$scores'. If the output of 'RGWAS.twostep.epi.' is 'res', 'input' corresponds to 'res$epistasis$scores'. See: Value of RGWAS.epistasis

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position. This is map information for SNPs which are tested epistatic effects.

Cumulative position (over chromosomes) of each marker

If TRUE, draw 3d plot

If TRUE, draw 2d plot

The title of 3d plot. If this argument is NULL, trait name is set as the title.

The title of 2d plot. If this argument is NULL, trait name is set as the title.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveAt = NULL, the plot is not saved.

A n _ 1 \times p matrix of phenotype data. rownames(pheno.mat) should be genotype (line; accesion; variety) names.

A n _ 2 \times m matrix of marker genotype data. rownames(geno.mat) should be genotype (line; accesion; variety) names.

A vector of genotype (line; accesion; variety) names which correpond to phenotypic values.

A vector of genotype (line; accesion; variety) names for marker genotype data (duplication is not recommended).

Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.

If this argument is TRUE, the list for mixed model equation (ZETA) will be returned.

If this argument is TRUE, phenotype and genotype data for GWAS will be returned.

Numeric vector including the values that are computed in parallel.

The function to be applied to each element of 'vec' argument. This function must only have one argument.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

When count is TRUE, you can know how far RGWAS has ended with percent display.

The estimated results of haplotype network by 'estNetwork' function for one

Name of trait of interest. This will be used in the title of the plots.

You can specify the haplotype block (or gene set, SNP-set) of interest by the name of haplotype block in 'geno'. This will be used in the title of the plots.

If TRUE, the function will return the plot of haplotype network.

The information of subpopulations.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

This argument specifies how to save the plot of phylogenetic tree. The function offers 'png', 'pdf', 'jpg', and 'tiff'.

We will show the MDS (multi-dimensional scaling) plot, and this argument is a vector of two integers specifying that will define which MDS dimension will be plotted. The first and second integers correspond to the horizontal and vertical axes, respectively.

A vector of two integers or characters specifying the colors of connection between nodes for the original and complemented haplotypes, respectively.

A vector of two characters specifying the line types of connection between nodes for the original and complemented haplotypes, respectively.

A vector of two integers specifying the line widths of connection between nodes for the original and complemented haplotypes, respectively.

A vector of two integers specifying the plot types for the positive and negative genotypic values respectively.

A vector of two integers or characters specifying color of complemented haplotypes for the positive and negative genotypic values respectively.

A vector of integers or characters specifying color of original haplotypes for the positive and negative genotypic values respectively. The length of the vector should equal to the number of subpopulations.

A numeric specifying the maximum point size of the plot.

A numeric specifying the minimum point size of the plot.

If TRUE, the function will return the ggplot version of haplotype network. It offers the precise information on subgroups for each haplotype.

A numeric specifying the maximum point size of the plot for the ggplot version of haplotype network, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

A numeric specifying the minimum point size of the plot for the ggplot version of haplotype network, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

alpha (parameter that indicates the opacity of a geom) for original haplotype with positive / negative effects. alpha for complemented haplotype will be same as the alpha for original haplotype with negative effects.

The estimated results of phylogenetic analysis by 'estPhylo' function for one

Name of trait of interest. This will be used in the title of the plots.

You can specify the haplotype block (or gene set, SNP-set) of interest by the name of haplotype block in 'geno'. This will be used in the title of the plots.

If TRUE, the function will return the plot of phylogenetic tree.

The information of subpopulations.

When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save. When saveName = NULL, the plot is not saved.

This argument specifies how to save the plot of phylogenetic tree. The function offers 'png', 'pdf', 'jpg', and 'tiff'.

A vector of two integers specifying the plot types for the positive and negative genotypic values respectively.

A vector of two integers or chracters specifying color of nodes for the positive and negative genotypic values respectively.

A vector of integers or chracters specifying color of tips for the positive and negative genotypic values respectively. The length of the vector should equal to the number of subpopulations.

A numeric specifying the maximum point size of the plot.

A numeric specifying the minimum point size of the plot.

If TRUE, the edge branch of phylogenetic tree wiil be colored.

If TRUE, lavels for tips will be shown.

If TRUE, the function will return the ggplot version of phylogenetic tree. It offers the precise information on subgroups for each haplotype.

A numeric specifying the maximum point size of the plot for ggtree, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

A numeric specifying the minimum point size of the plot for ggtree, relative to the range of x and y-axes (0 < cexMaxForGG <= 1).

alpha (parameter that indicates the opacity of a geom) for tip with positive / negative effects. alpha for node will be same as the alpha for tip with negative effects.

A vector of -log10(p) for each marker

A n \times m genotype matrix where n is sample size and m is the number of markers.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

The inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package.MM = ’RAINBOWR''.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

The log-likelihood for the null model.

A list with

$values

Eigen values

$vectors

Eeigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

The hyper-parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

The log-likelihood for the null model.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times n Gram (kernel) matrix which may indicate some interaction with SNP-sets to be tested.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

The log-likelihood for the null model.

A list with

$values

Eigen values

$vectors

Eeigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

The hyper-parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times n Gram (kernel) matrix which may indicate some interaction with SNP-sets to be tested.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

The log-likelihood for the null model.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

The inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package.MM = ’RAINBOWR''.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the tdeviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

If this argument is TRUE, dominance effect is included in the model, and additive x dominance and dominance x dominance are also tested as epistatic effects. When you use inbred lines, please set this argument FALSE.

As default, the function also tests the self-interactions among the same SNP-sets. If you want to avoid this, please set 'skip.self.int = TRUE'.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of SGS, where S = I - X(X'X)^{-1}X', G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the tdeviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

If this argument is TRUE, dominance effect is included in the model, and additive x dominance and dominance x dominance are also tested as epistatic effects. When you use inbred lines, please set this argument FALSE.

As default, the function also tests the self-interactions among the same SNP-sets. If you want to avoid this, please set 'skip.self.int = TRUE'.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times n matrix. You should assign ZKZ', where K is covariance (relationship) matrix and Z is its design matrix.

A n \times n matrix. You should assign identity matrix I (diag(n)).

A n \times n matrix. The Moore-Penrose generalized inverse of SV0S, where S = X(X'X)^{-1}X' and V0 = \sigma^2_u Gu + \sigma^2_e Ge. \sigma^2_u and \sigma^2_e are estimators of the null model.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the test statistic l1' F l1 is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where l1 is the first derivative of the log-likelihood and F is the Fisher information. And r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

If this argument is TRUE, dominance effect is included in the model, and additive x dominance and dominance x dominance are also tested as epistatic effects. When you use inbred lines, please set this argument FALSE.

As default, the function also tests the self-interactions among the same SNP-sets. If you want to avoid this, please set 'skip.self.int = TRUE'.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

A n \times n matrix. You should assign ZKZ', where K is covariance (relationship) matrix and Z is its design matrix.

A n \times n matrix. You should assign identity matrix I (diag(n)).

A n \times n matrix. The Moore-Penrose generalized inverse of SV0S, where S = X(X'X)^{-1}X' and V0 = \sigma^2_u Gu + \sigma^2_e Ge. \sigma^2_u and \sigma^2_e are estimators of the null model.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the test statistic l1' F l1 is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where l1 is the first derivative of the log-likelihood and F is the Fisher information. And r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

If you have information of gene, you can use it to perform kernel-based GWAS. You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2). In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker, which correspond to the marker names of "geno" argument.

If this argument is TRUE, dominance effect is included in the model, and additive x dominance and dominance x dominance are also tested as epistatic effects. When you use inbred lines, please set this argument FALSE.

As default, the function also tests the self-interactions among the same SNP-sets. If you want to avoid this, please set 'skip.self.int = TRUE'.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A m \times q matrix. Interaction between each SNP and this matrix will also be tested. For example, principal components of genomic relationship matrix can be used as this matrix to test the interaction between SNPs and the genetic background.

Method for how to test SNPs and the interactions between SNPs and the genetic background. We offer three methods as follows:

"simultaneous": All effects (including SNP efects) are tested simultanously.

"snpSeparate": SNP effects are tested as one effect, and the other interaction effects are simulateneously.

"oneByOne": All efects are tested separately, one by one.

Whether or not including SNP effects into the tested effects.

The inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package.MM = ’RAINBOWR''.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

The package name to be used when solving mixed-effects model. We only offer the following three packages: "RAINBOWR", "MM4LMM" and "gaston". Default package is 'gaston'. See more details at EM3.general.

A m \times q matrix. Interaction between each SNP and this matrix will also be tested. For example, principal components of genomic relationship matrix can be used as this matrix to test the interaction between SNPs and the genetic background.

Method for how to test SNPs and the interactions between SNPs and the genetic background. We offer three methods as follows:

"simultaneous": All effects (including SNP efects) are tested simultanously.

"snpSeparate": SNP effects are tested as one effect, and the other interaction effects are simulateneously.

"oneByOne": All efects are tested separately, one by one.

Whether or not including SNP effects into the tested effects.

The inverse of H = ZKZ' + \lambda I where \lambda = \sigma^2_e / \sigma^2_u.

Setting n.core > 1 will enable parallel execution on a machine with multiple cores. This argument is not valid when 'parallel.method = "furrr"'.

Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".

When 'parallel.method = "mclapply"', we utilize pbmclapply function in the 'pbmcapply' package with 'count = TRUE' and mclapply function in the 'parallel' package with 'count = FALSE'.

When 'parallel.method = "furrr"', we utilize future_map function in the 'furrr' package. With 'count = TRUE', we also utilize progressor function in the 'progressr' package to show the progress bar, so please install the 'progressr' package from github (https://github.com/futureverse/progressr). For 'parallel.method = "furrr"', you can perform multi-thread parallelization by sharing memories, which results in saving your memory, but quite slower compared to 'parallel.method = "mclapply"'.

When 'parallel.method = "foreach"', we utilize foreach function in the 'foreach' package with the utilization of makeCluster function in 'parallel' package, and registerDoParallel function in 'doParallel' package. With 'count = TRUE', we also utilize setTxtProgressBar and txtProgressBar functions in the 'utils' package to show the progress bar.

We recommend that you use the option 'parallel.method = "mclapply"', but for Windows users, this parallelization method is not supported. So, if you are Windows user, we recommend that you use the option 'parallel.method = "foreach"'.

When P3D = TRUE, variance components are estimated by REML only once, without any markers in the model. When P3D = FALSE, variance components are estimated by REML for each marker separately.

A list with

$values

Eigen values

$vectors

Eigen vectors

The result of the eigen decompsition of G = ZKZ'. You can use "spectralG.cpp" function in RAINBOWR. If this argument is NULL, the eigen decomposition will be performed in this function. We recommend you assign the result of the eigen decomposition beforehand for time saving.

The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions. This argument is only valid when ‘package.MM = ’RAINBOWR''.

Specifies the minimum minor allele frequency (MAF). If a marker has a MAF less than min.MAF, it is assigned a zero score.

When count is TRUE, you can know how far RGWAS has ended with percent display.

A n \times m genotype matrix where n is sample size and m is the number of markers.

A n \times 1 vector. A vector of phenotypic values should be used. NA is allowed.

A n \times p matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.

A list of variance (relationship) matrix (K; m \times m) and its design matrix (Z; n \times m) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!

The log-likelihood for the null model.

A n \times n matrix. You should assign ZKZ', where K is covariance (relationship) matrix and Z is its design matrix.

A n \times n matrix. You should assign identity matrix I (diag(n)).

n \times n matrix. The Moore-Penrose generalized inverse of SV0S, where S = X(X'X)^{-1}X' and V0 = \sigma^2_u Gu + \sigma^2_e Ge. \sigma^2_u and \sigma^2_e are estimators of the null model.

Data frame of map information where the first column is the marker names, the second and third column is the chromosome amd map position, and the forth column is -log10(p) for each marker.

It determines how to calculate kernel. There are three methods.

"gaussian"

It is the default method. Gaussian kernel is calculated by distance matrix.

"exponential"

When this method is selected, exponential kernel is calculated by distance matrix.

"linear"

When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.

The hyper parameter for gaussian or exponential kernel. If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.

If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE. When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p). (So the dimension of this gram matrix will be smaller.) The result won't be changed, but the time for the calculation will be shorter.

When haplotype = TRUE, you can set the number of haplotypes which you expect. Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap. When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.

Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance". You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")

This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP. More precisely, the number of SNPs will be 2 * window.size.half + 1.

This argument determines how often you test markers. If window.slide = 1, every marker will be tested. If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.

RAINBOWR assumes the test statistic l1' F l1 is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r). where l1 is the first derivative of the log-likelihood and F is the Fisher information. And r is the degree of freedom. The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.

In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE. If weighting.center = FALSE, weights are not taken into account.

You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs. For example, you can assign SNP effects from the information of gene annotation.