Fit the high-dimensional multi-study robust factor model

Description

Fit the high-dimensional multi-study robust factor model which learns latent features and accounts for the heterogeneity among source.

Usage

MultiRFM(
  XList,
  q = 15,
  qs = rep(2, length(XList)),
  epsELBO = 1e-05,
  maxIter = 30,
  verbose = TRUE,
  seed = 1
)

Arguments

Details

None

Value

return a list including the following components:(1) F, a list composed by the posterior estimation of study-shared factor matrix for each study; (2) H, a list composed by the posterior estimation of study-specified factor matrix for each study; (3) Sf, a list consisting of the posterior estimation of covariance matrix of study-shared factors for each study; (4) Sh, a list consisting of the posterior estimation of covariance matrix of study-specified factors for each study; (5) A, the loading matrix corresponding to study-shared factors; (6) B, a list composed by the loading matrices corresponding to the study-specified factors; (7) mu,the mean of XList;(8) ELBO: the ELBO value when algorithm stops; (9) ELBO_seq: the sequence of ELBO values. (10) time_use, the elapsed time for model fitting.

Examples

p <- 100
nvec <- c(150,200); qs <- c(2,2)
datList <- gendata_simu_multi(seed=1, nvec=nvec, p=p, q=3, qs=qs, rho=c(5,5),
        err.type='mvt', sigma2_eps = 1, nu=3)
XList <- datList$Xlist;
res <- MultiRFM(XList, q=3, qs= qs)
str(res)

Generate Simulated Multi-Study Factor Analysis Data

Description

Generate simulated data for multi-study factor analysis under different error distributions. The data follows a factor model with common factors (shared across studies) and study-specific factors (unique to each study), plus noise.

Usage

gendata_simu_multi(
  seed = 1,
  nvec = c(100, 300),
  p = 50,
  q = 3,
  qs = rep(2, length(nvec)),
  err.type = c("gaussian", "mvt", "exp", "t", "mixnorm", "pareto"),
  rho = c(1, 1),
  sigma2_eps = 0.1,
  nu = 1
)

Arguments

Details

The simulated data follows the multi-study factor model:

Xs = mu0s + Fs x A0 + Hs x B0s + epsilons

True parameters ('A0', 'Blist0', 'mu0') are generated with orthogonal constraints to ensure identifiability.

Value

A list containing the simulated data and true parameter values (for model evaluation):

• Xlist: List of matrices. Each element is a data matrix (ns × p) for study s, where ns = 'nvec[s]' (sample size of study s), p = number of variables.

• mu0: Matrix (p × S). True mean vector for each variable (row) in each study (column), where S = 'length(nvec)' (number of studies).

• A0: Matrix (p × q). True common factor loadings (shared across all studies) — constructed as the first q columns of an orthogonal matrix ('A1') generated internally. This is the "ground truth" that modeling functions (e.g., MultiRFM) aim to estimate.

• Blist0: List of matrices. Each element is a true study-specific factor loadings matrix (p × qs[s]) for study s. Constructed from orthogonal matrices (similar to 'A0') and scaled by 'rho[2]'. Another "ground truth" for model evaluation.

• Flist: List of matrices. Each element is a true common factor score matrix (ns × q) for study s, generated from a standard normal distribution. These are the latent common factor values used to generate 'Xlist'.

• Hlist: List of matrices. Each element is a true study-specific factor score matrix (ns × qs[s]) for study s, generated from a standard normal distribution. Latent specific factor values used to generate 'Xlist'.

• q: Integer. Number of common factors used for data generation (same as input 'q', for reference).

• qs: Numeric vector. Number of study-specific factors used for data generation (same as input 'qs', for reference).

Author(s)

Wei Liu

Examples

# Example 1: Gaussian error (2 studies, 100/200 samples, 50 variables)
set.seed(123)
sim_data <- gendata_simu_multi(
  seed = 123,
  nvec = c(100, 200),
  p = 50,
  q = 3,          # 3 common factors
  qs = c(2, 2),   # 2 specific factors per study
  err.type = "gaussian",
  rho = c(1, 1),
  sigma2_eps = 0.1
)
str(sim_data)  # Check structure of simulated data

# Extract true parameters for model evaluation
true_A <- sim_data$A0        # True common loadings
true_B1 <- sim_data$Blist0[[1]]  # True specific loadings (study 1)

Select the number of factors

Description

Select the number of factors that are shared among studies q and thos that are specific to individual studies(qs).More details are in Section 3.1 of the article.

Usage

selectFac.MultiRFM(
  XList,
  q_max = 15,
  qs_max = 4,
  method = c("SSVR", "CUP"),
  threshold = 1e-05,
  cup.upper = 0.95,
  epsELBO = 1e-05,
  maxIter = 30,
  verbose = TRUE,
  seed = 1
)

Arguments

Details

None

Value

return a list contains the following components:(1) q, the number of shared factors; (2) qs,the number of specified factors.

Examples

p <- 100
nvec <- c(150,200); qs <- c(2,2)
datList <- gendata_simu_multi(seed=1, nvec=nvec, p=p, q=3, qs=qs, rho=c(5,5),
        err.type='mvt', sigma2_eps = 1, nu=3)
XList <- datList$Xlist;
## Set maxIter=5 for demonstration while set it to 30 in the formal run.
hqlist <- selectFac.MultiRFM(XList, q_max=6, qs_max= rep(4,2), maxIter = 5) #
str(hqlist)