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R-CMD-check coverage cran cran-dl

Latent Variable Models: lava

A general implementation of Structural Equation Models with latent variables (MLE, 2SLS, and composite likelihood estimators) with both continuous, censored, and ordinal outcomes (Holst and Budtz-Joergensen (2013) <10.1007/s00180-012-0344-y>). Mixture latent variable models and non-linear latent variable models (Holst and Budtz-Joergensen (2020) <10.1093/biostatistics/kxy082>). The package also provides methods for graph exploration (d-separation, back-door criterion), simulation of general non-linear latent variable models, and estimation of influence functions for a broad range of statistical models.

Installation

install.packages("lava", dependencies=TRUE)
library("lava")
demo("lava")

For graphical capabilities the Rgraphviz package is needed (first install the BiocManager package)

# install.packages("BiocManager")
BiocManager::install("Rgraphviz")

or the igraph or visNetwork packages

install.packages("igraph")
install.packages("visNetwork")

The development version of lava may also be installed directly from github:

# install.packages("remotes")
remotes::install_github("kkholst/lava")

Citation

To cite that lava package please use one of the following references

Klaus K. Holst and Esben Budtz-Joergensen (2013). Linear Latent Variable Models: The lava-package. Computational Statistics 28 (4), pp 1385-1453. http://dx.doi.org/10.1007/s00180-012-0344-y

@article{lava,
  title = {Linear Latent Variable Models: The lava-package},
  author = {Klaus Kähler Holst and Esben Budtz-Jørgensen},
  year = {2013},
  volume = {28},
  number = {4},
  pages = {1385-1452},
  journal = {Computational Statistics},
  doi = {10.1007/s00180-012-0344-y}
}

Klaus K. Holst and Esben Budtz-Jørgensen (2020). A two-stage estimation procedure for non-linear structural equation models. Biostatistics 21 (4), pp 676-691. http://dx.doi.org/10.1093/biostatistics/kxy082

@article{lava_nlin,
  title = {A two-stage estimation procedure for non-linear structural equation models},
  author = {Klaus Kähler Holst and Esben Budtz-Jørgensen},
  journal = {Biostatistics},
  year = {2020},
  volume = {21},
  number = {4},
  pages = {676-691},
  doi = {10.1093/biostatistics/kxy082},
}

Examples

Structural Equation Model

Specify structural equation models with two factors

m <- lvm()
regression(m) <- y1 + y2 + y3 ~ eta1
regression(m) <- z1 + z2 + z3 ~ eta2
latent(m) <- ~ eta1 + eta2
regression(m) <- eta2 ~ eta1 + x
regression(m) <- eta1 ~ x

labels(m) <- c(eta1=expression(eta[1]), eta2=expression(eta[2]))
plot(m)

plot of chunk lvm1

Simulation

d <- sim(m, 100, seed=1)

Estimation

e <- estimate(m, d)
e
#>                     Estimate Std. Error  Z-value   P-value
#> Measurements:                                             
#>    y2~eta1           0.95462    0.08083 11.80993    <1e-12
#>    y3~eta1           0.98476    0.08922 11.03722    <1e-12
#>     z2~eta2          0.97038    0.05368 18.07714    <1e-12
#>     z3~eta2          0.95608    0.05643 16.94182    <1e-12
#> Regressions:                                              
#>    eta1~x            1.24587    0.11486 10.84694    <1e-12
#>     eta2~eta1        0.95608    0.18008  5.30910 1.102e-07
#>     eta2~x           1.11495    0.25228  4.41951 9.893e-06
#> Intercepts:                                               
#>    y2               -0.13896    0.12458 -1.11537    0.2647
#>    y3               -0.07661    0.13869 -0.55241    0.5807
#>    eta1              0.15801    0.12780  1.23644    0.2163
#>    z2               -0.00441    0.14858 -0.02969    0.9763
#>    z3               -0.15900    0.15731 -1.01076    0.3121
#>    eta2             -0.14143    0.18380 -0.76949    0.4416
#> Residual Variances:                                       
#>    y1                0.69684    0.14858  4.69004          
#>    y2                0.89804    0.16630  5.40026          
#>    y3                1.22456    0.21182  5.78109          
#>    eta1              0.93620    0.19623  4.77084          
#>    z1                1.41422    0.26259  5.38570          
#>    z2                0.87569    0.19463  4.49934          
#>    z3                1.18155    0.22640  5.21883          
#>    eta2              1.24430    0.28992  4.29195

Model assessment

Assessing goodness-of-fit, here the linearity between eta2 and eta1 (requires the gof package)

# install.packages("gof", repos="https://kkholst.github.io/r_repo/")
library("gof")
set.seed(1)
g <- cumres(e, eta2 ~ eta1)
plot(g)

plot of chunk gof1

Non-linear measurement error model

Simulate non-linear model

m <- lvm(y1 + y2 + y3 ~ u, u ~ x)
transform(m,u2 ~ u) <- function(x) x^2
regression(m) <- z~u2+u

d <- sim(m,200,p=c("z"=-1, "z~u2"=-0.5), seed=1)

Stage 1:

m1 <- lvm(c(y1[0:s], y2[0:s], y3[0:s]) ~ 1*u, u ~ x)
latent(m1) <- ~ u
(e1 <- estimate(m1, d))
#>                     Estimate Std. Error  Z-value  P-value
#> Regressions:                                             
#>    u~x               1.06998    0.08208 13.03542   <1e-12
#> Intercepts:                                              
#>    u                -0.08871    0.08753 -1.01344   0.3108
#> Residual Variances:                                      
#>    y1                1.00054    0.07075 14.14214         
#>    u                 1.19873    0.15503  7.73233

Stage 2

pp <- function(mu,var,data,...) cbind(u=mu[,"u"], u2=mu[,"u"]^2+var["u","u"])
(e <- measurement.error(e1, z~1+x, data=d, predictfun=pp))
#>             Estimate Std.Err    2.5%   97.5%   P-value
#> (Intercept)  -1.1181 0.13795 -1.3885 -0.8477 5.273e-16
#> x            -0.0537 0.13213 -0.3127  0.2053 6.844e-01
#> u             1.0039 0.11504  0.7785  1.2294 2.609e-18
#> u2           -0.4718 0.05213 -0.5740 -0.3697 1.410e-19
f <- function(p) p[1]+p["u"]*u+p["u2"]*u^2
u <- seq(-1, 1, length.out=100)
plot(e, f, data=data.frame(u))

plot of chunk nlin1

Simulation

Studying the small-sample properties of a mediation analysis

m <- lvm(y~x, c~1)
regression(m) <- y+x ~ z
eventTime(m) <- t~min(y=1, c=0)
transform(m,S~t+status) <- function(x) survival::Surv(x[,1],x[,2])
plot(m)

plot of chunk mediation1

Simulate from model and estimate indirect effects

onerun <- function(...) {
    d <- sim(m, 100)
    m0 <- lvm(S~x+z, x~z)
    e <- estimate(m0, d, estimator="glm")
    vec(summary(effects(e, S~z))$coef[,1:2])
}
val <- sim(onerun, 100)
summary(val, estimate=1:4, se=5:8, short=TRUE)
#> 100 replications                 Time: 3.667s
#> 
#>         Total.Estimate Direct.Estimate Indirect.Estimate S~x~z.Estimate
#> Mean           1.97292         0.96537           1.00755        1.00755
#> SD             0.16900         0.18782           0.15924        0.15924
#> SE             0.18665         0.18090           0.16431        0.16431
#> SE/SD          1.10446         0.96315           1.03183        1.03183
#>                                                                        
#> Min            1.47243         0.54497           0.54554        0.54554
#> 2.5%           1.63496         0.61228           0.64914        0.64914
#> 50%            1.95574         0.97154           0.99120        0.99120
#> 97.5%          2.27887         1.32443           1.27807        1.27807
#> Max            2.45746         1.49491           1.33446        1.33446
#>                                                                        
#> Missing        0.00000         0.00000           0.00000        0.00000

Add additional simulations and visualize results

val <- sim(val,500) ## Add 500 simulations
plot(val, estimate=c("Total.Estimate", "Indirect.Estimate"),
     true=c(2, 1), se=c("Total.Std.Err", "Indirect.Std.Err"),
     scatter.plot=TRUE)

plot of chunk simres1

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.