| lamle.fit {lamle} | R Documentation |
Model Fit Statistics for an Estimated Latent Variable Model
Description
A function to compute model fit statistics for latent variable models estimated with lamle. Currently only computes the standardized root mean square residuals (SRMSR) from the model-implied correlation matrix based on the estimated model parameters and the sample correlation matrix.
Usage
lamle.fit(obj, obs, N = NULL, z = NULL, seed = NULL,
use = "complete", residmat = FALSE)
Arguments
obj |
An estimated model from function lamle. |
obs |
The observed data matrix, with missing values coded as NA. Ordinal data must be coded as successive integers starting from 1. |
N |
A numeric scalar indicating the multiplier of the sample size in the data to use when computing the model fit statistics. |
z |
An optional matrix of latent variable values to use when computing the model fit statistics. |
seed |
The seed to use when simulating data. |
use |
A character vector indicating how the correlaion matrix used for the SRMSR statistic should be estimated. See function cor() for details. |
residmat |
Optional argument to return the full residual correlation matrix. |
Value
A numeric vector with fit statistics.
Author(s)
Björn Andersson <bjoern.h.andersson@gmail.com> and Shaobo Jin <shaobo.jin@statistik.uu.se>
References
Andersson, B., and Xin, T. (2021). Estimation of latent regression item response theory models using a second-order Laplace approximation. Journal of Educational and Behavioral Statistics, 46(2) 244-265. <doi:10.3102/107699862094519>
Jin, S., Noh, M., and Lee, Y. (2018). H-Likelihood Approach to Factor Analysis for Ordinal Data. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 530-540. <doi:10.1080/10705511.2017.1403287>
Shun, Z., and McCullagh, P. (1995). Laplace approximation of high dimensional integrals. Journal of the Royal Statistical Society: Series B (Methodological), 57(4), 749-760. <doi:10.1111/j.2517-6161.1995.tb02060.x>
Examples
##### Load required package.
library(mvtnorm)
##### Generate ordinal data from the GPCM
#####
##### Item parameter generation
set.seed(123)
GPCMa <- runif(10, 0.8, 2)
GPCMb <- vector("list", 10)
for(i in 1:10) GPCMb[[i]] <- -c(runif(1, -3, -2),
runif(1, -1.5, -0.5),
runif(1, 0, 1),
runif(1, 1.5, 2.5))
GMCMa2d <- matrix(0, nrow = 10, ncol = 2)
GMCMa2d[1:5, 1] <- GPCMa[1:5]
GMCMa2d[6:10, 2] <- GPCMa[6:10]
##### Latent variables in two groups
n <- 200
set.seed(1234)
covmat2d <- diag(rep(1, 2))
covmat2d[!diag(2)] <- 0.6
latmat2dA <- rmvnorm(n, c(0, 0), covmat2d)
latmat2dB <- rmvnorm(n, c(1, 1), covmat2d)
##### Observed data
set.seed(12345)
dataGPCM2d <- matrix(NA, nrow = 2 * n, ncol = 10)
dataGPCM2d[1:n, ] <- DGP(GMCMa2d, GPCMb, rep("GPCM", 10),
latmat2dA)
dataGPCM2d[(n + 1):(2 * n), ] <- DGP(GMCMa2d, GPCMb,
rep("GPCM", 10), latmat2dB)
##### Setup two-dimensional independent-clusters model
mydim2d <- matrix(NA, nrow = 10, ncol = 2)
mydim2d[1:5, 1] <- 1
mydim2d[6:10, 2] <- 1
##### Lap(2)
estLap2 <- lamle(y = dataGPCM2d[1:n,], model = mydim2d,
modeltype = rep(c("GPCM", "GRM"), 5),
method = "lap", accuracy = 2, optimizer =
"BFGS", inithess = "crossprod")
lamle.fit(estLap2, dataGPCM2d[1:n,], N = 10)