immer_latent_regression: Unidimensional Latent Regression

Description

Fits a unidimensional latent regression \(\theta_{ig}=Y_{ig} \bm{\beta} + \varepsilon_{ig}\) with group-specific variances \(Var(\varepsilon _{ig} )=\sigma^2_g\) based on the individual likelihood of a fitted model.

Usage

immer_latent_regression(like, theta=NULL, Y=NULL, group=NULL, weights=NULL,
   conv=1e-05, maxit=200, verbose=TRUE)
# S3 method for immer_latent_regression
summary(object, digits=3, file=NULL, ...)
# S3 method for immer_latent_regression
coef(object, ...)
# S3 method for immer_latent_regression
vcov(object, ...)
# S3 method for immer_latent_regression
logLik(object, ...)
# S3 method for immer_latent_regression
anova(object, ...)

Value

List containing values (selection)

coef: Parameter vector
vcov: Covariance matrix for estimated parameters
beta: Regression coefficients
gamma: Standard deviations
beta_stat: Data frame with \(\bm{\beta}\) parameters
gamma_stat: Data frame with standard deviations
ic: Information criteria
deviance: Deviance
N: Number of persons
G: Number of groups
group: Group identifier
iter: Number of iterations

Arguments

like: Matrix containing the individual likelihood \(L( \bm{X} | \theta )\)
theta: Grid of \(\bm{\theta}\) values
Y: Predictor matrix
group: Group identifiers
weights: Optional vector of weights
conv: Convergence criterion
maxit: Maximum number of iterations
verbose: Logical indicating whether progress should be displayed
object: Object of class immer_latent_regression
digits: Number of digits after decimal to print
file: Name of a file in which the output should be sunk
...: Further arguments to be passed.

References

Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model. A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.): Multivariate and mixture distribution Rasch models: Extensions and applications (pp. 55-76). New York: Springer.

Examples

Run this code

if (FALSE) {
#############################################################################
# EXAMPLE 1: Latent regression for Rasch model with simulated data
#############################################################################

library(sirt)

#-- simulate data
set.seed(9877)
I <- 15  # number of items
N <- 700 # number of persons per group
G <- 3   # number of groups
b <- seq(-2,2,len=I)
group <- rep( 1:G, each=N)
mu <- seq(0,1, length=G)
sigma <- seq(1, 1.5, length=G)
dat <- sirt::sim.raschtype( stats::rnorm( N*G, mean=mu[group], sd=sigma[group] ), b)

#-- estimate Rasch model with JML
mod1 <- immer::immer_jml( dat )
summary(mod1)

#-- compute individual likelihood
like1 <- IRT.likelihood(mod1)

#-- estimate latent regression
mod2 <- immer::immer_latent_regression( like=like1, group=group)
summary(mod2)
}