Unidimensional Latent Regression
immer_latent_regression.RdFits 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, ...)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.
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
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.
See also
See TAM::tam.latreg for latent regression estimation
in the TAM package.
Examples
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)
}