immer_latent_regression: Unidimensional Latent Regression

In immer: Item Response Models for Multiple Ratings

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 class 'immer_latent_regression'
summary(object, digits=3, file=NULL, ...)

## S3 method for class 'immer_latent_regression'
coef(object, ...)

## S3 method for class 'immer_latent_regression'
vcov(object, ...)

## S3 method for class 'immer_latent_regression'
logLik(object, ...)

## S3 method for class '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

Note

The IRT.likelihood method can be used for extracting the individual likelihood.

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

## Not run: 
#############################################################################
# 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)

## End(Not run)

immer documentation built on May 29, 2024, 11:52 a.m.