plRasch (version 1.0)

RaschPLE: Fit Rasch Family Models Using Pseudolikelihood Esitmation

Description

This function fits Rasch family models using pseudolikelihood esitmation. It is capable of dealing with polytomous items, and multidimensional latent variables.

Usage

RaschPLE(data, item.mtx, trait.mtx)

Arguments

data

is a data frame or matrix with rows indicating individuals, columns indicating items, and the entry values indicating the choices.

item.mtx

is the adjacency matrix between items and latent traits

trait.mtx

is the adjacency matrix for latent traits

Value

coefficients

estimated item parameter beta

se

standard error of beta

covb

covariance matrix of the estimated parameter beta

Details

The model is $$P(X[v,i] = h) = \frac{\exp( w[i,h]' \theta[v] + \beta[i,h] ) }{\sum_l \exp( w[i,l]' \theta[v] + \beta[i,l] ) } $$ where

X[v,i] is the response of vth individual to ith item; w[i,h] is a vector of known category weights or scores for response h of ith item; theta[v] is a vector of latent traits for vth individual; beta[i,h] is the item difficulty parameter for ith item; associated with response h.

The function only returns the item parameter beta.

Essentially, it is a wrapper function: the equvialent llla model is fitted.

References

Anderson, C.J., Li, Z., & Vermunt, J.K. (2007). Estimation of models in the Rasch family for polytomous items and multiple latent variables. Journal of Statistical Software, 20.

See Also

llla

Examples

NCAT <- 2;
NITEM <- 4;
NEXAMINEE <- 50;
BETA <- c(-1, 0, 0.5, 1)
set.seed(1);
rasch.sim <- simRasch(ncat=NCAT, nitem=NITEM, nexaminee=NEXAMINEE, beta=BETA)
sim.data <- rasch.sim$data
colnames(sim.data) <- paste("I", 1:NITEM, sep='')
## The model item adjacency matrix and the latent trait adjacency matrix
item.mtx <- rep(1, NITEM);
trait.mtx <- 1;

plfit.rasch <- RaschPLE(sim.data, item.mtx, trait.mtx)
plfit.rasch