Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Rebecca Killick, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
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Authors: Carolyn J. Anderson, Zhushan Li, Jeroen K. Vermunt
Title: Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables
Abstract: The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.

Page views:: 11483. Submitted: 2006-10-01. Published: 2007-02-02.
Paper: Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables     Download PDF (Downloads: 12413)
plRasch_0.1.tar.gz: R source package Download (Downloads: 2011; 9KB) v20i06.R: R example code from the paper Download (Downloads: 2018; 444B)

DOI: 10.18637/jss.v020.i06

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Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.