Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

By Carolyn J. Anderson, Zhushan Li, Jeroen K. Vermunt. 2007

61 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0d7c67cf6caa122a13968e0c41c8f4221839e9fc

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model (2010, methodology): “This estimation is analogous to that of pairwise conditional estimation of item parameters already well established in the literature ( Anderson, Li, & Vermunt, 2007; Andrich & Luo, 2003; Choppin, 1968; Zwinderman, 1995).”
The estimation of item response models with the lmer function from the lme4 package in R (2011, methodology): “ The eRm package (Mair and Hatzinger 2007) using conditional maximum likelihood estimation for the Rasch model, the partial credit and rating scale models, and the corresponding models with property covariates; The plRasch package (Anderson et al. 2007) using maximum likelihood and pseudolikeliho”