Estimation of models in a Rasch family for polytomous items and multiple latent variables

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

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1-36
Number of pages36
JournalJournal of Statistical Software
Volume20
Issue number6
DOIs
StatePublished - May 2007

Fingerprint

Association Model
Latent Variables
Pseudo-likelihood
Linear Model
Latent Trait
Rasch Model
Log-linear Models
Logistic Regression Model
Standard error
Likelihood Function
Maximum Likelihood Estimate
Maximum Likelihood Estimation
Model
Estimate
Likelihood
Recovery
Simulation Study
Family
Latent variables
Interaction

Keywords

  • Conditionally specified models
  • Log-linear-by-linear association models
  • Logistic regression
  • Multinomial logistic regression
  • Pseudo-likelihood estimation
  • R

ASJC Scopus subject areas

  • Software
  • Statistics and Probability

Cite this

Estimation of models in a Rasch family for polytomous items and multiple latent variables. / Anderson, Carolyn J.; Li, Zhushan; Vermunt, Jeroen K.

In: Journal of Statistical Software, Vol. 20, No. 6, 05.2007, p. 1-36.

Research output: Contribution to journalArticle

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