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Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models

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  • Carolyn Anderson

Abstract

Multiple choice items on tests and Likert items on surveys are ubiquitous in educational, social and behavioral science research; however, methods for analyzing of such data can be problematic. Multidimensional item response theory models are proposed that yield structured Poisson regression models for the joint distribution of responses to items. The methodology presented here extends the approach described in Anderson, Verkuilen, and Peyton (2010) that used fully conditionally specified multinomial logistic regression models as item response functions. In this paper, covariates are added as predictors of the latent variables along with covariates as predictors of location parameters. Furthermore, the models presented here incorporate ordinal information of the response options thus allowing an empirical examination of assumptions regarding the ordering and the estimation of optimal scoring of the response options. To illustrate the methodology and flexibility of the models, data from a study on aggression in middle school (Espelage, Holt, and Henkel 2004) is analyzed. The models are fit to data using SAS. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Carolyn Anderson, 2013. "Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 276-303, July.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:2:p:276-303
    DOI: 10.1007/s00357-013-9131-x
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    References listed on IDEAS

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    7. Anderson, Carolyn J. & Li, Zhushan & Vermunt, Jeroen K., 2007. "Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i06).
    8. Iliopoulos, G. & Kateri, M. & Ntzoufras, I., 2007. "Bayesian estimation of unrestricted and order-restricted association models for a two-way contingency table," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4643-4655, May.
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