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Modeling Polytomous Item Responses Using Simultaneously Estimated Multinomial Logistic Regression Models

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  • Carolyn J. Anderson
  • Jay Verkuilen
  • Buddy L. Peyton

Abstract

Survey items with multiple response categories and multiple-choice test questions are ubiquitous in psychological and educational research. We illustrate the use of log-multiplicative association (LMA) models that are extensions of the well-known multinomial logistic regression model for multiple dependent outcome variables to reanalyze a set of items from a large political psychology survey. In particular, LMA models are shown to provide a useful analysis of items when the proper scoring rule for them is unclear. They also clearly reveal the performance of the items when instructions were altered to suppress “Don’t know†responses. LMA models can be fit rapidly using commonly available software.

Suggested Citation

  • Carolyn J. Anderson & Jay Verkuilen & Buddy L. Peyton, 2010. "Modeling Polytomous Item Responses Using Simultaneously Estimated Multinomial Logistic Regression Models," Journal of Educational and Behavioral Statistics, , vol. 35(4), pages 422-452, August.
    • Handle: RePEc:sae:jedbes:v:35:y:2010:i:4:p:422-452
    DOI: 10.3102/1076998609353117
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    References listed on IDEAS

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    1. Joe, Harry & Liu, Ying, 1996. "A model for a multivariate binary response with covariates based on compatible conditionally specified logistic regressions," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 113-120, December.
    2. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    3. 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).
    4. Carolyn Anderson & Hsiu-Ting Yu, 2007. "Log-Multiplicative Association Models as Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 72(1), pages 5-23, March.
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