In this study, the authors extend the standard item response model with internal restrictions on item difficulty (MIRID) to fit polytomous items using cumulative logits and adjacent-category logits. Moreover, the new model incorporates discrimination parameters and is rooted in a multilevel framework. It is a nonlinear mixed model so that existing parameter estimation procedures and computer packages for nonlinear mixed models can be directly adopted to estimate the parameters. Through simulations, it was found that the SAS NLMIXED procedure could recover the parameters fairly well and produce appropriate standard errors, except when the two-parameter adjacent-category logits MIRID was fit to data with a small sample size and a short test length; overall, cumulative logits yielded a better parameter recovery than adjacent-category logits. A real data set about guilt was analyzed with gender as a Level 2 predictor to illustrate applications and applications of the new model. Further model generalization is discussed. Copyright © 2010 Sage Publications.
CitationWang, W.-C., & Jin, K.-Y. (2010). A generalized model with internal restrictions on item difficulty for polytomous items. Educational and Psychological Measurement, 70(2), 181-198.
- Cumulative logits
- Adjacent-category logits
- Nonlinear mixed model
- Multilevel model