A Note on Conditional and Quasi-Conditional Maximum Likelihood Estimation for Polytomous Item Response Models

Abstract

Several item response models have been proposed to account for individual differences in response scale use that extend existing models to include respondent-specific threshold parameters. Inference for these models is based on marginal maximum likelihood by specifying distributional assumptions for the threshold parameters. This article shows that for three of these models—the rating scale, proportional odds, and sequential rating scale models—estimators for item location parameters can be derived using conditional maximum likelihood. The advantages of these estimators are that the likelihood functions are in closed-form and do not involve distributional assumptions concerning respondent-specific parameters, and so estimates are relatively easy to obtain numerically and do not require distributional assumptions and so are robust to individual differences in response scale use. A set of brief simulation studies are provided for illustration.