A Polytomous Nonlinear Mixed Model for Item Analysis

The study presented the formulation of an IRT model for polytomously scored Likert-type data under the framework of the nonlinear mixed model. The formulated polytomous nonlinear mixed model (PNLMM) was demonstrated to be equivalent to Muraki's rating scale model (1990). Due to the flexibility of the framework the PNLMM was easily extended into a model for differential item functioning analysis and a regression-type model with a person-level covariate. Using simulations the accuracy of SAS PROC NLMIXED in estimating the latent trait and the item parameters for the PNLMM was examined through eight common indicators. The correlations between PROC NLMIXED and PARSCALE estimates for model parameters were also evaluated. The results and their educational importance were discussed.