Partial Credit Model: Estimations and Tests of Fit with Pcmodel

Abstract

The partial credit and rating scale models are classical models from item response theory; they belong to the generalized linear latent and mixed model family and allow one to analyze questionnaires such as patient-reported outcomes. Few goodness-of-fit testing procedures have been proposed for such models, and few computer programs implement such tests. Here we describe two tests: the R1m test (which tests the overall adequacy of the model to the data) and the Si test (which evaluates the contribution of each item to a possible lack of fit). We also propose two commands: pcmodel, which implements partial credit or rating scale models, and pcmtest, which tests the adequacy of such models to the data.