A GENERALIZED PARTIAL CREDIT MODEL: APPLICATION OF AN EM ALGORITHM

Abstract

The Partial Credit model with a varying slope parameter has been developed, and it is called the Generalized Partial Credit model. The item step parameter of this model is decomposed to a location and a threshold parameter, following Andrich's Rating Scale formulation. The EM algorithm for estimating the model parameters was derived. The performance of this generalized model is compared with a Rasch family of polytomous item response models based on both simulated and real data. Simulated data were generated and then analyzed by the various polytomous item response models. The results obtained demonstrate that the rating formulation of the Generalized Partial Credit model is quite adaptable to the analysis of polytomous item responses. The real data used in this study consisted of NAEP Mathematics data which was made up of both dichotomous and polytomous item types. The Partial Credit model was applied to this data using both constant and varying slope parameters. The Generalized Partial Credit model, which provides for varying slope parameters, yielded better fit to data than the Partial Credit model without such a provision. Index terms: item response model polytomous item response model the Partial Credit model the Rating Scale model the Nominal Response model NAEP