A Generalized Partial Credit Model: Application of an EM Algorithm

TLDR

The study develops a generalized partial credit model (GPCM) that extends the PCM by incorporating a varying slope parameter. The authors derive an EM algorithm for estimating the GPCM, decompose item step parameters into location and threshold components, and evaluate the model on simulated data and National Assessment of Educational Progress mathematics data, comparing it to Rasch family polytomous models. The GPCM’s rating formulation proves adaptable to polytomous data, and it achieves superior fit compared to the standard PCM.

Abstract

The partial credit model (PCM) with a varying slope parameter is developed and called the generalized partial credit model (GPCM). The item step parameter of this model is decomposed to a location and a threshold parameter, following Andrich's (1978) rating scale formulation. The EM algorithm for estimating the model parameters is derived. The performance of this generalized model is compared on both simulated and real data to a Rasch family of polytomous item response models. Simulated data were generated and then analyzed by the various polytomous item response models. The results demonstrate that the rating formulation of the GPCM is quite adaptable to the analysis of polytomous item responses. The real data used in this study consisted of the National Assessment of Educational Progress (Johnson & Allen, 1992) mathematics data that used both dichotomous and polytomous items. The PCM was applied to these data using both constant and varying slope parameters. The GPCM, which provides for varying slope parameters, yielded better fit to the data than did the PCM.