The Influence of Dimensionality on Estimation in the Partial Credit Model

Abstract

Of the polytomous item response theory models, Masters's partial credit (PC) model has evoked a great deal of interest. Given some of the PC model's areas of application (e.g., assessing the clinical competence of physicians), it is reasonable to suspect some degree of multidimensionality in the data. This study was concerned with the effect of multidimensionality on PC parameter estimation. Both noncompensatory and compensatory data sets were generated. Within these two classes of data sets, the data differed from one another with respect to the interdimensional association between two abilities, θ1 and θ2. Analysis consisted of root mean square error (RMSE), bias, Pearson product-moment correlations, standardized root mean squared differences, standardized differences between means, and descriptive statistics. For the compensatory conditions, the RMSE and bias plots showed that the ability estimate more accurately estimated the average θ than either θ1 or θ2. With increasing interdimensional association, the differences in RMSE and in bias with respect to θ1, θ2, and the average θ diminished, although one ability appeared to be better estimated throughout the θ continuum than did the other ability. The RMSE plots for the noncompensatory data sets showed a pattern similar to that of the compensatory data. However, when the test was divided into its component dimensions, the RMSE with respect to one of the examinees' abilities was less than the RMSE with respect to average θ as well as the other ability; these differences between the RMSEs with respect to θ1, θ2, and average θ diminished with increasing interdimensional association. Results are encouraging for individuals interested in using the Rasch family of models.