The Covariate-Adjusted Frequency Plot for the Rasch Poisson Counts Model

  • Heinz Holling Statistics and Quantitative Methods, Faculty of Psychology and Sports Science University of Munster, M ¨ unster, Germany
  • Walailuck Bohning Statistics and Quantitative Methods, Faculty of Psychology and Sports Science University of Munster, M ¨ unster, Germany
  • Dankmar Bohning Southampton Statistical Sciences Research Institute Mathematics & Medicine, Southampton, SO17 1BJ, UK
Keywords: Frequency plot, Goodness-of-fit, Model Diagnostics, Graphical Display, Residual Analysis

Abstract

The Rasch Poisson Counts model is an appropriate item response theory (IRT) model for analyzing many kinds of count data in educational and psychological testing. The evaluation of a fitted Rasch Poisson model by means of a graphical display or graphical device is difficult and, hence, very much an open problem, since the observations come from different distributions. Hence methods, potentially straightforward in the univariate case, cannot be applied for this model. However, it is possible to use a method, called the covariate–adjusted frequency plot, which incorporates covariate information into a marginal frequency plot. We utilize this idea here to construct a covariate-adjusted frequency plot for the Rasch Poisson Counts model. This graphical method is useful in illustrating goodness-of-fit of the model as well as identifying potential areas (items) with problematic fit. A case study using typical data from a frequently used intelligence test illustrates the method which is easy to use.
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