The Effect of Sparseness on Power of Goodness-of-Fit Tests for the Rasch Model

• Activity Number: 287
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Mark Reiser*+
• Affiliation(s): Arizona State University
• Keywords: latent trait model ; Monte Carlo simulation ; factor analysis ; goodness of fit

Abstract

The Rasch model is similar to factor analysis in that it posits a continuous latent variable underlying observed variable responses, but it differs from factor analysis in that observed variables are categorical, the latent variable is a priori unidimensional, and factor loadings are a priori constrained equal. It has been shown that the Rasch model can be estimated as a log-linear model. An application of the Rasch model often involves a large number of observed variables and a sparse cross-classification table. In this paper, the power of goodness-of-fit tests for the Rasch model is examined under conditions of sparseness by using Monte Carlo simulations. Goodness of fit for the Rasch model can be tested by using traditional approaches, such as the Pearson or Likelihood Ratio statistics, which rely on a large sample approximation to the chi-square distribution for obtaining p-values. As is well-known, the chi-square approximation may not be valid if expected frequencies under the model are small. A new test statistic that uses only the second-order marginals is developed and included in the comparison. Monte Carlo bootstrapping is also applied to traditional statistics.