Lack-of-Fit Diagnostics Based on Standardized Residuals and Orthogonal Components of Pearson's Chi-Square

• Activity Number: 252
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Maduranga Kasun Dassanayake* and Mark Reiser
• Companies: Arizona State University and Arizona State University
• Keywords: Item response model ; Statistical power ; Orthogonal components ; Monte Carlo simulation ; Standardized residuals

Abstract

The Pearson and likelihood ratio statistics are commonly used to test goodness of fit for models applied to data from a multinomial distribution. When data are from a table formed by the cross classification of a large number of variables, these statistics may have low power and inaccurate Type I error rate due to sparseness. Pearson's statistic can be decomposed into orthogonal components associated with the marginal distributions of observed variables, and an omnibus fit statistic can be obtained as a sum of these components. When the statistic is a sum of components for lower-order marginals, it has good performance for Type I error rate and statistical power even when applied to a sparse table. In this study the individual components are examined as lack-of-fit diagnostics for models fit to binary cross-classified variables. Monte Carlo simulations are used to study the statistical power of individual orthogonal components to detect the source of the model lack-of-fit. The performance of orthogonal components as diagnostics is also compared to adjusted standardized residuals.