252 – Methodology: Model Fit
Lack-of-Fit Diagnostics Based on Standardized Residuals and Orthogonal Components of Pearson's Chi-Square
Maduranga Kasun Dassanayake
Arizona State University
Mark Reiser
Arizona State University, Tempe, Arizona
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.