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Activity Number: 252
Type: Contributed
Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
Sponsor: Social Statistics Section
Abstract #315773
Title: Lack-of-Fit Diagnostics Based on Standardized Residuals and Orthogonal Components of Pearson's Chi-Square
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

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.

Authors who are presenting talks have a * after their name.

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