Chi-Square Orthogonal Components for Assessing Goodness-of-Fit of Multidimensional Multinomial Data

• Activity Number: 30
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jelena Milovanovic*+
• Keywords: Pearson Statistic ; limited information statistic ; Monte Carlo simulation

Abstract

In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when interest is directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is sometimes considered to produce an omnibus test that gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this research, orthogonal components defined on distributions for first- and second-order marginals are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category variables. Ordinal categories are assumed. A subset of these orthogonal components can be used to construct test statistics that allow one to identify the source of lack-of-fit and provide higher power compared to Pearson's test when the model under the null hypothesis is false. The derived goodness-of-fit tests are evaluated with studies of Type I error rate and power for detecting two-way associations that are not accounted for under the null hypothesis of a categorical variable factor analysis model.