Power Comparisons for Testing Nested Models Using Limited-Information Statistics

• Activity Number: 643
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Mark Reiser*+
• Companies: Arizona State University
• Keywords: multivariate discrete distribution ; likelihood ratio difference statistic ; orthogonal components ; composite null hypothesis

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, the common statistics may have low power and inaccurate Type I error level due to sparseness. Yet a test based on the difference of likelihood ratio statistics for nested models may have high power and accurate Type I error rate even if it is obtained from a sparse table. Several statistics that have been proposed from components of the Pearson statistic obtained on marginal distributions often have very good performance for Type I error rate and power when obtained from a sparse table. This paper compares the performance of the likelihood ratio difference statistic for nested models to statistics based on components from marginal distributions. The comparison includes test statistics from Christoffersson (1975), Reiser (1996, 2008), Bartholomew and Leung (2002), Tollenaar and Mooijaart (2003), and Maydeu-Olivares and Joe (2005).