Size and power considerations for testing loglinear models using phi-divergence test statistics

Abstract

In this article, we assume that categorical data axe distributed according to a multinomial distribution whose probabilities follow a loglinear model. The inference problem we consider is that of hypothesis testing in a loglinear-model setting. The null hypothesis is a composite hypothesis nested within the alternative. Test statistics are chosen from the general class of phi-divergence statistics. This article collects together the operating characteristics of the hypothesis test based on both asymptotic (using large-sample theory) and finite-sample (using a designed simulation study) results. Members of the class of power divergence statistics are compared, and it is found that the Cressie-Read statistic offers an attractive alternative to the Pearson-based and the likelihood ratio-based test statistics, in terms of both exact and asymptotic size and power.