Phi-divergence statistics for the likelihood ratio order: an approach based on log-linear models

TL;DR

This paper introduces phi-divergence based test statistics within log-linear models to assess the likelihood ratio order among treatments, offering improved accuracy and power over classical methods.

Contribution

It develops a new class of phi-divergence test-statistics for likelihood ratio order testing using log-linear models, with theoretical and empirical validation.

Findings

Phi-divergence tests have closer size to nominal levels.

They demonstrate higher power than classical likelihood ratio tests.

The approach is effective for small and moderate sample sizes.

Abstract

When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing wether the treatments are equally effective or not. One way to do that is to test if the likelihood ratio order is strictly verified. A method based on log-linear models is derived to make statistical inference and phi-divergence test-statistics are proposed for the test of interest. Focussed on loglinear modeling, the theory associated with the asymptotic distribution of the phi-divergence test-statistics is developed. An illustrative example motivates the procedure and a simulation study for small and moderate sample sizes shows that it is possible to find phi-divergence test-statistic with an exact size closer to nominal size and higher power in comparison with the classical likelihood ratio.