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When some treatments are ordered according to the categories of an ordinalcategorical variable (e.g., extent of side effects) in a monotone order, onemight be interested in knowing wether the treatments are equally effective ornot. One way to do that is to test if the likelihood ratio order is strictlyverified. A method based on log-linear models is derived to make statisticalinference and phi-divergence test-statistics are proposed for the test ofinterest. Focussed on loglinear modeling, the theory associated with theasymptotic distribution of the phi-divergence test-statistics is developed. Anillustrative example motivates the procedure and a simulation study for smalland moderate sample sizes shows that it is possible to find phi-divergencetest-statistic with an exact size closer to nominal size and higher power incomparison with the classical likelihood ratio.

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