  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.
