Using simulation to inspect the performance of a test, in particular tests of the parallel regressions assumption in ordered logit and probit models

In this talk, we will show how to use simulations in Stata to explore to what extent and under what circumstances a test is problematic. We will illustrate this for a set of tests of the parallel regression assumption in ordered logit and probit models: the Brant, likelihood ratio, Wald, score, and Wolfe-Gould test of the parallel regression assumption. A common impression is that these tests tend to be too anti-conservative; that is, they tend to reject a true null hypothesis too often. We will use simulations to try to quantify when and to what extent this is the case. We will also use these simulations to create a more robust bootstrap variation of the tests. The purpose of this talk is twofold: first, we want to explore the performance of these tests. For this purpose, we will present a new program, oparallel, that implements all tests and their bootstrap variation. Second, we want to give more general advice on how to use Stata to create simulations when one has doubts about a certain test. For this purpose, we will present the simpplot command, which can help to interpret the p-values returned by such a simulation.