Small Samples and Ordered Logistic Regression

The logistic regression proportional odds model is popular for analyzing studies with an ordered categorical outcome. In contingency table analysis, from a Type I error perspective, it is often thought best to collapse categories with sparse cell counts to improve asymptotic approximations used for testing hypotheses. Moreover, in the proportional odds model, it is natural to collapse adjacent categories of outcome since the slope parameter remains unchanged. This article asks the question: Is it really beneficial to do so? Using simulations, we show that in small samples collapsing categories produces Wald tests that are too conservative. Our simulations indicate that this is mainly due to stochastic dependence between the numerator and the denominator of the Wald statistic.