Saddlepoint Tests for Accurate and Robust Inference on Overdispersed Count Data

We are concerned with testing composite hypotheses about regression coefficients in small samples when the response variable consists of overdispersed counts. We adapt three recently developed tests to the negative binomial regression model and detail, for general M-estimators, the non-trivial computational aspects involved in their implementation, some of which remained obscure in the literature until now. Under regularity conditions, these tests feature a relative error property with respect to the asymptotic chi squared distribution, thus yielding highly accurate p-values even in small samples. Through extensive simulations, we show how these new tests outperform the traditional Wald, score and likelihood ratio tests in terms of actual level, and study their power. Moreover, we highlight that inference based on robust (bounded influence) versions of these tests remains reliable when the sample does not entirely conform to the model assumptions. The use of all these procedures is illustrated with data coming from a recent randomized controlled trial, with a sample size of 52 observations. An R package implementing all tests studied here is readily available.

Journal article

Computational Statistics & Data Analysis 107, 162–175