Semiparametric negative binomial regression models

Negative-binomial (NB) regression models have been widely used for analysis of count data displaying substantial overdispersion (extra-Poisson variation). However, no formal lack-of-fit tests for a postulated parametric model for a covariate effect have been proposed. Therefore, a flexible parametric procedure is used to model the covariate effect as a linear combination of fixed-knot cubic basis splines or B-splines. Within the proposed modeling framework, a log-likelihood ratio test is constructed to evaluate the adequacy of a postulated parametric form of the covariate effect. Simulation experiments are conducted to study the power performance of the proposed test.