Semiparametric Negative Binomial Regression Models

Abstract

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.

Keywords:

• B-spline
• Lack-of-fit test
• Log-likelihood ratio test
• Negative binomial
• Overdispersion
• Profile likelihood

Mathematics Subject Classification:

• 62G05
• 62G08
• 62G10
• 62G20

Acknowledgments

The author thanks a referee whose helpful comments improved the presentation. This publication was made possible by Grant Number UL1 RR024146 from the National Center for Research Resources (NCRR), a component of the National Institutes of Health (NIH), and NIH Roadmap for Medical Research.