A test for lack-of-fit of zero-inflated negative binomial models

Chin-Shang Li; Shen Ming Lee; Ming Shan Yeh

doi:10.1080/00949655.2019.1577856

A test for lack-of-fit of zero-inflated negative binomial models

Chin-Shang Li, Shen Ming Lee, Ming Shan Yeh

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

When a count data set has excessive zero counts, nonzero counts are overdispersed, and the effect of a continuous covariate might be nonlinear, for analysis a semiparametric zero-inflated negative binomial (ZINB) regression model is proposed. The unspecified smooth functional form for the continuous covariate effect is approximated by a cubic spline. The semiparametric ZINB regression model is fitted by maximizing the likelihood function. The likelihood ratio procedure is used to evaluate the adequacy of a postulated parametric functional form for the continuous covariate effect. An extensive simulation study is conducted to assess the finite-sample performance of the proposed test. The practicality of the proposed methodology is demonstrated with data of a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.

Original language	English (US)
Journal	Journal of Statistical Computation and Simulation
DOIs	https://doi.org/10.1080/00949655.2019.1577856
State	Published - Jan 1 2019
Externally published	Yes

Keywords

B-splines
count data
likelihood ratio
overdispersion
zero-inflated negative binomial
zero-inflated Poisson

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Statistics, Probability and Uncertainty
Applied Mathematics

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abstract = "When a count data set has excessive zero counts, nonzero counts are overdispersed, and the effect of a continuous covariate might be nonlinear, for analysis a semiparametric zero-inflated negative binomial (ZINB) regression model is proposed. The unspecified smooth functional form for the continuous covariate effect is approximated by a cubic spline. The semiparametric ZINB regression model is fitted by maximizing the likelihood function. The likelihood ratio procedure is used to evaluate the adequacy of a postulated parametric functional form for the continuous covariate effect. An extensive simulation study is conducted to assess the finite-sample performance of the proposed test. The practicality of the proposed methodology is demonstrated with data of a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.",

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