Premium
Local influence measure of zero‐inflated generalized Poisson mixture regression models
Author(s) -
Chen XueDong,
Fu YingZi,
Wang XueRen
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5560
Subject(s) - overdispersion , count data , negative binomial distribution , poisson distribution , quasi likelihood , zero inflated model , poisson regression , mathematics , statistics , generalized linear model , regression analysis , econometrics , population , demography , sociology
In many practical applications, count data often exhibit greater or less variability than allowed by the equality of mean and variance, referred to as overdispersion/underdispersion, and there are several reasons that may lead to the overdispersion/underdispersion such as zero inflation and mixture. Moreover, if the count data are distributed as a generalized Poisson or a negative binomial distribution that accommodates extra variation not explained by a simple Poisson or a binomial model, then the dispersion occurs too. In this paper, we deal with a class of two‐component zero‐inflated generalized Poisson mixture regression models to fit such data and propose a local influence measure procedure for model comparison and statistical diagnostics. At first, we formally develop a general model framework that unifies zero inflation, mixture as well as overdispersion/underdispersion simultaneously, and then we mainly investigate two types of perturbation schemes, the global and individual perturbation schemes, for perturbing various model assumptions and detecting influential observations. Also, we obtain the corresponding local influence measures. Our method is novel for count data analysis and can be used to explore these essential issues such as zero inflation, mixture, and dispersion related to zero‐inflated generalized Poisson mixture models. On the basis of the results of model comparison, we could further conduct the sensitivity analysis of perturbation as well as hypothesis test with more accuracy. Finally, we employ here a simulation study and a real example to illustrate the proposed local influence measures. Copyright © 2012 John Wiley & Sons, Ltd.