Double Poisson-Tweedie Regression Models

Petterle Ricardo R., Bonat Wagner H. (), Kokonendji Célestin C., Seganfredo Juliane C., Moraes Atamai and da Silva Monica G.
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Petterle Ricardo R.: Sector of Health Sciences, Medical School, Paraná Federal University, Curitiba, Brazil
Bonat Wagner H.: Department of Statistics, Paraná Federal University, Curitiba, Brazil
Kokonendji Célestin C.: Laboratoire de Mathématiques de Besançon, Bourgogne Franche-Comté University, Besançon, France
Seganfredo Juliane C.: Departamento de Saúde Comunitária, Paraná Federal University, Curitiba, Brazil
Moraes Atamai: Departamento de Saúde Comunitária, Paraná Federal University, Curitiba, Brazil
da Silva Monica G.: Departamento de Saúde Comunitária, Paraná Federal University, Curitiba, Brazil

The International Journal of Biostatistics, 2019, vol. 15, issue 1, 15

Abstract: In this paper, we further extend the recently proposed Poisson-Tweedie regression models to include a linear predictor for the dispersion as well as for the expectation of the count response variable. The family of the considered models is specified using only second-moments assumptions, where the variance of the count response has the form μ+ϕμp$\mu + \phi \mu^p$, where µ is the expectation, ϕ and p are the dispersion and power parameters, respectively. Parameter estimations are carried out using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions. The performance of the fitting algorithm is investigated through simulation studies. The results showed that our estimating function approach provides consistent estimators for both mean and dispersion parameters. The class of models is motivated by a data set concerning CD4 counting in HIV-positive pregnant women assisted in a public hospital in Curitiba, Paraná, Brazil. Specifically, we investigate the effects of a set of covariates in both expectation and dispersion structures. Our results showed that women living out of the capital Curitiba, with viral load equal or larger than 1000 copies and with previous diagnostic of HIV infection, present lower levels of CD4 cell count. Furthermore, we detected that the time to initiate the antiretroviral therapy decreases the data dispersion. The data set and R code are available as supplementary materials.

Keywords: Poisson-Tweedie distribution; double generalized linear models; estimating functions; CD4 count; human immunodeficiency virus (HIV); overdispersion (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/ijb-2018-0119

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