Zero-inflated Generalized Poisson Regression Models Research Articles

Zero-Inflated Generalized Poisson Regression Model with an Application to Domestic Violence Data

The generalized Poisson regression model has been used to model dispersed count data. It is a good competitor to the negative binomial regression model when the count data is over-dispersed. Zero-inflated Poisson and zero-inflated negative binomial regression models have been proposed for the situations where the data generating process results into too many zeros. In this paper, we propose a zero-inflated generalized Poisson (ZIGP) regression model to model domestic violence data with too many zeros. Estimation of the model parameters using the method of maximum likelihood is provided. A score test is presented to test whether the number of zeros is too large for the generalized Poisson model to adequately fit the domestic violence data

GEE-based zero-inflated generalized Poisson model for clustered over or under-dispersed count data

ABSTRACTThe zero-inflated regression models such as zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) or zero-inflated generalized Poisson (ZIGP) regression models can model the count data with excess zeros. The ZINB model can handle over-dispersed and the ZIGP model can handle the over or under-dispersed count data with excess zeros as well. Moreover, the count data may be correlated because of data collection procedure or special study design. The clustered sampling approach is one of the examples in which the correlation among subjects could be defined. In such situations, a marginal model using generalized estimating equation (GEE) approach can incorporate these correlations and lead up to the relationships at the population level. In this study, the GEE-based zero-inflated generalized Poisson regression model was proposed to fit over and under-dispersed clustered count data with excess zeros.

PENERAPAN REGRESI ZERO INFLATED GENERALIZED POISSON (ZIGP) PADA DATA OVERDISPERSION

Zero Inflated Generalized Poisson (ZIGP) is a regression model used to analyze Poisson distributed discrete data which contains mostly zero and tends to experience overdispersion (varians value greater than the mean value). The purpose of this research is to find out the best model and the factors which influence the maternal mortality in Bali Province in year 2016 by using ZIGP regression model. The data used in this research was data from health profile Bali Province with the object totally 57 district rate data has proportion of zeros value more than 50% on the response variable. The analysis result of ZIGP data on maternal mortality cannot modeled using the ZIGP so ZIGP regression model became ZIP model . The best model which resulted from ZIP regression got one free variable which have significant impact towards the total number of maternal mortality. This significant variabel is the percentage of mother did visiting to K1.

Efficiency of Zero-Inflated Generalized Poisson Regression Model on Hospital Length of Stay Using Real Data and Simulation Study

Efficiency of Zero-Inflated Generalized Poisson Regression Model on Hospital Length of Stay Using Real Data and Simulation Study

Bivariate zero-inflated generalized Poisson regression model with flexible covariance

ABSTRACTThis paper introduces several forms of nested bivariate zero-inflated generalized Poisson (BZIGP) regression model which can be fitted to bivariate and zero-inflated count data. The main advantage of having several forms of BZIGP regression model is that they are nested and allow likelihood ratio test to be performed for choosing the best model. In addition, the BZIGP regression models have flexible forms of marginal mean–variance relationship, can be fitted to bivariate and zero-inflated count data with positive or negative correlations, and allow additional overdispersion of the two response variables. The BZIGP regression models are fitted to the Australian Health Survey data.

Multilevel zero-inflated Generalized Poisson regression modeling for dispersed correlated count data

Poisson or zero-inflated Poisson models often fail to fit count data either because of over- or underdispersion relative to the Poisson distribution. Moreover, data may be correlated due to the hierarchical study design or the data collection methods. In this study, we propose a multilevel zero-inflated generalized Poisson regression model that can address both over- and underdispersed count data. Random effects are assumed to be independent and normally distributed. The method of parameter estimation is EM algorithm base on expectation and maximization which falls into the general framework of maximum-likelihood estimations. The performance of the approach was illustrated by data regarding an index of tooth caries on 9-year-old children. Using various dispersion parameters, through Monte Carlo simulations, the multilevel ZIGP yielded more accurate parameter estimates, especially for underdispersed data.

Functional Form for the Zero-Inflated Generalized Poisson Regression Model

The generalized Poisson (GP) regression is an increasingly popular approach for modeling overdispersed as well as underdispersed count data. Several parameterizations have been performed for the GP regression, and the two well known models, the GP-1 and the GP-2, have been applied. The GP-P regression, which has been recently proposed, has the advantage of nesting the GP-1 and the GP-2 parametrically, besides allowing the statistical tests of the GP-1 and the GP-2 against a more general alternative. In several cases, count data often have excessive number of zero outcomes than are expected in the Poisson. This zero-inflation phenomenon is a specific cause of overdispersion, and the zero-inflated Poisson (ZIP) regression model has been proposed. However, if the data continue to suggest additional overdispersion, the zero-inflated negative binomial (ZINB-1 and ZINB-2) and the zero-inflated generalized Poisson (ZIGP-1 and ZIGP-2) regression models have been considered as alternatives. This article proposes a functional form of the ZIGP which mixes a distribution degenerate at zero with a GP-P distribution. The suggested model has the advantage of nesting the ZIP and the two well known ZIGP (ZIGP-1 and ZIGP-2) regression models, besides allowing the statistical tests of the ZIGP-1 and the ZIGP-2 against a more general alternative. The ZIP and the functional form of the ZIGP regression models are fitted, compared and tested on two sets of count data; the Malaysian insurance claim data and the German healthcare data.

Testing for varying zero-inflation and dispersion in generalized Poisson regression models

Homogeneity of dispersion parameters and zero-inflation parameters is a standard assumption in zero-inflated generalized Poisson regression (ZIGPR) models. However, this assumption may be not appropriate in some situations. This work develops a score test for varying dispersion and/or zero-inflation parameter in the ZIGPR models, and corresponding test statistics are obtained. Two numerical examples are given to illustrate our methodology, and the properties of score test statistics are investigated through Monte Carlo simulations.

A Bayesian Approach for Zero-Inflated Count Regression Models by Using the Reversible Jump Markov Chain Monte Carlo Method and an Application

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors.

Can Pseudo-nitzschia blooms be modeled by coastal upwelling in Lisbon Bay?

Marine planktonic diatoms of the genus Pseudo-nitzschia Peragallo have been responsible for amnesic shellfish poisoning (ASP) events worldwide through the production of the neurotoxin domoic acid (DA). In order to better understand the dynamics of the toxic events of Pseudo-nitzschia there is the need to describe their seasonal and spatial patterns. The main goal of this work is to establish the relation between a physical variable easily measured like coastal upwelling and the presence of Pseudo-nitzschia blooms, in Lisbon Bay. Phytoplankton samples were collected once a week from June 2001 to May 2005 and daily upwelling index were calculated based on values of geostrophic winds. Data of sea surface temperature, upwelling index, and Pseudo-nitzschia concentrations were used to construct statistical models to evaluate the seasonal variation and the relation between all parameters. Due to the nature of the time series involved in the study, it was applied the Zero-Inflated Generalized Poisson Regression Model. An initial spectral analysis was applied to the upwelling data in order to accurately understand the characteristics of the coastal upwelling. The results obtained indicate a close relation between upwelling events and Pseudo-nitzschia blooms which occurred during spring and summer. The mathematical model that describes Pseudo-nitzschia blooms in Lisbon Bay shows a lag of 4–6 days between the upwelling events and the presence of Pseudo-nitzschia in the monitoring station.