Zero-inflated Generalized Poisson Regression Research Articles

Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model

We propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and hypothesis testing, both simultaneously and partially, for significant parameters of the MZIGPR model. The steps of the EM algorithm for obtaining the parameter estimator are also described in this article. We use Berndt–Hall–Hall–Hausman (BHHH) numerical iteration to optimize the EM algorithm. Simultaneous testing is carried out using the maximum likelihood ratio test (MLRT) and the Wald test to partially assess the hypothesis. The proposed MZIGPR model is then used to model the three response variables: the number of maternal childbirth deaths, the number of postpartum maternal deaths, and the number of stillbirths with four predictors. The units of observation are the sub-districts of the Pekalongan Residency, Indonesia. The indicate overdispersion in the data on the number of maternal childbirth deaths and stillbirths, and underdispersion in the data on the number of postpartum maternal deaths. The empirical studies show that the three response variables are significantly affected by all the predictor variables.

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

Geographically weighted bivariate zero inflated generalized Poisson regression model and its application

This study discusses the development of Zero Inflated Generalized Poisson Regression (ZIGPR) with two response variables, that is Bivariate ZIGPR (BZIGPR). The extension of the ZIGPR model by considering spatial factor called Geographically Weighted Zero Inflated Generalized Poisson Regression (GWBZIGPR). The GWBZIGPR produces a local parameter estimator for each location of observation. The parameter estimation using the Maximum Likelihood Estimation (MLE) method obtained an equation that did not closed-form so that the numerical iteration of Berndt Hall Hall Hausman (BHHH) is used. The data used in this study are the number of pregnant maternal mortality and postpartum maternal mortality data in 91 sub-districts in Pekalongan Residency, Central Java Province. The results showed that the Akaike Information Criterion Corrected (AICc) value in the GWBZIGPR model is smaller than BZIGPR, so it means that the GWBZIGPR is better than the BZIGPR for modeling the number of pregnant maternal mortality and postpartum maternal mortality in Pekalongan Residency. The results of this study will assist local governments in anticipating the causes of maternal mortality.

Bivariate zero inflated generalized Poisson regression model in the number of pregnant maternal mortality and the number of postpartum maternal mortality in the Central Java Province in 2017

Excess zero is one of the problems in Generalized Poisson regression where the number of responses is contained zero exceeds 60 percent. One of the statistical methods have been developed is Zero Inflated Generalized Poisson Regression (ZIGPR). If there are two response variables, the appropriate regression analysis is Bivariate ZIGPR (BZIGPR). This study aims to determine the factors that influence the number of pregnant maternal mortality and the number of postpartum maternal mortality in 91 sub districts in Pekalongan Residency, Central Java Province 2017 through by the BZIGPR. The variables are percentage of K1 pregnancy examinations, percentage of K4 pregnancy examinations, percentage of deliveries assisted by health workers, percentage of pregnant women who received Fe3, percentage of TT2 + immunization in pregnant women, ratio of midwives per 100,000 population and percentage of obstetric complications management. The estimation of BZIGPR parameters using the Maximum Likelihood Estimation (MLE) method which results in a non-linear form so that, it is solved by the Berndt Hall-Hall Hausman (BHHH) iteration method. The result hypothesis testing using the Maximum Likelihood Ratio Test (MLRT) is reject null hypothesis. BZIGPR produces 2 regression models ln and logit . The predictor variables that affect response Y1 and Y2 on model ln are all of predictor variables. The predictor variables that affect response Y1 on model logit are all of predictor variables while the predictor variables that affect response Y2 are all of predictor variables except percentage of pregnant TT2 + immunization women and percentage of midwives per 100,000 population.

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

Assessment of length of stay in a general surgical unit using a zero-inflated generalized Poisson regression

Background: The effective use of limited health care resources is of prime importance. Assessing the length of stay (LOS) is especially important in organizing hospital services and health system. This study was conducted to identify predictors of LOS among patients who were admitted to a general surgical unit. Methods: In this cross-sectional study, the sample included all patients who were admitted to the general surgical unit of Shariati hospital in 2013 (n= 334). To determine the factors affecting LOS, Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated generalized Poisson (ZIGP) regression models were fitted using R software, and then the best model was selected. Results: Among all 334 patients, the mean (±SD) age of the patients was 45.2 (±16.47) years and 220 (65.9%) of them were male. The results revealed that based on ZIGP model, type of surgery (appendicitis, abdomen and its contents, hemorrhoids, lung, and skin), type of insurance, comorbid diseases (hypertension, heart disease, and hyperlipidemia), place of residence (local and non-local), age, and number of tests had significant effects on the LOS of GS patients. Conclusion: According to the Akaike information criterion (AIC) in each fitted model, it was found that ZIGP regression model is more appropriate than ZIP and ZINB regression models in assessing LOS in GS patients, especially due to the presence of excess zeros and overdispersion in count data.

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.

Sayıma Dayalı Elde Edilen Verilerin Modellenmesinde Sıfır Değer Ağırlıklı Genelleştirilmiş Poisson Regresyonun Kullanılması

In this study zero-inflated generalized Poisson reg ression was applied to the modelling of mite numbers data based on count. The subjects of the zero-inflated generalized Poisson regression are three parameters as mean, overdispersion and zero-inflated dispersion. The overdispersion and zero-inflated dispersion levels range was obtained to be quite high. However, it was found that zero-inflated data and overdispersion had an important effect on mite counts (p < 0.01). It was obtained that 36% (130 observations) of the total numbers of mite had zero values. The effects of all independent variables were found to be statistically significant on mite counts (p < 0.05). The results showed that the differences among regions and varieties regarding the mite counts were statistically significant (p < 0.01).

Modeling the mite counts having overdispersion and excess values ofzero using zero-inflated generalized poisson regression

The aim of this study was to apply for zero-inflated generalized Poisson regression in the modelling of mite counts that include excess values of zero and overdispersion. The results of, as mean regression, overdispersion and zero-inflated regression, were determined in three stages. It was obtained that 33.33% (120 observations) of the total numbers of mite taken as a dependent variable to model had zero values. The overdispersion parameter range was detected to be quite high. It was determined that zero-inflated data and overdispersion had an important effect on mite counts (P less than 0.01). The effects of region, month, year, varieties, temperature and humidity were found to be statistically significant on mite counts (P less than 0.01). The number of eggs found in harmful mites (Aculus schlechtendali) in the Starking variety was relatively higher than in the Golden variety. The results displayed that the differences among regions and varieties regarding the number of eggs found in harmful mites were statistically significant (P less than .01).

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.

Locating Multiple Interacting Quantitative Trait Loci with the Zero-Inflated Generalized Poisson Regression

We consider the problem of locating multiple interacting quantitative trait loci (QTL) influencing traits measured in counts. In many applications the distribution of the count variable has a spike at zero. Zero-inflated generalized Poisson regression (ZIGPR) allows for an additional probability mass at zero and hence an improvement in the detection of significant loci. Classical model selection criteria often overestimate the QTL number. Therefore, modified versions of the Bayesian Information Criterion (mBIC and EBIC) were successfully used for QTL mapping. We apply these criteria based on ZIGPR as well as simpler models. An extensive simulation study shows their good power detecting QTL while controlling the false discovery rate. We illustrate how the inability of the Poisson distribution to account for over-dispersion leads to an overestimation of the QTL number and hence strongly discourages its application for identifying factors influencing count data. The proposed method is used to analyze the mice gallstone data of Lyons et al. (2003). Our results suggest the existence of a novel QTL on chromosome 4 interacting with another QTL previously identified on chromosome 5. We provide the corresponding code in R.

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.

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton–Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F 2 intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.

Score Test for Zero Inflated Generalized Poisson Regression Model

In certain applications involving count data, it is sometimes found that zeros are observed with a frequency significantly higher (lower) than predicted by the assumed model. Examples of such applications are cited in the literature from engineering, manufacturing, economics, public health, epidemiology, psychology, sociology, political science, agriculture, road safety, species abundance, use of recreational facilities, horticulture and criminology. In this article, a zero adjusted generalized Poisson distribution is studied and a score test is developed, with and without covariates, to determine whether such an adjustment is necessary. Examples, with and without covariates, are provided to illustrate the results.