scholarly journals Marginal regression models for clustered count data based on zero-inflated Conway-Maxwell-Poisson distribution with applications

Biometrics ◽  
2015 ◽  
Vol 72 (2) ◽  
pp. 606-618 ◽  
Author(s):  
Hyoyoung Choo-Wosoba ◽  
Steven M. Levy ◽  
Somnath Datta
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Regression Models ◽  
Marginal Regression

scholarly journals Overdispersion study of poisson and zero-inflated poisson regression for some characteristics of the data on lamda, n, p

2016 ◽  
Vol 2 (3) ◽  
pp. 140
Author(s):  
Lili Puspita Rahayu ◽  
Kusman Sadik ◽  
Indahwati Indahwati
Keyword(s):  
Sample Size ◽  
Poisson Distribution ◽  
Count Data ◽  
Poisson Regression ◽  
Regression Models ◽  
Rare Events ◽  
Discrete Distribution ◽  
Data Simulation ◽  
Response Variable ◽  
Pearson Residual

Poisson distribution is one of discrete distribution that is often used in modeling of rare events. The data obtained in form of counts with non-negative integers. One of analysis that is used in modeling count data is Poisson regression. Deviation of assumption that often occurs in the Poisson regression is overdispersion. Cause of overdispersion is an excess zero probability on the response variable. Solving model that be used to overcome of overdispersion is zero-inflated Poisson (ZIP) regression. The research aimed to develop a study of overdispersion for Poisson and ZIP regression on some characteristics of the data. Overdispersion on some characteristics of the data that were studied in this research are simulated by combining the parameter of Poisson distribution (λ), zero probability (p), and sample size (n) on the response variable then comparing the Poisson and ZIP regression models. Overdispersion study on data simulation showed that the larger λ, n, and p, the better is the model of ZIP than Poisson regression. The results of this simulation are also strengthened by the exploration of Pearson residual in Poisson and ZIP regression.

scholarly journals Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data

2019 ◽  
Vol 20 (5) ◽  
pp. 443-466
Author(s):  
Eduardo E Ribeiro ◽  
Walmes M Zeviani ◽  
Wagner H Bonat ◽  
Clarice GB Demetrio ◽  
John Hinde
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Regression Models ◽  
Maximum Likelihood Estimators ◽  
Location Parameter ◽  
Heavy Tail ◽  
Simulation Studies ◽  
Dispersion Parameters ◽  
Supplementary Material ◽  
Two Parameter

The COM–Poisson distribution is a two-parameter generalization of the Poisson distribution that can deal with under-, equi- and overdispersed count data. Unfortunately, its location parameter does not correspond to the expectation, which complicates the parameter interpretation. In this article, we propose a straightforward reparametrization of the COM–Poisson distribution based on an approximation to the expectation. Estimation and inference are done using the likelihood paradigm. Simulation studies show that the maximum likelihood estimators are unbiased and consistent for both regression and dispersion parameters. In addition, the nature of the deviance surfaces suggests that these parameters are also orthogonal for most of the parameter space, which is advantageous for interpretation, inference and computational efficiency. Study of the distribution’s properties, through a consideration of dispersion, zero-inflation and heavy tail indexes, together with the results of data analyses show the flexibility over standard approaches. The computational routines and datasets are available in the supplementary material.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

Scalable Bayesian variable selection regression models for count data

2020 ◽  
pp. 187-219 ◽  
Author(s):  
Yinsen Miao ◽  
Jeong Hwan Kook ◽  
Yadong Lu ◽  
Michele Guindani ◽  
Marina Vannucci
Keyword(s):  
Variable Selection ◽  
Count Data ◽  
Regression Models ◽  
Bayesian Variable Selection

Nonlinear regression models for correlated count data

1992 ◽  
Vol 3 (2) ◽  
pp. 211-222 ◽  
Author(s):  
R. T. Burnett ◽  
J. Shedden ◽  
D. Krewski
Keyword(s):  
Nonlinear Regression ◽  
Count Data ◽  
Regression Models ◽  
Nonlinear Regression Models

Managing Inflation

2016 ◽  
Vol 63 (1) ◽  
pp. 77-87 ◽  
Author(s):  
William H. Fisher ◽  
Stephanie W. Hartwell ◽  
Xiaogang Deng
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Excess Zeros ◽  
Binomial Regression ◽  
Negative Binomial Models ◽  
Using Data ◽  
Over Dispersion ◽  
Binomial Models

Poisson and negative binomial regression procedures have proliferated, and now are available in virtually all statistical packages. Along with the regression procedures themselves are procedures for addressing issues related to the over-dispersion and excessive zeros commonly observed in count data. These approaches, zero-inflated Poisson and zero-inflated negative binomial models, use logit or probit models for the “excess” zeros and count regression models for the counted data. Although these models are often appropriate on statistical grounds, their interpretation may prove substantively difficult. This article explores this dilemma, using data from a study of individuals released from facilities maintained by the Massachusetts Department of Correction.

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