A Doubly-Inflated Poisson Distribution and Regression Model

Sheth-Chandra, Manasi; Chaganty, N. Rao; Sabo, Roy

doi:10.1007/978-3-030-11431-2_7

Cited by 4 publications

(8 citation statements)

References 10 publications

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“…Frequencies of 0 and 1 were larger in the observed DMFT count than other counts. , , and ZIP models have also been compared [4].…”

Section: Introductionmentioning

confidence: 99%

“…Where and In this model, probabilities and can depend on covariates using the logit-link function and mean can relate to covariates with the log-link function [4]. In clinical research, it is frequently observed that data are correlated due to hierarchical, multilevel, longitudinal, repeated measure, and cluster study designs.…”

Section: Introductionmentioning

confidence: 99%

“…In the DIP study by Chandra (2011), parameters' estimates have been examined through maximum likelihood and the method of moments techniques. Moreover, in a study conducted by Sengupta et al (2015)., parameters' estimate has been obtained using the maximum likelihood method [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Analysis of Doubly Inflated Poisson Regression for Correlated Count Data: Application to DMFT Data

Chaboki

Baghban

Baghfalaki

et al. 2022

ebph

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Outcome variables in clinical studies sometimes include count data with inflation in two points (usually zero and k (k>0)). Doubly inflated models can be adopted for modeling these types of data. In statistical modeling, the association among subjects due to longitudinal or cluster study designs is considered by random effects models. In this article, we proposed a doubly inflated random effects model using the Bayesian approach for correlated count data with inflation in two values, and compared this model with Bayesian zero-inflated Poisson and Bayesian Poisson models. The parameters’ estimates by these models were obtained by Markov Chain Monte Carlo method using OpenBUGS software. Bayesian models were compared using the deviance information criterion. To this end, we utilized the total number of decayed, missed, and filled teeth of 12-year-old children and also conducted a simulation study. Results of real data and the simulation study revealed that the proposed model is fitted better than previous models.

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“…Frequencies of 0 and 1 were larger in the observed DMFT count than other counts. , , and ZIP models have also been compared [4].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Analysis of Doubly Inflated Poisson Regression for Correlated Count Data: Application to DMFT Data

Chaboki

Baghban

Baghfalaki

et al. 2022

ebph

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“…Lin and Tsai [1] proposed a zero-and k-inflated Poisson regression model (ZkIP) to analyze such data. Sheth et al [2] also introduced two forms of ZkIP models, known as doubly inflated Poisson (DIP) models. In this article, we study the ZkIP form given by Lin and Tsai [1].…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we study the ZkIP form given by Lin and Tsai [1]. It is the same as the second DIP model proposed by Sheth et al [2].…”

Section: Introductionmentioning

confidence: 99%

EM Estimation for Zero- and k-Inflated Poisson Regression Model

Arora

Chaganty

2021

Computation

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Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we provide details for obtaining parameter estimates of the ZkIP regression model using the Expectation–Maximization (EM) algorithm for a given data. We derive the standard errors of the EM estimates by computing the complete, missing, and observed data information matrices. We present the analysis of two real-life data using the methods outlined in the paper.

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