The zero-inflated Conway–Maxwell–Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Barriga, Gladys Dorotea Cacsire; Louzada, Francisco

doi:10.1016/j.stamet.2013.11.003

Cited by 33 publications

(23 citation statements)

References 20 publications

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“…Ignoring overdispersion causes confidence intervals to be too narrow and inflates the rate of false positives in statistical tests (Rhodes, 2015). When data are either over-or underdispersed, they can be modeled with the lesser-known, Conway-Maxwell-Poisson distribution (Shmueli et al, 2005;Lynch et al, 2014;Barriga and Louzada, 2014). Depending on the dispersion, the upper tail of the Conway-Maxwell-Poisson distribution can be either longer or shorter than that of the Poisson (Sellers and Shmueli, 2010).…”

Section: Introductionmentioning

confidence: 99%

glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling

Brooks¹,

Kristensen²,

Benthem³

et al. 2017

The R Journal

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4,500

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Count data can be analyzed using generalized linear mixed models when observations are correlated in ways that require random effects. However, count data are often zero-inflated, containing more zeros than would be expected from the typical error distributions. We present a new package, glmmTMB, and compare it to other R packages that fit zero-inflated mixed models. The glmmTMB package fits many types of GLMMs and extensions, including models with continuously distributed responses, but here we focus on count responses. glmmTMB is faster than glmmADMB, MCMCglmm, and brms, and more flexible than INLA and mgcv for zero-inflated modeling. One unique feature of glmmTMB (among packages that fit zero-inflated mixed models) is its ability to estimate the Conway-Maxwell-Poisson distribution parameterized by the mean. Overall, its most appealing features for new users may be the combination of speed, flexibility, and its interface's similarity to lme4.

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Section: Introductionmentioning

confidence: 99%

glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling

Brooks¹,

Kristensen²,

Benthem³

et al. 2017

The R Journal

6,850

4,500

View full text Add to dashboard Cite

show abstract

“…This section illustrates the study's methodology with the apple cultivar data set which was extracted from Ridout, Hinde, and Demétrio (2001) and analyzed by Galea, Leiva-Sanchez, and Paula (2004) and Barriga and Louzada (2014). The data refer to 270 micropropagated shoots from the columnar apple cultivar Trajan.…”

Section: Applicationmentioning

confidence: 99%

Estimation and influence diagnostics for zero-inflated hyper-Poisson regression model: full Bayesian analysis

Cancho

Bao

Fiorucci

et al. 2017

Communications in Statistics - Theory and Methods

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The purpose of this paper is to develop a Bayesian analysis for the zeroinflated hyper-Poisson model. Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the model and the Bayes estimators are compared by simulation with the maximum-likelihood estimators. Regression modeling and model selection are also discussed and case deletion influence diagnostics are developed for the joint posterior distribution based on the functional Bregman divergence, which includes ψ-divergence and several others, divergence measures, such as the Itakura-Saito, Kullback-Leibler, and χ 2 divergence measures. Performance of our approach is illustrated in artificial, real apple cultivation experiment data, related to apple cultivation.

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“…Zero-inflated models have become quite popular in the literature to deal with situations where there are excess zeros, leading to overdispersion in data (Consul and Jain, 1973;Van den Broek, 1995;del Castillo and Pérez-Casany, 2005;Yang et al, 2007;Samani et al, 2012;Barriga and Louzada, 2014;Choo-Wosoba et al, 2015). In particular, the zero-inflated power series (ZIPS) model (Gupta et al, 1995) is one method to allow for overdispersion or underdispersion.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian cure rate model with dispersion induced by discrete frailty

Cancho

Zavaleta

Macera

et al. 2018

CSAM

Self Cite

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In this paper, we propose extending proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured. Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. This proposal also allows for a realistic description of non-risk individuals, since individuals cured due to intrinsic factors (immunes) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. We put the proposed model in a Bayesian framework and use a Markov chain Monte Carlo algorithm for the computation of posterior distribution. A simulation study is conducted to assess the proposed model and the computation algorithm. We also discuss model selection based on pseudo-Bayes factors as well as developing case influence diagnostics for the joint posterior distribution through ψ-divergence measures. The motivating cutaneous melanoma data is analyzed for illustration purposes.

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The zero-inflated Conway–Maxwell–Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Cited by 33 publications

References 20 publications

glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling

glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling

Estimation and influence diagnostics for zero-inflated hyper-Poisson regression model: full Bayesian analysis

A Bayesian cure rate model with dispersion induced by discrete frailty

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