The COM‐Poisson model for count data: a survey of methods and applications

Sellers, Kimberly F.; Borle, Sharad; Shmueli, Galit

doi:10.1002/asmb.918

Cited by 169 publications

(109 citation statements)

References 43 publications

(94 reference statements)

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“…where the approximation holds for ν ≤ 1 or λ > 10 ν (Sellers et al 2011); see Minka et al (2003) for details. More generally, the associated moment generating function of X is M X (t) =…”

Section: The Conway-maxwell-poisson Distributionmentioning

confidence: 99%

“…The model has further been applied for various data problems including fitting word lengths (Wimmer et al 1994), modeling online sales Borle et al 2006) and customer behavior (Borle et al 2007), analyzing traffic accident data (Lord et al 2008), and for use as a disclosure limitation procedure to protect individual privacy ). See Sellers et al (2011) for additional overview and discussion. …”

Section: Z(λe T ν)mentioning

confidence: 99%

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A flexible distribution class for count data

2017

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The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution -a two-parameter generalization of the Poisson distribution that can accommodate data over-or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model's flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion.

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Section: The Conway-maxwell-poisson Distributionmentioning

confidence: 99%

Section: Z(λe T ν)mentioning

confidence: 99%

A flexible distribution class for count data

2017

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“…and the maximum likelihood estimation can thus be achieved by iteratively solving the set of normal equations. 13 …”

Section: Conway-maxwell-poisson (Com-poisson) Regression Modelmentioning

confidence: 99%

Determination of the Affecting Factors of the Number of Babies Born Alive in Multiple Pregnancies with Poisson Models

Erkan¹,

Evkaya²,

Türkan³

2017

Turkiye Klinikleri J Biostat

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Objective: Multiple pregnancies occurred more frequently with being widespread of the assisted reproduction techniques. The recent researches showed that the possibility of multiple pregnancies has been increased by some factors such as twin pregnancy experience in the family, mothers at later ages, social properties and the number of live-born infants. The main aim of this study is to identify the statistically significant factors affecting the multiple pregnancies using count data models. Material and Methods: In this study, the number of babies born alive for the pregnant who have multiple pregnancy diagnose are considered in 2015 for a specific location, Ankara province in Turkey. For this purpose, the effects of mother's age, the number of pregnancy, the method of delivery, mother's blood type and previous births of the mother are statistically analyzed using various count data models. Results: Quasi Poisson and Conway-Maxwell-Poisson (COM) regression models are used due to under-dispersion problem and these models are compared for the data set. As a result of comparison, the advantage of COM Poisson regression to other count regression models are illustrated with a real data set. According to results of COM Poisson, the number of pregnant and method of delivery (specifically cesarean type) has significant impact on the number of live-born infants at %99 significance level and the blood type of pregnant has significant impact at %95 significance level. However, the cesarean delivery has negative impact on the number of live-born infants. Conclusion: The main indicator of existence of under-dispersion is significant so fitting COMPoisson to the data in this study is meaningful. For the model selection, based on AIC values of Poisson and COM-Poisson models, the latter one is smaller hence fits better. After recovering the problem of underdispersion for the count data with COM Poisson regression, the number of pregnancy and the method of delivery has been determined as the best predictor. Besides, the blood types were identified as additional explanatory variable, but with lower significance level.Keywords: Multiple Pregnancy; quasi poisson regression; under-dispersion, COM Poisson regression ÖZET Amaç: Günümüzde yardımcı üreme tekniklerinin giderek yaygınlaşması ile çoğul gebeliklere daha sık rastlanmaya başlanmıştır. Son yıllarda yapılan araştırmalara göre, ailede daha önceden ikiz gebelik olması, ileri anne yaşı, toplumsal özellikler ve canlı doğan bebek sayısı gibi faktörlerin çoklu gebelik görülme olasılığını artırdığı gözlemlenmiştir. Bu çalışmanın esas amacı çoğul gebelikleri etkileyen istatistiksel olarak anlamlı faktörleri sayım modelleri kullanarak belirlemektir. Gereç ve Yöntemler: Bu çalışmada 2015 yılında Ankara ilinde çoklu gebelik tanısı konmuş gebelerin doğum sonuçlarına göre canlı doğan bebek sayısı dikkate alınmıştır. Bu amaçla, annenin yaşı, kaçıncı gebeliği olduğu, doğum yöntemi, kan grubu ve önceki doğum durumu gibi faktörlerin etkileri istatistiksel olarak sayım modelleri kullanı...

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“…The COM-Poisson distribution was first introduced in 1962 by Conway and Maxwell; only in 2008 it was evaluated in the context of a GLM by Guikema and Coffelt (2008), Lord et al (2008) and Sellers and Shmueli (2010). The COM-Poisson distribution is a two parameter generalization of the Poisson distribution that is flexible enough to describe a wide range of count data distributions (Sellers & Shmueli, 2010); since its revival, it has been further developed in several directions and applied in multiple fields (Sellers et al, 2011).…”

Section: Accounting For Dispersionmentioning

confidence: 99%

Accounting for Dispersion and Correlation in Estimating Safety Performance Functions. An Overview Starting from a Case Study

Giuffrè¹,

Granà²,

Giuffrè³

et al. 2013

MAS

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In statistical analysis of crash count data, as well as in estimating Safety Performance Functions (SPFs), the failure of Poisson equidispersion hypothesis and the temporal correlation in annual crash counts must be considered to improve the reliability of estimation of the parameters. After a short discussion on the statistical tools accounting for dispersion and correlation, the paper presents the methodological path followed in estimating a SPF for urban four-leg, signalized intersections. Since the case study exhibited signs of underdispersion, a Conway-Maxwell-Poisson Generalized Linear Model (GLM) was fitted to the data; then a quasi-Poisson model in the framework of Generalized Estimating Equations (GEEs) was performed in order to account for correlation.Results confirm that dispersion and correlation are phenomena that cannot be eluded in the estimation of SPFs under penalty of loss of efficiency in estimating model parameters. Generalized Estimating Equations overcome this problem allowing to incorporate together dispersion and temporal correlation when a quasi-Poisson distribution is used for modeling crash data. Moreover, whereas GEE regression is handy (many statistical software packages have already implemented GEE functions), the interest of COM-Poisson regression, because of difficulties in interpreting the model parameters and in arranging COM-Poisson codes, is still limited to the research field.

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The COM‐Poisson model for count data: a survey of methods and applications

Cited by 169 publications

References 43 publications

A flexible distribution class for count data

A flexible distribution class for count data

Determination of the Affecting Factors of the Number of Babies Born Alive in Multiple Pregnancies with Poisson Models

Accounting for Dispersion and Correlation in Estimating Safety Performance Functions. An Overview Starting from a Case Study

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