Evaluating the double Poisson generalized linear model

Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique

doi:10.1016/j.aap.2013.07.017

Cited by 30 publications

(24 citation statements)

References 25 publications

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“…More nonmixture models presenting dual properties of over-and underdispersion are: the compound generalized Poisson distribution, 32 the Katz System yielding the generalized event count model, 33,34 or the Conway-Maxwell Poisson model. 35,36 A further reason for observing underdispersion is data truncation. Right truncation is observed when events above a fixed value (c r ) are not counted, whereas left truncation occurs when the censoring affects counts below a set value (c l ).…”

Section: Count Model Components For Data Violating Poisson Assumptionmentioning

confidence: 99%

Modeling and Simulation of Count Data

Plan

2014

CPT Pharmacom & Syst Pharma

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Count data, or number of events per time interval, are discrete data arising from repeated time to event observations. Their mean count, or piecewise constant event rate, can be evaluated by discrete probability distributions from the Poisson model family. Clinical trial data characterization often involves population count analysis. This tutorial presents the basics and diagnostics of count modeling and simulation in the context of pharmacometrics. Consideration is given to overdispersion, underdispersion, autocorrelation, and inhomogeneity.

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Section: Count Model Components For Data Violating Poisson Assumptionmentioning

confidence: 99%

Modeling and Simulation of Count Data

Plan

2014

CPT Pharmacom & Syst Pharma

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“…The first parameterization, proposed by Winkelmann and applied to crash data first by Oh et al ., assumes that the time elapsed between each two successive crashes (waiting time) follows a gamma distribution. This approach implies that crash events are “dependent in the sense that the occurrence of at least one event (in contrast to none) up to time t influences the probability of a further occurrence in t +∆ t .” Nonetheless, while crash counts can sometimes have a temporal correlation, they are often described as independent observations . Recently, Daniels et al .…”

Section: Introductionmentioning

confidence: 99%

“…used a different parameterization of the gamma model in which they assumed that the crash frequency itself follows a continuous gamma density function. Two major theoretical shortcomings exist for this assumption: it implies that crash counts of zero are not possible, and that noninteger crash counts may be observed . Both implications are obviously fallacious.…”

Section: Introductionmentioning

confidence: 99%

Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

et al. 2014

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The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.

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“…Other extensions based on Poisson models include the Conway-Maxwell-Poisson model (Lord, Geedipally, & Guikema, 2010;Lord, Guikema, & Geedipally, 2008), the double Poisson model (Zou, Geedipally, & Lord, 2013), the hyper-Poisson model (Khazraee, Sáez-Castillo, Geedipally, & Lord, 2014), the Poisson-lognormal model (Park & Lord, 2007), the Poisson-Weibull model (Cheng, Geedipally, & Lord, 2013), among others. The Conway-Maxwell-Poisson model, double Poisson model, and hyper-Poisson model can handle both over-and under-dispersion, although under-dispersion is rarely seen in crash data.…”

Section: Crash-frequency Modelingmentioning

confidence: 99%

Performance Assessment of Road Barriers in Indiana

Zou¹

2016

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Evaluating the double Poisson generalized linear model

Cited by 30 publications

References 25 publications

Modeling and Simulation of Count Data

Modeling and Simulation of Count Data

Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

Performance Assessment of Road Barriers in Indiana

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