A hyper-Poisson regression model for overdispersed and underdispersed count data

Sáez-Castillo, A. J.; Sánchez, Antonio Conde

doi:10.1016/j.csda.2012.12.009

Cited by 60 publications

(44 citation statements)

References 26 publications

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“…Furthermore, Saez-Castillo and Conde-Sanchez (19) showed how the overdispersed case of the hP distribution (i.e., when λ > 1) can be viewed as a Poisson compound distribution with a confluent hypergeometric distribution. An interested reader is referred to their work for the derivation.…”

Section: Hyper-poisson Distributionmentioning

confidence: 99%

“…Saez-Castillo and Conde-Sanchez (19) developed an hP GLM framework to model discrete count data. In this approach, both the mean and the dispersion parameters of the hP distribution can depend on the covariates.…”

Section: Generalized Linear Modelmentioning

confidence: 99%

“…The code developed by Saez-Castillo and Conde-Sanchez, (19) in the software R, (29) is used in this study. The program uses functions nlm and optim to maximize the log-likelihood, and optimize to solve Equation (6) numerically.…”

Section: Model Estimationmentioning

confidence: 99%

“…From Equation and using the method of moments, the following relationship between the distribution variance (σ 2 ) and mean (μ) is obtained:

σ^{2} = θ_{2} + (θ_{2} - (λ - 1)) μ - μ^{2} .

…”

Section: Introductionmentioning

confidence: 99%

“…Very recently, Saez-Castillo and Conde-Sanchez (19) formulated a GLM framework for a two-parameter generalization of the Poissonxbrk distribution, called the hyper-Poisson (hP, hereafter) distribution. The primary objective of this study is to examine the potential application of the hP GLM in the field of highway safety to model crash count data.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Hyper-poisson Distributionmentioning

confidence: 99%

Section: Generalized Linear Modelmentioning

confidence: 99%

Section: Model Estimationmentioning

confidence: 99%

“…From Equation and using the method of moments, the following relationship between the distribution variance (σ 2 ) and mean (μ) is obtained:

σ^{2} = θ_{2} + (θ_{2} - (λ - 1)) μ - μ^{2} .

…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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Narrative abilities in early implanted children

et al. 2014

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An Improved Method for the Estimation and Comparison of Mortality Rates in Fish from Catch‐Curve Data

Mainguy

Moral

2021

N American J Fish Manag

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Catch‐curve analyses are routinely used to estimate instantaneous mortality (Z) in fish, and as the age‐frequency data are often overdispersed, the application of a variance bias‐correction factor has been recommended. The extensions of the Poisson generalized linear model (GLMPoisson) may, however, constitute a better alternative, as they model the variance (SE) in counts more adequately with their specific dispersion parameter for more accurate estimations and statistical comparisons. To test this idea, simulated age‐frequency data generated under four dispersion scenarios were analyzed according to six currently available methods and compared with the results of a GLMPoisson and five of its extensions to evaluate each method‐specific bias in Z ± SE estimates. Empirical age‐frequency data from sampled Walleye Sander vitreus and Arctic Char Salvelinus alpinus populations in Québec, Canada, were then used to illustrate the applicability of our GLM‐based method, which relies on the behavior of Pearson residuals to assess model adequacy and an information‐theoretic approach for model selection. All analyses revealed that Z‐estimates were generally accurate among the methods considered, except under the most likely situation of quadratic overdispersion met in ecological studies, for which only the negative binomial type 2 and the mean‐parametrized Conway–Maxwell–Poisson (CMP) extensions were adequate to estimate both Z and its SE. Linearly overdispersed data were best modeled by the negative binomial type 1 and generalized Poisson (GLMGP) extensions; the GLMCMP and GLMGP were the most appropriate to model underdispersed data, whereas the GLMPoisson adequately modeled equi‐dispersed data, similar to the Chapman and Robson (1960) method. Statistical comparisons of Z ± SE for grouping factors, such as year or site, were correctly achieved when the most adequate and statistically supported GLMPoisson extension was applied. Altogether, the proposed GLM‐based method should help to circumvent the identified issues related to SE estimation for statistical inferences about mortality rates for fisheries management decision making.

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A hyper-Poisson regression model for overdispersed and underdispersed count data

Cited by 60 publications

References 26 publications

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

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

Narrative abilities in early implanted children

An Improved Method for the Estimation and Comparison of Mortality Rates in Fish from Catch‐Curve Data

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