Journal ArticleDOI
Tests for Detecting Overdispersion in Poisson Regression Models
TLDR
In this article, the authors developed tests for detecting extra-Poisson variation in counting data, which can be obtained as score tests against arbitrary mixed Poisson alternatives and are generalizations of tests of Fisher (1950) and Collings and Margolin (1985).Abstract:
Poisson regression models are widely used in analyzing count data. This article develops tests for detecting extra-Poisson variation in such situations. The tests can be obtained as score tests against arbitrary mixed Poisson alternatives and are generalizations of tests of Fisher (1950) and Collings and Margolin (1985). Accurate approximations for computing significance levels are given, and the power of the tests against negative binomial alternatives is compared with those of the Pearson and deviance statistics. One way to test for extra-Poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models; for example, negative binomial models can be used in this way (Cameron and Trivedi 1986; Lawless 1987a). The tests in this article require only the Poisson model to be fitted. Two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels. Simu...read more
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Negative Binomial Regression
TL;DR: In this article, the authors introduce the concept of risk in count response models and assess the performance of count models, including Poisson regression, negative binomial regression, and truncated count models.
Journal ArticleDOI
Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models
TL;DR: The regression models appropriate for counted data have seen little use in psychology and are likely to be misleading unless restrictive assumptions are met, and 3 alternative regression models are presented.
Journal ArticleDOI
Regression-based tests for overdispersion in the Poisson model☆
TL;DR: In this article, regression-based tests for mean-variance equality were proposed in a very general setting, which requires specification of only the mean variance relationship under the alternative, rather than the complete distribution whose choice is usually arbitrary.
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Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models
TL;DR: This article presented several modifications of the Poisson and negative binomial models for count data to accommodate cases in which the number of zeros in the data exceed what would typically be predicted by either model.
References
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Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Book
Continuous univariate distributions
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.