On modelling overdispersion of counts

Abstract

For counts it often occurs that the observed variance exceeds the nominal variance of the claimed binomial, multinomial or Poisson distributions. We study how models can be extended to cope with this phenomenon: a survey of literature is given. We focus on modelling, not on estimation or testing statistical hypotheses. The attention is restricted to independent observations.

The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives

“…The distribution of precipitation over the month (by hour or even minute) is likely to be highly influential in generating crashes, but generally the analyst only has precipitation 2 In count-data models, actual estimates of overdispersion can potentially be influenced by a variety of factors, such as the clustering of data (neighborhood, regions, etc. ), unaccounted temporal correlation, and model miss-specification (Gourvieroux and Visser, 1997;Poormeta, 1999;Cameron and Trivedi, 1998). While model estimates of overdispersion can be attributed to these factors, Lord et al (2005b) argued that there is a fundamental explanation for overdispersion that can be shown by viewing crash data as the product of Bernoulli trials with an unequal probability of events (this is also known as Poisson trials).…”

Reproductive output of mosses under experimental warming on Fildes Peninsula, King George Island, maritime Antarctica

“…To determine the effect of species (Bartramia patens, Hennediella antarctica, and Polytrichastrum alpinum), treatment (OTC and control), site (La Cruz Plateau and Juan Carlos Point), and interactions among these effects on sporophyte production over 2 years, we used a generalized linear model with a Poisson distribution, using JMP [48], and post hoc tests, using Infostat [22]. We used Akaike Information Criterion (AIC) and overdispersion analysis to evaluate potential models and determine which interactions to include [27,42]. We used an ANOVA to determine the effects of treatment (OTC and control), species (H. antarctica and B. patens), and interactions between these factors on whole sporophyte length, capsule length, and seta length using Infostat [22].…”

The INARCH(1) Model for Overdispersed Time Series of Counts

“…Typical reasons for overdispersion are the presence of positive correlation between the monitored events (Friedman, 1993;Poortema, 1999;Paroli et al, 2000) or a variation in the probability of the monitored events (Heimann, 1996;Poortema, 1999;Christensen et al, 2003); further potential causes of overdispersion are discussed by (Jackson, 1972). …”