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A parametric model for heterogeneity in paired Poisson counts
Author(s) -
Goutis Constantinos,
Galbraith Rex F.
Publication year - 1996
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315334
Subject(s) - overdispersion , poisson distribution , negative binomial distribution , bivariate analysis , statistics , mathematics , quasi likelihood , count data , parametric model , poisson regression , parametric statistics , covariate , zero inflated model , wishart distribution , statistical physics , population , physics , multivariate statistics , demography , sociology
We present a model for data in the form of matched pairs of counts. Our work is motivated by a problem in fission‐track analysis, where the determination of a crystal's age is based on the ratio of counts of spontaneous and induced tracks. It is often reasonable to assume that the counts follow a Poisson distribution, but typically they are overdispersed and there exists a positive correlation between the numbers of spontaneous and induced tracks in the same crystal. We propose a model that allows for both overdispersion and correlation by assuming that the mean densities follow a bivariate Wishart distribution. Our model is quite general, having the usual negative‐binomial and Poisson models as special cases. We propose a maximum‐likelihood estimation method based on a stochastic implementation of the EM algorithm, and we derive the asymptotic standard errors of the parameter estimates. We illustrate the method with a data set of fission‐track counts in matched areas of zircon crystals.