Statistical Modelling 3 (2003), 99–108
Likelihood-based analysis of longitudinal count data using a
generalized Poisson model
P.J. Toscas
CSIRO Mathematical and Information Sciences,
P.O. Box 120,
Cleveland, QLD 4163,
Australia
eMail: peter.tosca@csiro.au
M.J. Faddy
School of Mathematics and Statistics,
University of Birmingham,
Birmingham, UK.
Abstract:
Models based on a generalization of the simple Poisson process
are discussed and illustrated with an analysis of some longitudinal
count data on frequencies of epileptic fits. The models enable a
broad class of discrete distributions to be constructed, which
cover a variety of dispersion properties that can be characterized
in an intuitive and appealing way by a simple parameterization. This
class includes the Poisson and negative binomial distributions as
well as other distributions with greater dispersion than Poisson,
and also distributions underdispersed relative to the Poisson
distribution. Comparing a number of analyses of the data shows
that some covariates have a more significant effect using this
modelling than from using mixed Poisson models. It is argued that
this could be due to the mixed Poisson models used in the other
analyses not providing an appropriate description of the residual
variation, with the greater flexibility of the generalized Poisson
modelling generally enabling more critical assessment of covariate
effects than more standard mixed Poisson modelling.
Keywords:
LONGITUDINAL DATA; NEGATIVE BINOMIAL DISTRIBUTION; OVERDISPERSION;
POISSON DISTRIBUTION; TRANSITION MODELS; UNDERDISPERSION.
Downloads:
MATLAB code and data file in zipped archive
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