Seminários de Estatística - ICMC/UFSCar - 11/11/2011

["Marinho G Andrade" <marinho@icmc.usp.br>]

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Seminários de Estatística - ICMC/UFSCar
"An Extended Random-effects Approach to Modeling Repeated, Overdispersed
Count Data"

Palestrante: Clarice G.B. Demétrio

Data: 11/11/2011
Hora: 14:00
Local: Sala 5101

Público: alunos, docentes e demais interessados

Resumo: Non-Gaussian outcomes are often modeled using members of the
so-called exponential family. The Poisson model for count data falls
within this tradition. The family in general, and the Poisson model in
particular, are at the same time convenient since mathematically elegant,
but in need of extension since often somewhat restrictive. Two of the main
rationales for existing extensions are (1) the occurrence of
overdispersion (Hinde and Demétrio 1998, Computational Statistics and Data
Analysis 27, 151-170), in the sense that the variability in the data is
not adequately captured by the model's prescribed mean-variance link, and
(2) the accommodation of data hierarchies owing to, for example,
repeatedly measuring the outcome on the same subject (Molenberghs and
Verbeke 2005, Models for Discrete Longitudinal Data, Springer), recording
information from various members of the same family, etc. There is a
variety of overdispersion models for count data, such as, for example, the
negative-binomial model. Hierarchies are often accommodated through the
inclusion of subject-specific, random effects. Though not always, one
conventionally assumes such random effects to be normally distributed.
While both of these issues may occur simultaneously, models accommodating
them at once are less than common.

This paper proposes a generalized linear model, accommodating
overdispersion and clustering through two separate sets of random effects,
of gamma and normal type, respectively ( Molenberghs, Verbeke and Demétrio
2007, LIDA, 13, 513-531). This is in line with the proposal by Booth,
Casella, Friedl and Hobert (2003, Statistical Modelling 3, 179-181). The
model extends both classical overdispersion models for count data (Breslow
1984, Applied Statistics 33, 38-44), in particular the negative binomial
model, as well as the generalized linear mixed model (Breslow and Clayton
1993, JASA 88, 9-25).

Apart from model formulation, we briefly discuss several estimation
options, and then settle for maximum likelihood estimation with both fully
analytic integration as well as hybrid between analytic and numerical
integration. The latter is implemented in the SAS procedure NLMIXED. The
methodology is applied to data from a study in epileptic seizures.



-- 
Marinho G. Andrade
Departamento de Matemática Aplicada e Estatística
Instituto de Ciências Matemáticas e de Computação
Universidade de São Paulo - Campus de São Carlos
C.P. 668, CEP 13560-970, São Carlos, SP

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