[ABE-L] Seminario DE-IMECC-UNICAMP

[Ronaldo Dias]

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dia 20/02/2020 as 14:00 na sala 221, IMECC-UNICAMP


*An Extended Random-effects Approach to Modeling Repeated, Overdispersed
Count Data*

*Clarice G.B. Demétrio*1, Geert Molenberghs2, Geert Verbeke3

*1**Departmeno de Ciências Exatas, ESALQ/USP, São Paulo, Brazil*

*2**Center for Statistics, Hasselt University, Diepenbeek, Belgium*

*3**Biostatistical Centre, Katholieke Universiteit Leuven, Leuven, Belgium*


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, Molenberghs et al, 2010, *Statistical Science, *
25: 325–347, Vangeneugden et al, 2011, *Journal of Applied Statistics*, 38:
215-232). 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.





-- 
Ronaldo Dias, Ph.D.
Professor
Dept. of Statistics-IMECC, UNICAMP
www.ime.unicamp.br/~dias
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