Seminário
Conjunto ICMC/UFSCar ? 11/11/2011 - 14h00
LOCAL: Sala 5101 do
ICMC-USP
TITLE: An Extended Random-effects Approach to Modeling Repeated,
Overdispersed Count Data
SPEAKER: Profa. Dra. Clarice
G. B. Demétrio ? ESALQ-USP
ABSTRACT: 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.
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