[ABE-L] Fwd: Lembrete: Seminário dia 02-08-2017 - Quarta-feira - 14 horas

[Clarice Garcia Borges Demetrio]

Segue a divulgação do Seminário que será ministrado pelo Prof. Dr. John
Hinde, no dia 02/08/2017, às 14 horas, no Departamento de Ciências Exatas,
ESALQ/USP.



*Over/Under-dispersion, zero-infation and Poisson-Tweedie models*
John Hinde1, Clarice Demétrio2 and Wagner Bonat3
1School of Mathematics, Statistics and Applied Mathematics, National
University
of Ireland, Galway, Ireland
2ESALQ/USP, Piracicaba, Brazil
3Paran a Federal University, Curitiba , Brazil
Email: john.hinde em nuigalway.ie

*Abstract*: The standard distributions for the analysis of count and
proportion data
are the Poisson and binomial distributions. Frequently, in practice they
are too
restrictive in that the variability in the data is either signi cantly
greater (overdis-
persed) or less (underdispersed) than that implied by the models variance
function.
For the analysis of count data, Nelder and McCullagh (1989) says that
overdisper-
sion is the norm and not the exception and this has been well studied, see
Hinde and
Demétrio (1999) and many subsequent articles presenting a wide range of
distribu-
tions. Although less common, underdispersion can arise, typically from
dependent
responses. For instance, when there is competition between plants and
animals this
can induce negative correlation in temporal and spatial counting processes.
Here we
will also consider how underdispersion can occur as a result of features of
the under-
lying counting, or data collection, process. The range of distributions for
modelling
underdispersed count data is relatively limited, although models can be
derived in
speci c situations.
A class of general models is presented based on Poisson-Tweedie factorial
dispersion
models with variance phi mu^p, where mu is the mean, phi and p are the
dispersion and
Tweedie power parameters, respectively. This class of models provides a
flexible and
comprehensive family including many standard discrete models. The family
provides
for modelling of overdispersed count data, including Neyman Type A,
Polya-Aeppli,
negative binomial, Poisson-inverse Gaussian and Hermite distributions, and
can
also accommodate zero-infation and underdispersion. For a general approach
we
consider an extended version of the Poisson-Tweedie model and discuss
estimation
of regression, dispersion and Tweedie power (variance function) parameters.
A full
description of the approach is given in Bonat et al. (2017).

References
Bonat, W., J rgensen, B, Kokonendji, C., Hinde, J. and Demétrio, C.G.B.
(2017)
Extended Poisson-Tweedie: properties and regression models for count data.
Statistical Modelling
(accepted)

Hinde, J. and Demétrio, C.G.B. (1998) Overdispersion: Models and
estimation.
Computational Statistics and Data Analysis. 27, 151{170.

McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. Chapman
and
Hall.








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