Multivariate Poisson regression with covariance structure |
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Authors: | Email author" target="_blank">Dimitris?KarlisEmail author Loukia?Meligkotsidou |
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Institution: | (1) Department of Statistics, Athens University of Economics and Business, 76, Patission Str., 10434 Athens, Greece;(2) Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom |
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Abstract: | In recent years the applications of multivariate Poisson models have increased, mainly because of the gradual increase in
computer performance. The multivariate Poisson model used in practice is based on a common covariance term for all the pairs
of variables. This is rather restrictive and does not allow for modelling the covariance structure of the data in a flexible
way. In this paper we propose inference for a multivariate Poisson model with larger structure, i.e. different covariance
for each pair of variables. Maximum likelihood estimation, as well as Bayesian estimation methods are proposed. Both are based
on a data augmentation scheme that reflects the multivariate reduction derivation of the joint probability function. In order
to enlarge the applicability of the model we allow for covariates in the specification of both the mean and the covariance
parameters. Extension to models with complete structure with many multi-way covariance terms is discussed. The method is demonstrated
by analyzing a real life data set. |
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Keywords: | data augmentation EM algorithm Markov chain Monte Carlo multivariate reduction crime data |
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