Statistics and Computing

, Volume 15, Issue 4, pp 255–265

Multivariate Poisson regression with covariance structure

Authors

    • Department of StatisticsAthens University of Economics and Business
  • Loukia Meligkotsidou
    • Department of Mathematics and StatisticsLancaster University
Article

DOI: 10.1007/s11222-005-4069-4

Cite this article as:
Karlis, D. & Meligkotsidou, L. Stat Comput (2005) 15: 255. doi:10.1007/s11222-005-4069-4

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.

Keywords

data augmentationEM algorithmMarkov chain Monte Carlomultivariate reductioncrime data

Copyright information

© Springer Science + Business Media, Inc. 2005