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Research on Poisson regression analysis for dependent data has been developedrapidly in the last decade. One of difficult problems in a multivariate case ishow to construct a cross-correlation structure and at the meantime make surethat the covariance matrix is positive definite. To address the issue, wepropose to use convolved Gaussian process (CGP) in this paper. The approachprovides a semi-parametric model and offers a natural framework for modelingcommon mean structure and covariance structure simultaneously. The CGP enablesthe model to define different covariance structure for each component of theresponse variables. This flexibility ensures the model to cope with data comingfrom different resources or having different data structures, and thus toprovide accurate estimation and prediction. In addition, the model is able toaccommodate large-dimensional covariates. The definition of the model, theinference and the implementation, as well as its asymptotic properties, arediscussed. Comprehensive numerical examples with both simulation studies andreal data are presented.

Regression Analysis for Multivariate Dependent Count Data Using Convolved Gaussian Processes