Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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Multivariate Covariance Generalized Linear Models

par ULRICH Michaël - publié le

Vendredi 20 février : Wagner Hugo Bonnat

(University of Southern Denmark & Universidade Federal do Paraná)

Multivariate Covariance Generalized Linear Models

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLM), designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a generalized Kronecker product. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves outcomes of mixed types, combined with longitudinal data and repeated measures, and the third involves a spatio-temporal analysis of rainfall data. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modelled by means of a link function and a linear predictor. The covariance structure is modelled by means of a covariance link function combined with a matrix linear predictor involving known matrices. The models are fitted using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal and spatial data, and spatio-temporal data.