Multivariate covariance generalized linear models

• Published in: Journal of the Royal Statistical Society Series C: Applied Statistics Vol. 65; no. 5; pp. 649 - 675
• Main Authors: Bonat, Wagner Hugo, Jørgensen, Bent
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.11.2016; John Wiley & Sons Ltd; Oxford University Press
• Subjects: Applied statistics; Counting; Covariance; Data analysis; Data processing; Generalized Kronecker product; Generalized linear models; Linear covariance model; Links; Mathematical models; Matrix linear predictor; Non-normal data; Pearson estimating function; Quasi-likelihood; Rain; Scoring; Spatiotemporal data; Statistics; Studies; Time series
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/rssc.12145

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. 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 response variables of mixed types, combined with repeated measures and longitudinal structures, and the third involves a spatiotemporal 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 models are fitted by 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 types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, spatial and spatiotemporal structures.