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Multivariate Covariance Generalized Linear Models with applications in R

Wagner Hugo Bonat
(Universidade Federal do Paran√° (UFPR))
Seminar
Tuesday, 2 April, 2019, at 13:15-14:00, in Koll. D (1531-211)
Abstract:
In this talk I will present a recent proposed framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), 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 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. McGLMs provide 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. Furthermore, we present the computational implementation in R through the package mcglm. Illustrations include mixed models, longitudinal data analysis, spatial models for areal data, models to deal with mixed outcomes and multivariate models for count data using the Poisson-Tweedie distribution.

 

Contact person: Rodrigo Labouriau