Multivariate Covariance Generalized Linear Models for the Analysis of Experimental Data

Wagner Hugo Bonat
wbonat at
Departamento de Estatística - UFPR
Walmes Marques Zeviani
walmes at
Departamento de Estatística - UFPR


The design and analysis of experiments have a prominent role in science and analysis of variance (ANOVA) methods have been the workhorse for analysis of such data for decades. Despite of the flexibility of the ANOVA framework in terms of experimental design, in general the models in this class deal only with a single independent Gaussian variable at once. In many experiments more than one response is of interest for the experimenter. A natural extension of the ANOVA methods for multivariate Gaussian data is the multivariate analysis of variance (MANOVA). However, the extension of MANOVA methods for non-Gaussian data is not thoroughly discussed in the literature.

The main goal of this course is to discuss the analysis of multivariate experimental data based on the recently proposed multivariate covariance generalized linear models (McGLM) framework (Bonat and Jørgensen; 2016)1. This class of models can deal with multiple non-Gaussian response variables and can easily be adapted to deal with the most commons types of experimental designs, including multilevel and longitudinal designs and correlated responses. McGLMs can be seen as a extension of the MANOVA approach for the analysis of non-Gaussian data.

We present the model specification along with strategies for model fitting and the associated R code. Through study cases, we shall discuss the benefits, drawbacks and cautions when using McGLMs. The R package mcglm (Bonat and Jørgensen; 2016) is presented and supplementary material as R (R Core Team; 2015)2 code and data sets will be made available for the students.

Key-words: multivariate response, generalized estimating equations, Poisson-Tweedie, count data.


  1. Bonat, W. H. and Jørgensen, B. (2016). Multivariate covariance generalized linear models, Journal of the Royal Statistical Society: Series C (Applied Statistics). to appear.

  2. R Core Team (2015). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.