Multivariate Generalised Linear Mixed Models and Some Extensions

Rodrigo Labouriau, Applied Statistics Laboratory, Department of Mathematics, Aarhus University

In this talk I will present some extensions of the classic generalised linear models generalised that allow flexible representations of multivariate data. The models discussed can represent multivariate scenarios where the different dimensions are modelled by different distributions and different link functions. For example, in one of the cases presented the three-dimensional response is composed of size measurements; counts and proportions are modelled by a gamma, a Poisson and a binomial distribution. The multivariate generalised linear models discussed allow specifying a common structure connecting the several dimensions of the model via random components. For instance, in the example referred above the structure of random components are used to represent and quantity common and specific genetic components. Examples of different nature will be presented including relatively large data sets (several millions of observations), complex data sets (gene expression data involving transcription levels of more than 50,000 genes and information on deep pedigrees) and incompletely observed data (complex multivariate versions of the Cox proportional model with discrete time).