## 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).