Title: Copula-based Multivariate Regression Models with gamlss Marginals
Abstract: Copulas provide a flexible way to model multivariate outcomes by decomposing information from their joint distribution into that from its marginal distributions and that of the chosen copula function which defines the dependence structure between the marginals. In the conditional case, copulas can include vectors of covariates for both the marginal distributions and the dependence parameters related to the copula function. Estimation is usually carried out by maximum likelihood methods.
Often the marginals require characteristics different to the multivariate normal case. In such cases the class of models within the gamlss family of generalised additive models for location, scale and shape distributions provides a wide range of alternatives including 3- and 4-parameter probability models accommodating asymmetric and leptokurtic or platykurtic patterns. Appropriate link functions can be specified with different linear predictors on each marginal’s covariates.
In this talk the possibilities of embedding gamlss marginals in copula-based multivariate regression models will be discussed. Two examples will be presented, on modelling bivariate refractive error data, and on modelling dates of birth and dates in cases of sudden infant death syndrome.