  A conceptual framework for the analysis of dichotomous and ordinal
polychotomous responses within a penalized multivariate Generalized Linear
Model is introduced. The proposed structure allows for a rather flexible
predictor specification through the inclusion of non-parametric and spatial
covariate effects, and the characterisation of the distribution of the
stochastic model components with copulae of univariate marginals. Analytic
derivations for the particular case of Gaussian marginals within a bivariate
system of dichotomous outcomes are also provided, and the framework is
subsequently illustrated through the estimation of the HIV prevalence in Zambia
using the 2007 DHS dataset.
