Discrete Responses in Bivariate Generalized Additive Models

TL;DR

This paper introduces a flexible framework for analyzing bivariate discrete responses using penalized multivariate GLMs, incorporating non-parametric effects and copula-based distribution modeling, demonstrated with HIV prevalence data.

Contribution

It develops a novel, comprehensive approach for modeling bivariate discrete data with non-parametric and copula components, extending existing methods.

Findings

Framework effectively models dichotomous and ordinal responses.

Application to HIV data demonstrates practical utility.

Analytic derivations for Gaussian marginals provided.

Abstract

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.