Bayesian Nonparametric Conditional Copula Estimation of Twin Data

TL;DR

This paper introduces a Bayesian nonparametric method using conditional copulas to analyze how socioeconomic status influences the dependence between twins' cognitive abilities, revealing environmental impacts vary with socio-economic levels.

Contribution

It extends existing copula models by incorporating covariate dependence in an infinite mixture framework, offering flexible estimation of conditional copulas.

Findings

Environmental factors are more influential in lower socio-economic families.

The proposed method accurately models the dependence structure conditioned on covariates.

The approach extends previous models to handle complex, covariate-dependent dependence patterns.

Abstract

Several studies on heritability in twins aim at understanding the different contribution of environmental and genetic factors to specific traits. Considering the National Merit Twin Study, our purpose is to correctly analyse the influence of the socioeconomic status on the relationship between twins' cognitive abilities. Our methodology is based on conditional copulas, which allow us to model the effect of a covariate driving the strength of dependence between the main variables. We propose a flexible Bayesian nonparametric approach for the estimation of conditional copulas, which can model any conditional copula density. Our methodology extends the work of Wu et al (2015) by introducing dependence from a covariate in an infinite mixture model. Our results suggest that environmental factors are more influential in families with lower socio-economic position.