  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.
