  Women in Colombia face difficulties related to the patriarchal traits of
their societies and well-known conflict afflicting the country since 1948. In
this critical context, our aim is to study the relationship between baseline
socio-demographic factors and variables associated to fertility, partnership
patterns, and work activity. To best exploit the explanatory structure, we
propose a Bayesian multivariate density regression model, which can accommodate
mixed responses with censored, constrained, and binary traits. The flexible
nature of the models allows for nonlinear regression functions and non-standard
features in the errors, such as asymmetry or multi-modality. The model has
interpretable covariate-dependent weights constructed through normalization,
allowing for combinations of categorical and continuous covariates.
Computational difficulties for inference are overcome through an adaptive
truncation algorithm combining adaptive Metropolis-Hastings and sequential
Monte Carlo to create a sequence of automatically truncated posterior mixtures.
For our study on Colombian women's life patterns, a variety of quantities are
visualised and described, and in particular, our findings highlight the
detrimental impact of family violence on women's choices and behaviors.
