Colombian Women's Life Patterns: A Multivariate Density Regression Approach
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Women in Latin America and the Caribbean face difficulties related to the patriarchal traits of their societies. In Colombia, the well-known conflict afflicting the country since 1948 has increased the risk for vulnerable groups. It is important to determine if recent efforts to improve the welfare of women have had a positive effect extending beyond the capital, Bogota. In an initial endeavor to shed light on this matter, we analyze cross-sectional data arising from the Demographic and Health Survey Program. 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 capture nonlinear regression functions and allow for 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. It can also accommodate censoring in one or more of the responses. 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.
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