Bayesian nonparametric modeling of contraceptive use in India

In analyzing demographic data it is important to flexibly model the relation between a variable of interest and a set of covariates. Most of the literature traditionally focuses on generalized linear models or generalized linear mixed models, with normally distributed random effects accounting for the hierarchical data structure. Inappropriately assuming the random effects to be normally distributed and restricting the predictor to evolve according to some parametric functional form can have a major impact on the quality of inferences, with biased estimates and mis-calibration of predictive intervals. Spurred by the attempt to flexibly study the determinants of contraceptive use in India, we propose a hierarchical Bayesian nonparametric model for analyzing binary responses. The model allows a subset of covariates to enter the predictor through a nonparametric specification via Gaussian process (GP) priors and exploits the Dirichlet process (DP) formulation to flexibly represent uncertainty in the distribution of the State-specific random intercepts. Employing the P\`olya-Gamma data augmentation, we develop an efficient Gibbs sampler. We illustrate performance via simulations, and apply the model to explore the determinants of contraceptive use in India.