Bayesian semiparametric modelling of contraceptive behavior in India via sequential logistic regressions

Family planning has been characterized by highly different strategic programs in India, including method-specific contraceptive targets, coercive sterilization, and more recent target-free approaches. These major changes in family planning policies over time have motivated a considerable interest towards assessing the effectiveness of the different planning programs. Current studies mainly focus on the factors driving the choice among specific subsets of contraceptives, such as the preference for alternative methods other than sterilization. Although this restricted focus produces key insights, it fails to provide a global overview of the different policies, and of the determinants underlying the choices from the entire range of contraceptive methods. Motivated by this consideration, we propose a Bayesian semiparametric model relying on a reparameterization of the multinomial probability mass function via a set of conditional Bernoulli choices. This binary decision tree is defined to be consistent with the current family planning policies in India, and coherent with a reasonable process characterizing the choice among increasingly nested subsets of contraceptive methods. The model allows a subset of covariates to enter the predictor via Bayesian penalized splines and exploits mixture models to flexibly represent uncertainty in the distribution of the State-specific random effects. This combination of flexible and careful reparameterizations allows a broader and interpretable overview of the policies and contraceptive preferences in India.