Mapping Well-Being Through a Mixture-of-Experts Fay-Herriot Model

Our research is motivated by estimation of the per capita wealth index in Bangladeshi upazilas, integrating data from the Demographic and Health Survey along with remote sensing covariates, in a small area estimation framework. The popular Fay-Herriot model shows relevant limitations when applied to our data, as it fails to manage adequately two (or more) distinct regimes in the data generating process, such as those implied by the rural/urban divide that characterizes many low and middle income countries. We extend the Fay-Herriot model through a Mixture-of-Experts, where areas are classified into groups within the estimation process. This adds flexibility while keeping relevant properties of the predictors such as design consistency and easy interpretation. In addition, this family of models defines the mixing probabilities through a logistic regression, turning out to be particularly convenient in the applied setting.