A Mixture-of-Experts model to deal with the rural/urban dichotomy in small area estimation

Abstract Small area estimation is a pivotal statistical methodology for generating reliable estimates of socio-economic indicators across small sub-populations. This research focuses on estimating the per capita wealth index in Bangladeshi upazilas, by integrating data from the Demographic and Health Survey with remote sensing covariates. The Fay–Herriot model, a prominent area-level model in small area literature, shows limitations when applied to our data. Notably, an exploratory analysis unveils two distinct regimes in the data-generating process, characterized by the rural/urban dichotomy. To tackle this issue, we extend the Fay–Herriot model through a Mixture-of-Experts, which classifies areas into groups within the estimation process. This enhances flexibility while preserving desirable properties, such as design consistency and interpretability of predictors. In addition, this family of models defines the mixing probabilities through a logistic regression, which proved to be particularly efficient in our applied setting, as demonstrated by a simulation study.