Flexible domain prediction using mixed effects random forests

This paper promotes the use of random forests as versatile tools for estimating spatially disaggregated indicators in the presence of small area‐specific sample sizes. Small area estimators are predominantly conceptualised within the regression‐setting and rely on linear mixed models to account for the hierarchical structure of the survey data. In contrast, machine learning methods offer non‐linear and non‐parametric alternatives, combining excellent predictive performance and a reduced risk of model‐misspecification. Mixed effects random forests combine advantages of regression forests with the ability to model hierarchical dependencies. This paper provides a coherent framework based on mixed effects random forests for estimating small area averages and proposes a non‐parametric bootstrap estimator for assessing the uncertainty of the estimates. We illustrate advantages of our proposed methodology using Mexican income‐data from the state Nuevo León. Finally, the methodology is evaluated in model‐based and design‐based simulations comparing the proposed methodology to traditional regression‐based approaches for estimating small area averages.