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Random forests and mixed effects random forests for small area estimation of general parameters: A poverty mapping case study in Mozambique

Krennmair, P.; Würz, N.; Schmid, T.; Tzavidis, N.

Abstract: The paper studies random forest and mixed effects random forest methods for the estimation of general small area parameters. To account for between-area heterogeneity, the proposed mixed effects random forest incorporates area-specific random effects and uses a new fitting algorithm with bootstrap bias correction for the random forest residual variance. General small area parameters are estimated through an area-specific distribution function, while uncertainty is assessed using a nonparametric block bootstrap. The methodology is applied to household consumption data from Mozambique to estimate district-level poverty indicators, including the head count ratio and poverty gap. Comparisons with model-based and direct estimators illustrate the benefits of incorporating random effects, the relevance of suitable data transformations, and the robustness of random forest-type methods. The results also emphasize that machine learning methods for small area estimation require careful statistical modelling rather than a purely black-box application.

Patrick Krennmair, Nora Würz, Timo Schmid & Nikos Tzavidis (2026): Random forests and mixed effects random forests for small area estimation of general parameters: A poverty mapping case study in Mozambique, The Annals of Applied Statistics, 20(1), 809–832. DOI: https://doi.org/10.1214/25-AOAS2126