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Flexible domain prediction using mixed effects random forests

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  • Patrick Krennmair
  • Timo Schmid

Abstract

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.

Suggested Citation

  • Patrick Krennmair & Timo Schmid, 2022. "Flexible domain prediction using mixed effects random forests," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1865-1894, November.
  • Handle: RePEc:bla:jorssc:v:71:y:2022:i:5:p:1865-1894
    DOI: 10.1111/rssc.12600
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    References listed on IDEAS

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    1. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
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    7. Hajjem, Ahlem & Bellavance, François & Larocque, Denis, 2011. "Mixed effects regression trees for clustered data," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 451-459, April.
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    9. Monique Graf & J. Miguel Marín & Isabel Molina, 2019. "A generalized mixed model for skewed distributions applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 565-597, June.
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    Cited by:

    1. Karina Acosta & Juliana Jaramillo-Echeverri & Daniel Lasso & Alejandro Sarasti-Sierra, 2024. "Informalidad municipal en Colombia," Documentos de trabajo sobre Economía Regional y Urbana 327, Banco de la Republica de Colombia.
    2. Tomasz .Zk{a}d{l}o & Adam Chwila, 2024. "A step towards the integration of machine learning and small area estimation," Papers 2402.07521, arXiv.org.

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