Flexible Domain Prediction using Mixed Effects Random Forests

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.

Small Area Estimation of Poverty and Wealth Using Geospatial Data: What have We Learned So Far?

“…[62] The second obstacle was the lack of an accepted method for uncertainty estimation. Although Athey et al [62] developed methods to estimate uncertainty for boosted regression forests, the random effect residual bootstrap developed by Chambers and Chandra [59] and first applied by Krennmair and Schmid [29] is also an attractive and simple option that appears to work well for wealth prediction using extreme gradient boosting in multiple contexts. [18] While the potential of regularly pairing survey data with geospatial data is clear, more work on research and tools is needed to further instil confidence in the estimates and facilitate use.…”

Trait–growth relationships in Colombian tropical dry forests: Incorporating intraspecific variation and trait interactions

“…This type of model allows us to account for potential nonlinear relationships as well as interactions among predictors, and has been successfully used to analyze similar questions (Pistón et al., 2019; Kamimura et al., 2023). We generated a set of models using mixed‐effect RF with the SAEforest package in R (R Core Team, R Foundation for Statistical Computing, Vienna, AT) (Krennmair, 2022), specifying the species as a random intercept and individual relative growth as the response variable. The modeling framework is reported in Figure 1.…”

“…We generated a set of models using mixed-effect RF with the SAEforest package in R (R Core Team, R Foundation for Statistical Computing, Vienna, AT) (Krennmair, 2022) the impact of the different shortcomings that are typical in analyses of trait-performance relationships, we simulated a set of alternative modeling decisions:…”

Untitled

“…Opsomer et al (2008) proposed penalized spline regression models. Recently, Krennmair and Schmid (2022) have used machine learning methods; in particular, mixed-effects random forests, for SAE.…”