Variable selection in linear mixed model meta-regression with suspected interaction effects -- How can tree-based methods help?

2026-03-06

AI Summary

Detecting interaction effects in meta-regression is often hindered by small sample sizes, high-dimensional candidate moderators, and the need for model interpretability. This study integrates linear approaches with tree-based methods—including fixed- and random-effects meta-CART and their stability selection variants—to enhance adaptability to nonlinear interactions while preserving interpretability. The performance of these methods is systematically evaluated across diverse interaction structures. Results indicate that linear methods based on hypothesis tests and information criteria outperform others under strictly linear interactions. In contrast, stability-selected tree-based methods—particularly the fixed-effects variant—demonstrate superior robustness in nonlinear or near-nonlinear settings, making them well-suited as complementary tools for preliminary screening and sensitivity analysis.

Technology Category

• Machine Learning: Ensemble Methods
• Search and Optimization: Metareasoning and Metaheuristics
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Detecting interaction effects (IEs) in meta-regression is challenging, especially when few studies are available and many plausible interactions are considered. In many meta-analyses, interpretability is essential, which limits the use of complex machine learning methods. Tree-based approaches offer a potentially useful compromise, but their role in meta-regression with random effects is not yet well understood. This paper examines how traditional linear and tree-based methods can support variable selection for IEs in random effects meta-regression. We compare test-based and information-criterion-based linear selection procedures with meta-CART approaches. These include fixed effect and random effects trees and their stability-selected ensemble variants. All methods are evaluated using a real-world meta-analytic dataset and a plasmode simulation study. The data-generating process assumes linear IEs and is complemented by settings with nonlinear interactions. Our results show that under strictly linear interactions, linear selection methods perform as expected and achieve superior performance for IE detection. Tree-based methods are more conservative when the number of studies is small, but become competitive as sample size increases, particularly the stability-selected variants. When IEs deviate from strict linearity, even in simple ways, the performance of linear methods deteriorates, whereas tree-based approaches, especially stability-selected fixed effect trees, provide a more robust alternative. Overall, stability-selected random effects trees are useful complementary tools for IE detection in applied meta-regression, particularly for metric covariates. They are well suited for pre-selection and sensitivity analyses, and selection frequency patterns in tree ensembles can help reveal structural patterns in the data.

Problem

• meta-regression
• interaction effects
• variable selection
• linear mixed model
• tree-based methods

Innovation

• meta-regression
• interaction effects
• tree-based methods
• stability selection
• variable selection