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Modified tree-based selection in hierarchical mixed-effect models with trees: A simulation study and real-data

Asrirawan1,2, Khairil Anwar Notodiputro2, Budi Susetyo2

  • 1Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Sulawesi Barat, Indonesia.

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Summary
This summary is machine-generated.

Two new statistical models, 3Trees-EvTree and 3Trees-CTree, improve hierarchical mixed-effects modeling by reducing bias and enhancing prediction accuracy over existing 3Trees methods.

Keywords:
3Trees-EvTree and 3Trees-CTreeConditional inferenceEvolutionary learningHierarchical dataMachine learningRegression tree

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Area of Science:

  • Statistical Learning
  • Mixed-Effects Modeling
  • Computational Statistics

Background:

  • Hierarchical mixed-effects models (3Trees) use classification and regression trees (CART) but suffer from greedy algorithms leading to overfitting and biased splits.
  • Existing 3Trees methods can be suboptimal, impacting overall model performance in statistical learning.
  • Limitations in current 3Trees approaches necessitate the development of more robust and accurate methods.

Purpose of the Study:

  • To introduce two novel methods, 3Trees-EvTree and 3Trees-CTree, designed to overcome the limitations of existing 3Trees models.
  • To enhance prediction accuracy and reduce bias in hierarchical mixed-effects modeling.
  • To evaluate the performance of the proposed methods against established techniques using simulations and real-world data.

Main Methods:

  • Development of two new algorithms: 3Trees-EvTree and 3Trees-CTree, building upon the 3Trees framework.
  • Utilizing classification and regression trees (CART) with improved algorithms to mitigate overfitting and split selection bias.
  • Performance evaluation using Mean Squared Error (MSE), Clustered MSE (ClusMSE), Prediction MSE (PMSE), Clustered PMSE (ClusPMSE), and bias criteria.

Main Results:

  • The 3Trees-EvTree method demonstrated superior parameter estimation and prediction accuracy compared to previous methods, particularly under clusMSE and clusPMSE metrics.
  • The 3Trees-CTree model showed strong performance in low-correlation settings and for semilinear functions.
  • Both proposed methods confirmed their superiority over competing methods in real-world dataset applications, including household expenditure estimation.

Conclusions:

  • The novel 3Trees-EvTree and 3Trees-CTree models effectively address the limitations of traditional 3Trees approaches in hierarchical mixed-effects modeling.
  • These advanced methods offer improved prediction accuracy and reduced bias, leading to more reliable statistical inferences.
  • The findings suggest that 3Trees-EvTree and 3Trees-CTree represent significant advancements for statistical learning and mixed-effects modeling applications.