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Updated: Sep 27, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Comparing methods for statistical inference with model uncertainty.

Anupreet Porwal¹, Adrian E Raftery^1,2

¹Department of Statistics, University of Washington, Seattle, WA 98195.

Proceedings of the National Academy of Sciences of the United States of America

|April 12, 2022

Summary

This summary is machine-generated.

Three adaptive Bayesian model averaging methods best handle linear regression model uncertainty. These adaptive Bayesian model averaging (BMA) approaches outperformed other methods in simulations, offering efficient variable selection.

Keywords:

Bayesian model averaging LASSO interval estimation model selection parameter estimation

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Area of Science:

Statistics
Computational Statistics
Data Science

Background:

Statistical models are crucial for tasks like parameter estimation and prediction.
Selecting the appropriate statistical model, especially for variable inclusion in linear regression, is a key challenge.
Existing methods for model selection, including Bayesian and penalized likelihood approaches, lack clear guidance on optimal usage.

Purpose of the Study:

To compare the performance of 21 popular variable selection methods for linear regression models.
To identify the most effective methods across various statistical tasks and practical data analysis scenarios.
To evaluate the computational efficiency and performance of top-performing Bayesian model averaging (BMA) methods.

Main Methods:

Conducted extensive simulation studies using real datasets to mimic practical data analysis situations.
Compared 21 popular variable selection methods, focusing on Bayesian and penalized likelihood techniques.
Implemented adaptive Bayesian model averaging (BMA) methods using Markov chain Monte Carlo (MCMC) with 10,000 iterations.

Main Results:

Three adaptive BMA methods, utilizing adaptive versions of Zellner’s g-prior, demonstrated superior performance across all evaluated statistical tasks.
Adaptive BMA methods with g dependent on sample size or estimated from data were most effective.
Two adaptive BMA methods (BMA with g=√n and empirical Bayes-local) showed computational competitiveness with the least absolute shrinkage and selection operator (LASSO).

Conclusions:

Adaptive Bayesian model averaging (BMA) methods are highly recommended for variable selection in linear regression.
These BMA approaches offer robust performance and computational efficiency, often surpassing traditional Bayesian model selection.
The findings provide practical guidance for researchers on choosing and implementing effective statistical modeling techniques.