Subsampling versus bootstrapping in resampling-based model selection for multivariable regression.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Multivariable regression models require stability assessment to ensure resistance to minor data fluctuations.
• Resampling techniques, particularly the bootstrap, are commonly used to evaluate model stability and variable importance.
• Potential limitations of the bootstrap have prompted interest in alternative methods like subsampling.

Purpose of the Study:

• To empirically compare the bootstrap and subsampling techniques for assessing multivariable regression model stability.
• To investigate the impact of these resampling methods on classical variable selection procedures.
• To evaluate model selection and variable inclusion frequencies derived from both techniques.

Main Methods:

• Implementation of variable selection procedures (e.g., backward elimination) on bootstrap and subsample datasets.
• Calculation of model selection frequencies and variable inclusion frequencies for each resampling method.
• Empirical comparison through analysis of two real-world datasets and a comprehensive simulation study.

Main Results:

• Subsampling demonstrated advantages over the bootstrap in the context of multivariable regression model stability assessment.
• Variable inclusion frequencies derived from subsampling provided robust insights into variable importance and model reliability.
• The study identified specific scenarios where subsampling outperforms the bootstrap in maintaining model integrity.

Conclusions:

• Subsampling is a viable and potentially superior alternative to the bootstrap for enhancing the stability analysis of regression models.
• The findings support the adoption of subsampling for more reliable variable selection and model evaluation in statistical modeling.
• Further research into subsampling's application across diverse regression techniques is warranted.