Regression with empirical variable selection: description of a new method and application to ecological datasets

Area of Science:

• Ecology
• Environmental Science
• Statistical Modeling

Background:

• Full-model and stepwise regression are widely used but problematic in ecological studies.
• Alternative methods like Akaike's Information Criterion (AIC) present challenges with numerous variables.
• Difficulty in interpreting competing models with diverse variable combinations hinders progress.

Purpose of the Study:

• Introduce Regression with Empirical Variable Selection (REVS) as an improved statistical approach.
• Quantify empirical support for each independent variable using all-subsets regression.
• Simplify post-hoc model comparison for complex ecological datasets.

Main Methods:

• REVS utilizes all-subsets regression to rank independent variables by empirical support.
• A series of models are generated sequentially, adding the next most-supported variable.
• The number of models generated equals the number of predictor variables, facilitating comparison.

Main Results:

• The optimal REVS model demonstrated higher R(2), lower AIC, and greater significance (P values) than traditional methods.
• REVS models showed improved predictive accuracy via split-sample validation.
• Across ten additional datasets, REVS consistently yielded higher R(2) values compared to full and stepwise models.

Conclusions:

• REVS is a valuable tool for analyzing complex ecological and environmental data.
• The method provides ecologically intuitive results, identifying core variables.
• REVS offers a more efficient and accurate alternative to conventional regression techniques.