Best Practices for Developing Linear Models With Multiple Explanatory Variables.

Area of Science:

• Statistics
• Computational Biology
• Data Science

Background:

• Linear models are fundamental statistical tools, but advanced methods are needed for large datasets.
• Handling numerous explanatory variables with moderate sample sizes presents unique challenges.
• Classic literature often overlooks crucial elements like two-way interactions and quadratic terms.

Purpose of the Study:

• To provide best practices for linear model selection with many predictors and moderate sample sizes.
• To highlight the importance of interaction and quadratic terms in linear modeling.
• To present a systematic approach for developing reliable linear models, including R code.

Main Methods:

• Variable screening using random forest.
• Subset selection techniques like stepwise regression.
• Model selection criteria (AIC, BIC, adjusted R², Mallows' Cp) and cross-validation.
• Shrinkage methods (lasso, ridge regression) and dimension reduction (PCR, PLS).

Main Results:

• Random forest is effective for initial variable screening in high-dimensional data.
• Shrinkage and dimension reduction techniques enhance model fitting and management.
• A systematic approach combining various methods leads to robust linear model development.

Conclusions:

• Best practices for linear model selection involve considering interactions and using advanced techniques.
• Random forest, stepwise regression, shrinkage, and dimension reduction are key tools.
• The provided R code facilitates a systematic approach to building effective linear models.