Model selection in multivariate adaptive regressions splines (MARS) using alternative information criteria.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Multivariate Adaptive Regression Splines (MARS) is a non-parametric method for high-dimensional data analysis.
• MARS excels at modeling complex, non-linear relationships without prior assumptions.
• Generalized Cross-Validation (GCV) is commonly used in MARS for model selection but faces criticism regarding smoothing parameters and model dimensionality.

Purpose of the Study:

• To address criticisms of GCV in MARS by exploring alternative information criteria.
• To identify the most effective information criterion for parsimonious model selection.
• To evaluate the performance of AIC, SBC, and ICss against GCV in MARS.

Main Methods:

• A simulation study was conducted using datasets with relevant and irrelevant variables.
• MARS was applied with GCV and alternative information criteria (AIC, SBC, ICss).
• A real-world dataset on loan defaults in Türkiye (2005-2019) was analyzed.

Main Results:

• The simulation study demonstrated the success of information criteria in selecting relevant variables.
• The ICss criterion was particularly effective in achieving parsimonious model selection.
• Analysis of loan default data confirmed the effectiveness of the ICss criterion.

Conclusions:

• Information criteria offer a viable alternative to GCV for MARS model selection.
• The ICss criterion provides a more parsimonious and effective approach to model building.
• This enhanced MARS framework improves the interpretability and efficiency of analyzing high-dimensional datasets.