Variable Selection in Function-on-Scalar Regression.

Area of Science:

• Statistics
• Functional Data Analysis
• Machine Learning

Background:

• Function-on-scalar regression models often involve numerous predictors, posing challenges for variable selection.
• Existing methods for these models typically do not address the correlation structure within residual curves.

Purpose of the Study:

• To develop a novel variable selection technique for function-on-scalar models that accounts for residual curve correlations.
• To enhance the accuracy and interpretability of regression models with functional responses.

Main Methods:

• Representing coefficient functions using B-spline bases to transform the problem into multivariate regression.
• Employing group-minimax concave penalty (MCP) for effective variable selection.
• Adapting generalized least squares for residual covariance by pre-whitening and developing an iterative algorithm for coefficient and covariance updates.

Main Results:

• The proposed iterative algorithm demonstrates performance comparable to pre-whitening with true covariance.
• The method significantly outperforms approaches that ignore the covariance structure of residuals.
• Application to stroke severity and motor control data yielded lower prediction errors compared to existing methods.

Conclusions:

• The developed method offers a robust approach to variable selection in function-on-scalar models, particularly when residual curves are correlated.
• This technique enhances predictive performance and provides a more accurate understanding of predictor effects in functional data.
• The findings have implications for analyzing complex biological and biomechanical data, such as motor control studies.