A quasi F-test for functional linear models with functional covariates and its application to longitudinal data

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Functional linear models are essential for analyzing complex data structures, including longitudinal and functional response data.
• Existing methods may lack efficient procedures for hypothesis testing with functional covariates and outcomes.

Purpose of the Study:

• To propose a novel quasi F-test for functional linear models with functional covariates and outcomes.
• To develop efficient computational methods for p-value approximation and individual predictor testing.

Main Methods:

• Development of a quasi F-test tailored for functional linear models.
• Implementation of numerical procedures for p-value calculation and approximation.
• Application to a real-world longitudinal depression dataset with methamphetamine use as a predictor.

Main Results:

• The proposed quasi F-test provides a statistically sound method for hypothesis testing in functional linear models.
• Simulation studies demonstrate the test's appropriate size and power.
• The procedure is illustrated effectively on longitudinal depression data.

Conclusions:

• The quasi F-test offers a valuable tool for analyzing functional data, particularly in longitudinal studies.
• The method facilitates the testing of individual predictors within functional linear models.
• This approach enhances the analytical capabilities for complex datasets in various scientific fields.