Modeling motor learning using heteroskedastic functional principal components analysis.

Area of Science:

• Statistics
• Functional Data Analysis
• Biostatistics

Background:

• Functional data analysis is crucial for understanding complex, time-varying measurements.
• Existing methods often focus on the mean of functional data, overlooking sources of variability.
• Understanding variability is key to identifying factors influencing data patterns, such as skill acquisition.

Purpose of the Study:

• To develop a novel statistical framework for estimating covariate effects on functional data variability.
• To extend functional principal components analysis (FPCA) by modeling the variance of principal component scores.
• To investigate factors influencing the variability in functional data, including subject-specific effects.

Main Methods:

• Proposed a novel method extending the functional principal components analysis (FPCA) framework.
• Modeled the variance of principal component scores as a function of covariates and subject-specific random effects.
• Applied the method to a dataset assessing upper extremity motor control to quantify changes in motion variance.

Main Results:

• The developed method effectively estimates population-level and subject-specific effects on functional data variability.
• Modeling the variance of principal component scores proved flexible and interpretable when principal components are largely invariant.
• Quantified a significant reduction in motion variance associated with skill learning in motor control tasks.

Conclusions:

• The novel FPCA-based approach provides a powerful tool for analyzing variability in functional data.
• This method offers interpretable insights into how covariates and individual differences impact data variation.
• The findings demonstrate the utility of the method in quantifying performance improvements through reduced variability, as seen in skill learning.