Functional quantile principal component analysis.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Traditional functional principal components analysis (FPCA) focuses on average data curves, potentially missing individual variations.
• Participant-specific quantile curves are crucial for understanding diverse behaviors, especially in fields like physical activity monitoring.
• Existing methods may struggle with outliers, heteroscedasticity, or skewed data common in real-world datasets.

Purpose of the Study:

• To introduce Functional Quantile Principal Component Analysis (FQPCA), a novel dimensionality reduction technique.
• To extend FPCA by enabling the examination of participant-specific quantile curves.
• To develop a robust methodology capable of capturing shifts in data scale and distribution across participants.

Main Methods:

• FQPCA borrows strength across participants to estimate underlying quantile patterns.
• Participant-level data is used to estimate loadings on these estimated quantile patterns.
• The method is applied to analyze physical activity data, specifically accelerometer data from NHANES.

Main Results:

• FQPCA successfully captures shifts in scale and distribution affecting individual quantile curves.
• The methodology demonstrates robustness against outliers, heteroscedasticity, and skewed data.
• Participant-level 10%, 50%, and 90% quantile curves for 24-hour activity patterns were generated.

Conclusions:

• FQPCA provides a powerful tool for analyzing complex, individual-level data beyond mean trends.
• This technique is well-suited for data from wearable devices, offering deeper insights into diurnal activity patterns.
• The proposed methodology is validated by simulations and available as an R package for broader application.