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Multilevel functional quantile principal component analysis
Álvaro Méndez-Civieta1,2, Ying Wei1, Jeff Goldsmith1
1Department of Biostatistics, Columbia University, 722 W 178 St, New York,NY 10032, United States.
Biostatistics (Oxford, England)
|June 15, 2026
Summary
A new method, Multilevel Functional Quantile Principal Component Analysis (MFQPCA), analyzes physical activity data from congestive heart failure patients. It reveals day-to-day variations in sedentary behavior and individual differences in vigorous activity.
Area of Science:
- Statistics
- Biostatistics
- Data Science
Background:
- Accelerometer data collection has advanced to long-term monitoring (weeks to years).
- Understanding physical activity requires analyzing variability beyond average values.
- Hierarchical data structures are common in health and activity monitoring.
Purpose of the Study:
- Introduce Multilevel Functional Quantile Principal Component Analysis (MFQPCA), a novel dimension-reduction technique.
- Extend Functional Quantile Principal Analysis to hierarchical functional data.
- Quantify and understand physical activity patterns beyond expected values in complex datasets.
Main Methods:
- Developed MFQPCA to decompose quantile-specific variability in hierarchical functional data.
- Applied MFQPCA to accelerometry data from congestive heart failure patients (4-9 months).
- Estimated between-participant and within-participant variability at different quantile levels (10%-90%).
Main Results:
- MFQPCA effectively captures complex distributional features and disentangles variability sources.
- Revealed that day-to-day variability is dominant in sedentary periods.
- Showed that between-participant differences increase with vigorous activity intensity.
Conclusions:
- MFQPCA provides a robust method for analyzing longitudinal changes in hierarchical functional data.
- The method facilitates a deeper understanding of physical activity patterns and their variability.
- An open-source R package (FunQ) makes MFQPCA accessible for broad applications.
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