Fast Multilevel Functional Principal Component Analysis

Abstract

We introduce fast multilevel functional principal component analysis (fast MFPCA), which scales up to high dimensional functional data measured at multiple visits. The new approach is orders of magnitude faster than and achieves comparable estimation accuracy with the original MFPCA. Methods are motivated by the National Health and Nutritional Examination Survey (NHANES), which contains minute-level physical activity information of more than 10, 000 participants over multiple days and 1440 observations per day. While MFPCA takes more than five days to analyze these data, fast MFPCA takes less than five minutes. A theoretical study of the proposed method is also provided. The associated function mfpca.face() is available in the R package refund. Supplementary materials for this article are available online.

Keywords:

• Functional principal component analysis
• Mixed model equations
• Multilevel models

Funding

Conflict of Interest

Dr. Crainiceanu is consulting with Bayer, Johnson and Johnson, and Cytel on methods development for wearable devices in clinical trials. The details of the contracts are disclosed through the Johns Hopkins University eDisclose system and have no direct or apparent relationship with the current article.

Supplementary Materials

fastMFPCA_supp.pdf Technical details of the method, proof of the theorem, and additional simulation and application results. (.pdf file)code.zip The R function mfpca.face() and the code for simulation. (.zip file)

Acknowledgments

We thank the editor, the associate editor, and two reviewers for their careful reading of the original manuscript and for their comments that significantly improved the article.

Additional information

Funding

This work was supported by the National Institute of Neurological Disorders and Stroke under Award Number R01 NS060910, R01 NS091307 and R01 NS112303; and National Institute on Aging under Award Number R01 AG064803.