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This study introduces a new regression model for complex functional data, analyzing physical activity patterns over time. The model effectively captures individual variations and identifies key factors influencing activity levels.

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Functional data analysis is crucial for understanding complex, time-dependent phenomena.
  • Generalized linear models and multilevel structures are increasingly used to analyze diverse data types.
  • Analyzing clustered functional responses requires advanced statistical methodologies.

Purpose of the Study:

  • To develop and validate a novel regression model for generalized, multilevel functional responses.
  • To analyze binary curves of physical activity data from a large cohort over multiple days.
  • To identify functional fixed effects and major sources of variability within and between subjects.

Main Methods:

  • Utilized a generalized linear model (GLM) to incorporate scalar covariates.
  • Employed multilevel functional principal components analysis (MFPCA) to decompose deviations.
  • Estimated parameters using a Bayesian framework with Stan and Hamiltonian Monte Carlo (HMC) sampling.
  • Used penalized splines for estimating fixed effect coefficient and principal component basis functions.

Main Results:

  • The proposed model demonstrated good estimation and inferential properties in simulations.
  • Successfully identified the effects of age and BMI on the time-specific probability of physical activity.
  • MFPCA revealed significant patterns of variability within and between subjects' activity levels.
  • The method showed reasonable computation times for moderate datasets.

Conclusions:

  • The developed regression model is effective for analyzing generalized, multilevel functional data.
  • The approach provides valuable insights into factors influencing time-varying behaviors like physical activity.
  • The methodology accounts for complex correlation structures inherent in clustered functional responses.
  • Publicly available code facilitates the application of this method in diverse scientific domains.