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Activity Number: 20
Type: Topic Contributed
Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #315077
Title: Generalized Multilevel Function-on-Scalar Regression and Principal Component Analysis
Author(s): Jeff Goldsmith* and Vadim Zipunnikov and Jennifer Schrack
Companies: Columbia University and Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health
Keywords: Accelerometry ; Bayesian Inference ; Generalized Functional Data ; Hamiltonian Monte Carlo ; Penalized Splines
Abstract:

We consider regression models for generalized, multilevel functional responses: functions are generalized in that they follow an exponential family distribution and multilevel in that they are clustered within groups or subjects. This data structure is increasingly common across scientific domains and is exemplified by our motivating example, in which binary curves indicating physical activity or inactivity are observed for nearly six hundred subjects over five days. We use a generalized linear model to incorporate scalar covariates into the mean structure, and decompose subject-specific and subject-day-specific deviations using multilevel functional principal components analysis. Model parameters are estimated in a Bayesian framework. Simulations designed to mimic the application have good estimation and inferential properties with reasonable computation times for moderate datasets, in both cross-sectional and multilevel scenarios; code is publicly available. In the application we identify effects of age and BMI on the time-specific change in probability of being active over a twenty-four hour period.


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