A Wavelet-Based Historical Functional Linear Mixed Model for Examining the Acute Health Effects of Pollution Exposure

• Activity Number: 186
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Elizabeth Malloy*+ and Brent Coull and Jeffrey S. Morris and Sara Adar and Helen Suh and Diane Gold
• Companies: American University and Harvard School of Public Health and The University of Texas MD Anderson Cancer Center and University of Michigan and Harvard School of Public Health and Harvard School of Public Health
• Keywords: Bayesian methods ; Historical functional linear model ; Functional data analysis ; Mixed Model ; Wavelets

Abstract

Data measured over time on a grid of discrete values collectively define a functional observation. Studies examining the acute health effects of pollution exposure are frequently interested in the prediction of a functional health outcome from a functional exposure measurement, such as airborne particulate matter or black carbon. We develop a wavelet-based historical functional linear mixed model which allows for the modeling of repeated measures of a continuous functional response and a functional predictor. We employ a novel use of wavelet-packets in a Bayesian setting to regularize the regression coefficient surface and force the historical time constraint, so that future values of the covariate function are not used to predict current or past values of the response function.