A Discussion of the Paper " Using Wavelet-based Functional Mixed Models to Characterize Population Heterogeneity in Accelerometer Profiles: a Case

from the paper We present a case study illustrating the challenges of analyzing accelerometer data taken from a sample of children participating in an intervention study designed to increase physical activity. An accelerometer is a small device worn on the hip that records the minuteby-minute activity levels throughout the day for each day it is worn. The resulting data are irregular functions characterized by many peaks representing short bursts of intense activity. We model these data using the wavelet-based functional mixed model. This approach incorporates multiple fixed-effects and random-effects functions of arbitrary form, the estimates of which are adaptively regularized using wavelet shrinkage. The method yields posterior samples for all functional quantities of the model, which can be used to perform various types of Bayesian inference and prediction. In our case study, a high proportion of the daily activity profiles are incomplete (i.e., have some portion of the profile missing), and thus cannot be modeled directly using the previously described method. We present a new method October 23: Greg Allenby, Marketing Department ”Choice Models in Marketing: Economic Assumptions, Challenges and Trends” Abstract: Direct utility models of consumer choice are reviewed and developed for understanding consumer preferences. We begin with a review of statistical models of choice, posing a series of modeling challenges that are resolved by considering economic foundations based on constrained utility maximization. Direct utility models differ from other choice models by directly modeling the consumer utility function used to derive the likelihood of the data through Kuhn-Tucker conditions. Recent advances in Bayesian estimation make the estimation of these models computationally feasible, offering advantages in model interpretation over models based on indirect utility, and descriptive models that Direct utility models of consumer choice are reviewed and developed for understanding consumer preferences. We begin with a review of statistical models of choice, posing a series of modeling challenges that are resolved by considering economic foundations based on constrained utility maximization. Direct utility models differ from other choice models by directly modeling the consumer utility function used to derive the likelihood of the data through Kuhn-Tucker conditions. Recent advances in Bayesian estimation make the estimation of these models computationally feasible, offering advantages in model interpretation over models based on indirect utility, and descriptive models that