Improved Random Effect Specification for Semiparametric Mixed Models

• Activity Number: 528
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: International Indian Statistical Association
• Author(s): Philip Reiss and Pei-Shien Wu* and Jeff Goldsmith
• Companies: New York University School of Medicine and New York University School of Medicine and Columbia University
• Keywords: penalized splines ; repeated measures ; functional principal components ; random score model ; longitudinal data ; developmental trajectory

Abstract

We consider semiparametric regression with longitudinal data, such as estimating the mean of a parameter of interest as a function of age, possibly adjusting for covariates. To capture variation among individual trajectories, previous work has generally considered either the "minimalist" approach of random intercepts or the "maximalist" approach of subject-specific curves. But often neither of these extremes is satisfactory: the random intercept model's assumption of parallel curves for all individuals is too restrictive, whereas too few data points are available to estimate individual curves reliably. We present a new, intermediate approach in which we estimate random scores with respect to a functional principal component basis. In practice the number of observations often varies among individuals; accordingly, we let each subject's number of random effects (scores) depend, in an optimal manner, on the number of observations for the given individual. Our methods are illustrated with a classic spinal bone mineral density data set and with data from a study of cortical thickness development.