Xin M. Tu
Department of Biostatistics and Clinical Epidemiology
School of Medicine
University of Pennsylvania
Monday, March 24, 2003
3:30 PM
Moos 2-620
Minneapolis Campus
Abstract:
We introduce a new class of semi-parametric (distribution-free) regression models
with functional responses. This class of functional response models (FRM) generalizes
the traditional regression models by defining the response variable as a function
of several responses from multiple subjects. By using such multiple-subjects-based
responses, the FRM not only integrates some popular non- and semi-parametric
approaches within a unified modeling framework, but also provides a platform
for developing new models for addressing limitations of existing non- and semi-models.
For example, by viewing the popular non-parametric two-sample Mann-Whitney-Wilcoxon
(MWW) as a regression under FRM, we can readily generalize it to account for
multiple groups and to examine second-order variability of the distributions
(MWW is based on comparing the median or first-order variability between two
distributions), the latter of which is an important consideration for effectiveness
studies. The FRM is also quite effective in addressing limitations of parametric
models. For example, latent variable models such as the linear mixed-effects
model (LMM) and the structural equation model (SEM) are popular in psychosocial
research. By developing new semi-parametric approaches under FRM, we can provide
robust estimates for both the population and cluster specific parameters. In
addition, these new models can even entertain interactions of random effects,
which are difficult to implement under existing inference theory.
Because of the dependency introduced by using multiple subjects in defining the response variable, existing generalized estimating equation (GEE) based approaches are not appropriate for making inference about FRM. A novel approach is developed to address the dependence issue by integrating the U-statistic theory with the GEE. The methodology is illustrated with a real data application in psychosocial research involving modeling correlated correlations within a longitudinal data setting.
A social tea will be held at 3:00 P.M. in A434 Mayo. All are Welcome.