Sponsoring Section/Society: WNAR
Session Slot: 8:30-10:20 Monday
Estimated Audience Size: xx-xxx
AudioVisual Request: xxx
Session Title: Exciting Developments In Methods For Repeated Measures
Theme Session: No
Applied Session: No
Session Organizer: Weiss, Robert Univ. of California at Los Angeles
Address: Department of Biostatistics UCLA School of Public Health Los Angeles, CA 90095-1772
Phone: (310) 206-9626
Fax: (310) 267-2113
Email: rob@rem.ph.ucla.edu
Session Timing: 110 minutes total (Sorry about format):
30 Minutes First Speaker 30 minutes Second Speaker 30 minutes Third Speaker 0 minutes Discussant - none Floor Discusion - 10 minutes
Session Chair: Weiss, Robert Univ. of California at Los Angeles
Address: Department of Biostatistics UCLA School of Public Health Los Angeles, CA 90095-1772
Phone: (310) 206-9626
Fax: (310) 267-2113
Email: rob@rem.ph.ucla.edu
1. Functional Linear Models for Longitudinal Data
Fan, Jianqing, University of North Carolina
Address: Deptment of Statistics University of North Carolina Chapel Hill, NC 27599-3260
Phone: 919-962-1358
Fax: 919-962-1279
Email: jfan@stat.unc.edu
Abstract: Functional linear models enhance significantly the flexibility of traditional linear models by allowing coefficients to depend smoothly on time. They include many useful statistical models used for longitudinal data and functional data. In this talk, a simple and powerful approach is introduced to estimate nonparametrically the coefficient functions of the functional linear models. The approach consists of two steps. The first step gives the raw estimate and its standard error of a coefficient function at each time point via using the traditional least-squares technique. In the second, the raw estimates are smoothed by using an existing nonparametric regression technique. Our approach is very flexible that it copes well with various degrees of smoothness of coefficient functions. Some asymptotic results for estimated coefficient functions are established. The applications to a dataset on CD4 counts and a dataset on nested samples of progesterone curves demonstrate that the proposed approach is indeed powerful in exploiting fine structure for longitudinal data.
2. Prior Distributions, Bayesian Computation, and Model Selection For Generalized Linear Mixed Models
Ibrahim, Joseph, Harvard University
Address: Department of Biostatistics, Dana Farber Cancer Institute, Mayer 3A.18, Boston MA
Phone: 617-632-3012
Fax:
Email: Joseph_Ibrahim@dfci.harvard.edu
Abstract: Generalized linear models serve as a useful class of regression models for discrete and continuous data. In applications such a longitudinal studies, observations are typically correlated. The correlation structure in the data is induced by introducing a random effect, leading to the generalized linear mixed model (GLMM). In this talk, we propose a class of informative prior distributions for the model parameters in a GLMM which are useful for variable subset selection. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified into a prior distribution for the current study. We derive theoretical and computational properties of the proposed priors, as well as examine properties of the implied posterior distributions. In addition, we develop novel computational methods for sampling from the posterior distribution of the parameters and computing posterior model probabilities. The computational methods are based on the idea of hierarchical centering (Gelfand et al., 1996), and are shown to be quite efficient for sampling from the posterior distribution for the models considered here. To compute the posterior model probabilities, we derive several key results that lead to efficient calculation, and show that only posterior samples from the full model are needed to estimate the posterior probabilities for all of the possible subset models. Real data sets are used to demonstrate the methodology.
3. Recent Developments In The Use Of Antedependence Models For Longitudinal Data
Zimmerman, Dale, University of Iowa
Address: 233 Schafer Hall, Dept. of Statisitcs and Actuarial Science, University of Iowa Iowa City, Iowa 52242
Phone: 319-335-0818
Fax:
Email: dzimmer@stat.uiowa.edu
Abstract: Antedependence (AD) models are a useful, though not widely known, class of models for the covariance structure of longitudinal data. Like stationary autoregressive models, AD models allow for serial correlation within subjects but they are more general in the sense that they do not stipulate that the variance is constant over time nor that correlations between measurements equidistant in time are equal. AD models will be briefly reviewed and some recent developments in the use of structured AD models will be given. A new graphical diagnostic for determining the order of the model also will be described.
List of speakers who are nonmembers: None