Organized By

Department of Statistics,
University of Florida

Funded By

National Security Agency
National Institute of Health (National Cancer Institute,
National Institute of Allergy and Infections Diseases,
National Institute of General Medical Science)

Co-chairs:    Malay Ghosh and André I. Khuri,
        University of Florida

Session Organizers:

    Alan Gelfand, University of Connecticut
    Malay Ghosh, University of Florida
    Nicholas Jewell, University of California, Berkeley
    André I. Khuri, University of Florida
    Peter McCullagh, University of Chicago
    Charles McCulloch, Cornell University
    Rob Tibshirani, University of Toronto
    Mike West, Duke University

Thursday, 29 September 1994

1:00-1:45p.m. Registration (Fee US$100.00) J. Wayne Reitz Union
rooms 361-363.
1:45-2:00p.m. Opening Remarks
2:00-3:30p.m. Invited Papers I: Foundations
J. Wayne Reitz Union 361-363

Organizer: Peter McCullagh, University of Chicago
Chair: Malay Ghosh, University of Florida

2:00p.m. Dual Likelihood.
Per Mykland, University of Chicago

2:30p.m. Some Remarks on Quadratic Exponential Models.
Peter McCullagh, University of Chicago

3:00-3:30p.m. Break

3:30-5:00p.m. Invited Papers II: Response Surface Methodology
J. Wayne Reitz Union 361-363

Organizer: Andre I. Khuri, University of Florida
Chair: Andre I. Khuri, University of Florida

3:30p.m. Designs for Logistic Regression: Single Stage
and Two Stage.
Raymond H. Myers, Virginia Polytechnic Institute.

4:00p.m. Utilizing Concentration-Response Data from Individual
Components to Detect Departures from Additivity in
Chemical Mixtures.
Chris Gennings and W. Hans Carter, Jr., Virginia
Commonwealth University

4:30p.m. Discussant: Kathryn Chaloner, University of Minnesota

5:15p.m.    Optional tour of Griffin-Floyd Hall, Dept. of Statistics
6:00-7:30p.m. Reception, University Auditorium/Friends of Music Room

Friday, 30 September 1994

Organizers: Malay Ghosh, University of Florida
Mike West, Duke University
Chair: Sharon-Lise Normand, Harvard University

8:30am Bayesian Tests and Model Diagnostics in Conditionally
Independent Hierarchical Models.
James Albert, Bowling Green State University
Siddhartha Chib, Washington University, St. Louis

9:00a.m. Bayesian Variable Selection for Generalized Linear
Models.
Joseph Ibrahim, Harvard University

9:30a.m. Generalized Linear Models With Random Effects-a
Bayesian Semiparametric Population Model
Peter Mueller, Duke University
Gary Rosner, Duke University

10:00-10:30am Break

10:30-12:00Noon Invited Papers IV: Applications

Organizer: N. P. Jewell, University of California, Berkeley
Chair: Myron Katzoff, National Center for Health Statistics

10:30a.m. Bootstrap Methods for Generalized Linear Models
Anthony Davison, University of Oxford.

11:00a.m. Application of Generalized Linear Models in Finite
Population Problems.
David Firth, University of Oxford

11:30a.m. Applications of Generalized Linear Models to the
Analysis of Aids Data.
Nicholas P. Jewell, University of California, Berkeley

12:00-12:20pm    Photo session on steps of JWRU Colonnade
12:20-2:00pm Lunch

2:00-3:30pm Invited Papers V: Generalized Mixed Linear Models

Organizer: Charles McCulloch, Cornell University
Chair: Ramon Littell, University of Florida

2:30p.m. Connections among Conditional ML, Nonparametric ML,
and Quasi-Symmetric ML Estimates for LOGIT Models
with Random Effects.
Alan Agresti, University of Florida

3:00p.m. Approximation Methods for Generalized Linear Mixed
Models.
Russell D. Wolfinger, SAS Institute, Inc.

3:30-4:00p.m. Break

4:00-5:20p.m. Contributed Papers I
Chair: James Booth, University of Florida

4:00p.m. Empirical Likelihood with Nuisance Parameters: Do the
Usual Higher Order Properties Hold?
Nicole A. Lazar, University of Chicago

4:20p.m. A Resampling Diagnostic for Generalized Linear Models.
Abhinanda Sarkar, Stanford University

4:40p.m. Regression Analysis of Proportions Obtained From a
Multivariate Binary Response.
Melinda L. Drum, University of Illinois

5:00pm Universal Optimality of Bayesian Experimental Designs
and Optimal Data Augmentations.
Dulal K. Bhaumik, University of South Alabama, Mobile
Pranab K. Sen, University of North Carolina, Chapel
Hill

4:00-5:20p.m. Contributed Papers II
Chair: Mark Becker, University of Michigan

4:00p.m. Optimal Tests for Nested Designs With Circular
Stationary Dependence
R. Khatree, Oakland University
D.N. Naik, Old Dominion University

4:20p.m. Bayesian Analysis of a Random Link Function in Binary
Response Regression
Sanjib Basu, University of Arkansas
Saurabh Mukhopadhyay, University of Connecticut

5:00p.m. A Model For The Analysis of Tuberculin Skin Test
Conversion Data Among Health Care Workers
Philip J. Smith, Center For Disease Control
and Prevention

6:30pm Banquet: University Centre Hotel
1535 S.W. Archer Road, Gainesville, FL

After Dinner Talk: P. K. Sen, University of North Carolina

Saturday, 1 October 1994

8:30-10:00am Invited Papers VI: Hierarchical Models

Organizers: Malay Ghosh, University of Florida
Alan Gelfand, University of Connecticut
Chair: Siddhartha Chib, Washington University, St. Louis

8:30a.m. Small Area Estimation for Discrete Data: A
Hierarchical Bayes Approach.
Malay Ghosh, University of Florida
Kannan Natarajan, Abbott Research Laboratories,
Illinois

9:00a.m. Construction of Hierarchical Generalized Linear
Models.
Mark S. Kaiser, Iowa State University
Noel Cressie, Iowa State University
Jaehyung Lee, Iowa State University

9:30a.m. Bayesian computations in hierarchical regression
models for discrete data, with applications.
Constantine Gatsonis, Harvard University

10:00-10:30am Break

10:30-12:00Noon Invited Papers VII: Computing

Organizer: Alan Gelfand, University of Connecticut
Chair: P. Laud, University of Wisconsin, Milwaukee

11:00a.m. Accessing and Accelerating Gibbs Sampler Convergence
for GLIM's.
Mary Kathryn Cowles, University of Nebraska, Omaha

11:30a.m. Title to be announced
Charles Geyer, University of Minnesota

12:00-2:00pm Lunch

2:00-3:30pm Invited Papers VIII: Inference

Organizer: Malay Ghosh, University of Florida
Rob Tibshirani, University of Toronto
Chair: Bimal K. Sinha, University of Maryland, Baltimore County

2:00p.m. Semiparametric Bayesian Inference for Binary
Regression.
Michael A. Newton, University of Wisconsin
Claudia Czado, University of Wisconsin
Rick Chappell, University of Wisconsin

2:30p.m. Overdispersed Generalized Linear Models
Dipak K. Dey, University of Connecticut
Alan E. Gelfand, University of Connecticut
Fengchun Peng, University of Connecticut

3:00p.m. Varying-Coefficient Models for Longitudinal Data.
Kiros Berhane, University of Toronto
Rob Tibshirani, University of Toronto

3:30-4:00pm Break

4:00-5:20pm Contributed Papers III

Chair: Jane Pendergast, University of Florida

4:00p.m. Practical Remarks on Autologistic Models for Spatial
Binary Data with Covariates.
Fred W. Huffer, Florida State University
Hulin Wu, Florida State University

4:40p.m. Local, Bayesian and Seqrential Optimum Designs for
Model Discrimination: The Class of Generalized Linear
Model
Antonio C M Ponce de Leon
St. George's Hosptial Medical School, London, UK

5:00p.m. Fitting Generalized Linear Models Using J
John Holt, University of Guelph, Ontario

    Efficient industrial experiments for reliability analysis of manufactured goods may consist in subjecting the units to higher stress levels than those of the usual working conditions. This results in the so called accelerated life tests where for each prefixed stress level the experiment ends after the failure of a certain prefixed proportion of units or a certain test time is reach. The aim of this paper is to determine estimates of the mean lifetime of the units under usual working conditions from censored failure data obtained under stress conditions. This problem is approached through generalized linear modeling and related inferential (classical or not) techniques considering different failure distributions (exponential, Weibull, piecewise exponential and extreme value) and a log-linear stress-response relationship. The general framework considered has as particular cases, among others, the inverse power law model, the Eyring model, the Arrhenius model and the generalized Eyring model. In order to illustrate the proposed methods some numerical examples are provided.

Fitting Generalized Linear Models Using J
John Holt
University of Guelph

    The functional programming language J and its powerful array processing capabilities facilitate statistical computations and provides a convenient environment for fitting generalized linear models. Its use is illustrated on GLMS, extensions to multinomial response models, some generalized mixed models and for modelling variance heterogeneity. Its suitability for use in teaching as well as research will be discussed.

Optimal Tests for Nested Designs with Circular Stationary Dependence
Ravi Khattree, Oakland University and
D.N. Naik, Old Dominion University

    Nested designs with correlated error structures occur naturally in many experiments. For these designs with balanced data, the derivation of optimal tests for testing the significance of a fixed effects or a variance component, is considered. The error is assumed to have a circular structure. It is shown that whenever these tests exist, they coincide with the likelihood ratio tests and also with the usual analysis of variance tests.

    Nested designs with correlated error structures occur naturally in many experiments. For these designs with balanced data, the derivation of optimal tests for testing the significance of a fixed effects or a variance component, is considered. The error is assumed to have a circular structure. It is shown that whenever these tests exist, they coincide with the likelihood ratio tests and also with the usual analysis of variance tests.

Generalized Linear Models with Random Effects -- A Bayesian Semiparametric Population Model
Peter Mueller and Gary Rosner, Duke University

    We propose a class of nonlinear population models with nonparametric second-stage priors and a generalized linear model profile function. The proposed models apply a flexible class of mixtures to implement the nonparametric second stage. The motivating example is a pharmacodynamic study involving longitudinal data on hematologic profiles of cancer patients undergoing chemotherapy. We describe a full posterior analysis in a Bayesian framework. This includes prediction of future observations (profiles and end points for new patients), estimation of the mean response function for observed individuals, and inference on population characteristics.

    The mixture model is specified and given a hyperprior distribution by means of a mixture of Dirichlet processes. Estimation is implemented by a combination of various Markov chain Monte Carlo schemes.

Local, Bayesian,and Sequential Optimum Designs for Model Discriminations: The Class of Generalized Linear Models
Antonio C M Ponce de Leon
Department of Public Health Sciences, St. George's Hosptial Medical School, Granmer Terrace, Tooting, London SW17 ORE, United Kingdom

    The problem of designing optimum experiments for discriminating between two rival regression models has been studied to a great extent in the last twenty five years. The subtleties of the problem are such that more than one approach has been proposed, leading to different solutions.

    More recently, the arrival of Generalized Linear Models (GLM) has provided statisticians with more powerful tools. However, there are still areas in which the current stage of GLM theory lies far beyond the sophistication achieved in ordinary linear models.

    One of such areas is experimental design for model discrimination. In this work, we attempt to fill this gap, though partially, by means of extending existing methodology for regression model discrimination to the case of GLM discrimination. More specifically, we follow the approach proposed by Atkinson and Fedorov (Biometrika 62 (1975a): 57-70).

Bayesian Analysis of a Random Link Function in Binary Response Regression
Sankib Basu, University of Arkansas
Saurabh Mukhopadhyay, University of Connecticut

    Binary response regression is a useful technique for analyzing categorical data. Popular binary models use special link functions such as the logit or the probit link. We assume that the inverse link function H is a random member of the class of normal scale mixture cdfs. We propose three different models for this random H: (i) H is a finite scale mixture with a Dirichlet distribution prior on the mixing distribution; (ii) H is a general scale mixture, the mixing distribution has a Dirichlet process prior; and (iii) H is a scale mixture of truncated normal distributions with the mixing distribution having a Dirichlet prior. We describe Bayesian analyses of these models using data augmentation and Gibbs sampling. Model diagnostics by cross validation of the conditional predictive distributions are proposed. These analyses are illustrated in two examples. Our proposed models match the performances of Bayesian probit and t link models in the first example whereas they out perform probit and t link models in the second example.