Contributed Session: Regression: Design & Analysis

Session Chair: Brad Biggerstaff, NIST

Informational Complexity Approach to Predictive Regression Models of Future Observations

Hamparsum Bozdogan
Dept. of Statistics, Univ. of Tennessee

This paper develops a new informational complexity (ICOMP) approach of this author (Bozdogan 1988, 1990, 1993, 1994) to predictive normal regression models in industrial processes in which one wishes to predict the future process. This is based on the work of Zellner and Chetty (1965), Levy and Perng (1984), Johnson and Geisser (1983), Geisser (1993), and others. ICOMP criterion is derived along with Akaike's (1973) classic AIC using noninformative priors on the parameters. This approach allows us to combine the past (or present) data and the future (or new) data to create a data adaptive modeling strategy. To put control limits on the future process and to identify influential observations which signal process changes a leave-one-out method is used. All possible subset selection of variables is introduced to select the best predictors of the future observations in a simultaneous fashion across different competing alternative models.

[Hamparsum Bozdogan, Dept. of Statistics, Univ. of Tennessee, Knoxville, TN 37996-0532 USA; bozdogan@utkvx.utk.edu ]

Latent Variable Methods for Multivariate Regression with Applications in Chemistry & Chemical Engineering

Alison J. Burnham
Roman Viveros
Dept. of Mathematics & Statistics, McMaster Univ.

John F. MacGregor
Dept. of Chemical Engineering, McMaster Univ.

Increasing complexity in chemical processes and advances in the measuring systems have resulted in a proliferation of data consisting of large numbers of highly correlated variables. This type of data leads naturally to the consideration of latent variable models where the underlying process can be described by a few latent variables with the rest of the variation in the data being noise. This talk will discuss some current applications for these latent variable methods in chemistry and chemical engineering. These applications will be in the areas of prediction, process description, process monitoring and process control. It will use these applications as a basis for discussing criteria for estimation of the latent variables and the resulting regression models.

[Alison J. Burnham, Dept. of Mathematics & Statistics, McMaster Univ., Hamilton, Ontario L8S 4K1, CANADA; aburnham@ilap.com ]

On Estimation in Linear Calibration Problems

Jinzhong Liao
Dept. of Statistics, Univ. of Michigan

A new estimator is considered for the linear calibration problem. It is related to the Bayesian estimator proposed in Hoadely (1970). The properties of the estimator are studied and comparisons are made with others in the literature through simulation and asymptotic results. It is shown to be asymptotically unbiased in certain situations, and it combines the arrtactive features of the classical and inverse estimators. This is joint work with Julian Faraway and Vijayan N. Nair.

[Jinzhong Liao, Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI 48109 USA; jliao@stat.lsa.umich.edu ]

Bayesian D-Optimal Designs for Heteroscedastic Polynomial Models

Holger Dette
Faculty of Mathematics, Ruhr Univ.

Weng Kee Wong
Dept. of Biostatistics, Univ. of California - Los Angeles

We consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially. However, this dependence is not known precisely and additional parameters are required in the model.

A Bayesian approach is adopted and Bayesian D-optimal designs on a compact design space are found analytically for estimating various subsets of the parameters. These designs are optimal within the class of all designs supported on a minimum number of support points but they could also be optimal within the class of all (non-singular) designs. Numerical examples are included.