Experimental Designs for Generalized Linear Models

This page contains supplemental information about the research on design of experiments for binary response, and GLM in general, conducted by Hovav Dror under the supervision of Prof. David M. Steinberg.

Introduction

Experimental Design is about choosing locations in which to take measurements. For example, choosing different drug doses in which to examine the success of a treatment. A lot has been written on experimental design for statistical linear models. But, often these models do not describe the problem well enough. Common examples are when the response is binary (“success” or “failure”) or when the response is discrete count data (fitting a Poisson model). Analysis of such data is familiar through Generalized Linear Models (GLM). This page is intended to give researchers tools for designing GLM experiments.

We also provide Bayesian tools that exploit discretization of the prior, for cases where the posterior distribution has a complex form. We use these tools as a reliable analysis of GLM when the sample size is small (regression techniques are only reliable asymptotically, for large samples).

The information is divided as follows:

Sequential Designs. Unlike one-stage experimental plans, that require the researcher to fix in advance the factor settings at which data will be observed, sequential experimental design allows updating and improving the experimental plan following the data already observed. Examples include “sensitivity tests” and “dose-response” plans, but our work goes a lot beyond these. We provide a technical report describing the new method proposed and evaluating its efficiency, source code for the algorithms and examples.

Bayesian Inference tools, exploiting a discretization of the prior distribution, are described and utilized in the sequential designs section, and source code focusing on this topic alone is available here.

One-Stage Designs, which are robust to most types of uncertainty an experimenter might face, are discussed. We provide a paper, source code for the algorithms and examples. The source code also includes a function for the non-trivial case of finding or augmenting a local D-optimal design for GLM.

Approximate Local D-optimal designs are also provided. While the algorithm provided for one-stage designs is both more efficient and more ordered, approximate designs may be of interest for an intuitive understanding of the expected locations which are D-optimal for a binary response, and also for designs of very high dimension.

Publications

Hovav A. Dror and David M. Steinberg (2008). Sequential Experimental Designs for Generalized Linear Models, Journal of the American Statistical Association, 103, 288-298.

Hovav A. Dror and David M. Steinberg (2006). Robust Experimental Design for Multivariate Generalized Linear Models, Technometrics Vol. 48, No. 4, 520-529.

Hovav A. Dror and David M. Steinberg (2005), Approximate Local D-optimal Experimental Design for Binary Response, Technical Report RP-SOR-0501, Tel Aviv University.

Office address: Schrieber Building, Department of Statistics and Operations Research, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel.

Last update: November 23, 2006