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.

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__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