‘Regular’ linear models have a fortunate
quality that their optimal design does not depend on the values of the unknown
coefficients. This is not true for generalized linear models, and is the origin
of the difficulties in constructing D-optimal experimental plans for GLM.

In our paper (*Technometrics*, (2006)),
we suggest both a procedure to find Local D-optimal designs, when the
coefficient values are known, and a robust method taking account of uncertainty
in these values. Download the paper.

Publication

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

__Source
Code for algorithm and examples__

Local D-optimal
Design script

The following is a
MATLAB script for a function aimed at finding Local D-optimal designs for
Poisson or Binary response (Logit, Probit or CLL link): DGLM.m

or augmenting a local
D-optimal design: GLMDAUG.m
(which also needs canddaugm.m
and InfoMtrxGLM.m)

__Robust
Design procedures__

The following
are two complete work through examples of finding robust experimental designs.
The procedure requires the function DGLM.m (see above), as
well as Nied1000.m & InfoMtrxGLM.m
(see below) and MATLAB with the statistical toolbox.

Logisitic model example,
4-dimensional, with a uniform prior: Section4Example.m

Poisson model example,
5-dimensional, normal prior, two competing models: Section6Example.m

Robustness for
different linear predictors and link functions: Section5Example.m

__Additional Files__

Calculating the Information Matrix
for Generalized Linear Models: InfoMtrxGLM.m

Neiderreiter quasi-sequence:

·
Algorithm for the
construction of Neiderreteiter sequences can be found at http://www.csit.fsu.edu/~burkardt/m_src/niederreiter2/niederreiter2.html,

·
The following file is
an output of the algorithm, containting 1000 vectors with 20 columns each: Nied1000.m

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*Back to the parent page: Experimental Design for GLM*