Robust Experimental Design for Multivariate GLM

‘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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