Design of Experiments for Generalized Linear Models with Random Blocks

Edgar Hassler
School of Computing, Informatics, and Decision Systems Engineering
Arizona State University, Tempe, AZ
ehassler@gmail.com

Douglas C. Montgomery
School of Computing, Informatics, and Decision Systems Engineering
Arizona State University, Tempe, AZ

Rachel T. Silvestrini
Industrial and Systems Engineering
Rochester Institute of Technology, Rochester, NY

Industrial experiments often involve non-normal responses and restrictions on randomization.  Though much work has been done to address the situation when the response is a member of the natural exponential family of distributions under complete randomization, very little work has been done to address this situation when complete randomization is not possible (e.g. random blocks, split plot designs, certain multiple response problems, et cetera).  An optimal-design approach based on quasi-likelihood and projected score functions is evaluated over a collection of binomial and Poisson models where the random effects are assumed to be normally distributed.  The proposed criterion is compared (via numerical estimation of the determinant of the exact expected information matrix) to more naïve approaches and is found to have superior performance.

2015 QPRC