D-optimal Factorial Designs under Generalized Linear Models

Abstract

Generalized linear models (GLMs) have been used widely for modeling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013 Yang, J., Mandal, A., Majumdar, D. (2013). Optimal designs for 2k factorial experiments with binary response. Technical Report, Available at: http://arxiv.org/pdf/1109.5320v4.pdf. [Google Scholar]) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this article, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multilevel predictors.