Robust designs for generalized linear models with possible overdispersion and misspecified link functions

We discuss robust designs for generalized linear models with protection for possible departures from the usual model assumptions. Besides possible inaccuracy in an assumed linear predictor, both problems of overdispersion and misspecification in link function are addressed. For logistic and Poisson models, as examples, we incorporate the variance function prescribed by a superior model similar to a generalized linear mixed model to address overdispersion, and adopt a parameterized generalized family of link functions to deal with the problem of link misspecification. The design criterion is the average mean squared prediction error (AMSPE). The exact optimal design, which minimizes the AMSPE, is also presented using examples on the toxicity of ethylene oxide to grain beetles, and on Ames Salmonella Assay.