Bootstrap aggregated designs for generalized linear models

Abstract

Many experiments require modeling a non-Normal response. In particular, count responses and binary responses are quite common. The relationship between predictors and the responses are typically modeled via a Generalized Linear Model (GLM). Finding D-optimal designs for GLMs, which reduce the generalized variance of the model coefficients, is desired. A common approach to finding optimal designs for GLMs is to use a local design, but local designs are vulnerable
to parameter misspecification. The focus of this paper is to provide designs for GLMs that are robust to parameter misspecification. This is done by applying a bagging procedure to pilot data, where the results of many locally optimal designs
are aggregated to produce an approximate design that reflects the uncertainty in the model coefficients. Results show that the proposed bagging procedure is robust to changes in the underlying model parameters. Furthermore, the proposed designs are shown to be preferable to traditional methods, which may be over-conservative.