Comparison of designs for generalized linear models under model misspecification

The purpose of this article is to demonstrate the use of the quantile dispersion graphs (QDGs) approach for comparing candidate designs for generalized linear models in the presence of model misspecification in the linear predictor. The proposed design criterion is based on the mean-squared error of prediction which incorporates the prediction variance and the bias caused by fitting the wrong model. The method of kriging is used to estimate the unknown function assumed to be the cause of model misspecification. The QDGs approach is also useful in assessing the robustness of a given design to values of the unknown parameters in the linear predictor. Three numerical examples are presented to illustrate the application of the proposed methodology.