Quantile Dispersion Graphs for Evaluating and Comparing Designs for Logistic Regression Models

Abstract

Response surface designs for fitting a generalized linear model depend on the unknown parameters of the postulated model. The use of any design optimality criterion would therefore require some prior knowledge of the parameters. In this talk, a graphical technique is described for comparing and evaluating designs for a logistic regression model. Quantiles of the scaled mean-squared error of prediction are obtained on concentric surfaces inside the region of experimentation. For a given design, these quantiles depend on the model's unknown parameters. Plots of the maxima and minima of the quantiles over the parameter space produce the so-called quantitle dispersion graphs. The plots provide a comprehensive assessment of the overall prediction capability of the design within the experimental region. They also depict the dependence of the design on the model's parameters.