Abstract

Designs for fitting a generalized linear model depend on the unknown parameters of the model. The use of any design optimality criterion would therefore require some prior knowledge of the parameters. In this article, a graphical technique is proposed 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 a region of interest, R. For a given design, these quantiles depend on the model's parameters. Plots of the maxima and minima of the quantiles, over a subset of the parameter space, produce the so-called quantile dispersion graphs (QDGs). The plots provide a comprehensive assessment of the overall prediction capability of the design within the region R. They also depict the dependence of the design on the model's parameters. The QDGs can therefore be conveniently used to compare several candidate designs. Two examples are presented to illustrate the proposed methodology.

Author Keywords: Binary response; Design dependence on unknown parameters; Generalized linear models; Prediction bias; Response surface methodology; Scaled mean-squared error of prediction

Article Outline

1. Introduction

2. The mean-squared error of prediction for GLMs

2.1. The prediction variance

2.2. The prediction bias

3. The MSEP for logistic regression models

4. Quantile dispersion graphs

5. Numerical examples

5.1. Example 1

5.2. Example 2

6. Concluding remarks

Appendix A. Derivation of formula (3.4)

References