Optimal Quadratic Response Surface Designs for Binomial Data

• Activity Number: 254
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 12:00 PM to 1:50 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Kenneth G. Russell*+
• Companies: University of Wollongong
• Keywords: logistic ; regression ; quadratic ; response ; optimal ; design

Abstract

Consider the estimation of a probability of success, p(x1,x2), thought to be a function of two predictor variables, x1 and x2, that are both under the control of the experimenter. The aim is to find where p is maximized. If appropriate data are collected at an array of points (x1,x2), then ln[p/(1-p)] can be modeled by a quadratic function in x1} and x2 using logistic regression, and the appropriate optimum point can be estimated. How do we select the experimental points? An extensive literature exists on optimal experimental designs for estimating response surfaces when the observations have a constant variance and the model is linear in the parameters. However, in the current situation, the model relating p to a quadratic function of x1 and x2 is nonlinear, and the variance of each observation depends on the unknown value of p at that point. This makes the problem very difficult. This poster describes the nature of the optimal design when the quadratic function for ln[p/(1-p)] is assumed known. It is hoped that this will assist in finding optimal designs when the quadratic function is unknown.