Minimax Designs for Logistic Regression in a Compact Interval

Abstract

Minimax designs for logistic regression with one design variable are considered where the design space is a general interval [a, b] on the straight real line. This corresponds to a weighted linear regression model for a specific weight function. Torsney and Lopez-Fidalgo (1995) computed maximum variance (MV-) optimal designs for simple linear regression for a general interval. Lopez-Fidalgo et al. (1998) gave MV-optimal designs for symmetric weight functions and symmetric intervals, [-b, b]. Computations for general intervals for logistic regression are much more complex. Using similar approaches to these two papers and the equivalence theorem, explicit minimax optimal designs are given for different regions of points (a, b) in the semi-plane b>a for the logistic model. This complements Dette and Sahm (1998) who give a method for computing MV-optimal designs without any restriction on the design space. From this, Standardized Maximum Variance (SMV-) optimal designs immediately follow. The same approach could be used for probit, double exponential, double reciprocal and some other popular models in the biomedical sciences.