Confidence bands for logistic regression with restricted predictor variables

Confidence bands are constructed for the logistic response function when there is an interval restriction on each of the predictor variables. The construction involves application of a general fitting procedure using Scheffé's S-method, described by Casella and Strawderman (1980, Journal of the American Statistical Association 75, 862-868). Specific details are given for the case of one predictor variable, along with details for a fixed-width alternative to the S-method bands. In the one-predictor case, Monte Carlo results suggest that both bands are conservative for small sample sizes, such as N = 25. By N = 200 the S-method's coverage probabilities are seen to attain their nominal levels while the fixed-width bands remain conservative. The procedures are exemplified with data from a genetic toxicology experiment.