Extensions to confidence region calculations for the path of steepest ascent

The method of steepest ascent plays an important role in response surface methodology by giving a direction for further experimentation after an initial factorial design. To determine whether the path of steepest ascent has been determined precisely enough, the fraction of all possible directions that are included in the confidence 'cone' around the fitted path of steepest ascent can be calculated. In this paper, extensions to the existing method are made to cover heterogeneous error variances, nonorthogonal designs and generalized linear models. We also propose a design criterion for augmenting a given experimental design in problems for which the path of steepest ascent has not been determined precisely enough.