  In this paper we extend the results of Radloff and Schwabe (2018), which
could be applied for example to Poisson regression, negative binomial
regression and proportional hazard models with censoring, to a wider class of
non-linear multiple regression models. This includes the binary response models
with logit and probit link besides other. For this class of models we derive
(locally) $D$-optimal designs when the design region is a $k$-dimensional ball.
For the corresponding construction we make use of the concept of invariance and
equivariance in the context of optimal designs as in our previous paper. In
contrast to the former results the designs will not necessarily be exact
designs in all cases. Instead approximate designs can appear. These results can
be generalized to arbitrary ellipsoidal design regions.
