  The gamma model is a generalized linear model for gamma-distributed outcomes.
The model is widely applied in psychology, ecology or medicine. In this paper
we focus on gamma models having a linear predictor without intercept. For a
specific scenario sets of locally D- and A-optimal designs are to be developed.
Recently, Gaffke et al. (2018) established a complete class and an essentially
complete class of designs for gamma models to obtain locally D-optimal designs.
However to extend this approach to gamma model without an intercept term is
complicated. To solve that further techniques have to be developed in the
current work. Further, by a suitable transformation between gamma models with
and without intercept optimality results may be transferred from one model to
the other. Additionally by means of The General Equivalence Theorem optimality
can be characterized for multiple regression by a system of polynomial
inequalities which can be solved analytically or by computer algebra. By this
necessary and sufficient conditions on the parameter values can be obtained for
the local D-optimality of particular designs. The robustness of the derived
designs with respect to misspecifications of the initial parameter values is
examined by means of their local D-efficiencies.
