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

Analytic solutions for locally optimal designs for gamma models having linear predictor without intercept