by Heiligers, B., Hilgers, R.-D..

**Series:** 2002-04, Preprints

- MSC:
- 62K05 Optimal designs
- 62J05 Linear regression

**Abstract:**

In many applications of mixture experiments in medicine or

biology, for example, not only the proportions of the

involved mixture ingredients, but also their total amount is

of particular interest. This calls for disigns in mixture

amount models, which are obtained from classical mixture

setups by including terms capturing the total amount,

simultaneously dropping the sidecondition on the proportions

to sum up to one. While design optimality usually depends

sensitively on the underlying model, we establish here a

close relation between admissible mixture, and admissible

mixture amount designs in additive and homogeneous models.

This particularly allows to obtain D-, A- and V-optimal

mixture amount from optimal mixture designs, and vice versa.

We present some examples in Becker's and Scheffé's mixture

models.

**Keywords:**

Admissibility, A-optimality, approximate design, Becker models, complete class, D-optimality, I-optimality, mixture amount experiments, mixture experiments, V-optimality, tic-type polynomials.

**This paper was published in:**

Statistica Sinica 13 (2003), 3, S.709-726.