On optimality criteria of experimental block designs under linear mixed models

Rok, strany: 1996, 45 - 52

Most of optimality criteria of experimental designs (for instance: $A$, $D$, $E$ or different kinds of universal optimality) were defined in a case of linear fixed model. All of the criteria are based on an information matrix for fixed parameters (treatments). In a case of mixed linear model there arises the question: “Is it reasonable to apply the same optimality criteria as in the fixed model?” We consider experimental designs under linear mixed models where the structure of dispersion matrix follows from a randomization model. The adequacy and applicability of such models to practical experiments were underlined by many authors. In the mixed model case interest often lies both on treatment parameters and on variance components and the information matrix can be defined for these two kinds of parameters. Even if we are interested only in fixed effects of the model, the information matrix defined for them depends on the dispersion matrix which is a function of variance components and also of other design parameters. It implies that applicability of some criteria becomes a troublesome question. In the paper we discuss this problem.

ISO 690:

Bogacka, B., Mejza, I. 1996. On optimality criteria of experimental block designs under linear mixed models. In Tatra Mountains Mathematical Publications, vol. 7, no.1, pp. 45-52. 1210-3195.

APA:

Bogacka, B., Mejza, I. (1996). On optimality criteria of experimental block designs under linear mixed models. Tatra Mountains Mathematical Publications, 7(1), 45-52. 1210-3195.