INFORMATION MATRICES FOR MIXED EFFECTS MODELS WITH APPLICATIONS TO THE OPTIMALITY OF REPEATED MEASUREMENTS DESIGNS

A theorem is proved on the structure of the information matrix for certain mixed effects models formed by making one of a number of fixed terms in a fixed effects model random. A typical application is in repeated measurements designs where the selected effect is a residual effect and the remaining effects are the direct treatment effect, the unit effect and the period effect. It tums out in general that under a suitable balance condition the information matrix for estimation of the treatment effect is completely symmetric for all values of the random effect variance, sigma2. This allows the use of 'proposition 1' of Kiefer (A Survey of Statistical Design and Linear Models, 1975) to establish universal optimality for all values of sigma2. The theorem is quite general and can be applied to several situations in which optimality has been proved for the fixed effects case.