"To estimate or to predict" - implications on the design for linear mixed models
Seminar Room 1, Newton Institute
During the last years mixed models have attracted an increasing popularity in many fields of applications due to advanced computer facilities. Although the main theme of the present workshop is devoted to optimal design of experiments for non-linear mixed models, it may be illustrative to elaborate the specific features of mixed models already in the linear case: Besides the estimation of population (location) parameters for the mean behaviour of the individuals a prediction of the response for the specific individuals under investigation may be of prior interest, for example in oncology studies to determine the further treatment of the patients investigated.
While there have been some recent developments in optimal design for estimating the population parameters, the problem of optimal design for prediction has been considered as completely solved since the seminal paper by Gladitz and Pilz (1982). However, the optimal designs obtained there require the population parameters to be known or may be considered as an approximation, if the number of individuals is large. The latter may be inadequate, when the resulting "optimal design" fails to allow for estimation of the population parameters. Therefore we will develop the theory and solutions for finite numbers of individuals. Finally we will illustrate the trade-off in optimal designs caused by the two competing aims of estimation and prediction by a simple example.
Gladitz, J. and J. Pilz (1982): Construction of optimal designs in random coefficient regression models. Statistics 13, 371-385.