Statistical Optimal Design Theory
Heinz Holling, Rainer Schwabe · 2017
Optimal design allows for estimating parameters of statistical models according to certain optimality criteria, for example, minimal standard errors of estimators. Thus, optimal designs may considerably reduce the number of experimental units and costs of empirical studies. Optimal design is applied in nearly all natural, social, and educational sciences. In the field of item response theory, it was introduced by Berger and van der Linden. In the Bayesian optimal design literature, mostly D-optimality has been dealt with. Unlike local D-optimality, several criteria for Bayesian D-optimality can be derived, dependent on where the weighting with the prior information occurs in the formula. The first is known as optimal test design and concerns the selection of items into a test to efficiently estimate person parameters. Optimal sampling or calibration designs refers to the search of the best sample of test-takers for estimating item parameters.