Marginally restricted sequential D‐optimal designs

In many experiments, not all explanatory variables can be controlled. When the units arise sequentially, different approaches may be used. The authors study a natural sequential procedure for “marginally restricted” D‐optimal designs. They assume that one set of explanatory variables (x 1 ) is observed sequentially, and that the experimenter responds by choosing an appropriate value of the explanatory variable x 2 . In order to solve the sequential problem a priori, the authors consider the problem of constructing optimal designs with a prior marginal distribution for x 1 . This eliminates the influence of units already observed on the next unit to be designed. They give explicit designs for various cases in which the mean response follows a linear regression model; they also consider a case study with a nonlinear logistic response. They find that the optimal strategy often consists of randomizing the assignment of the values of x 2 .