\(D\)-optimal design for a causal structure for completely randomized and random blocked experiments (Q2095788)

Summary: Most experimental design literature on causal inference focuses on establishing a causal relationship between variables, but there is no literature on how to identify a design that results in the optimal parameter estimates for a structural equation model (SEM). In this research, search algorithms are used to produce a \(D\)-optimal design for a SEM for three-stage least squares and full information maximum likelihood estimators. Then, a \(D\)-optimal design for the estimate of the model parameters of a mixed-effects SEM is obtained. The efficiency of each of the \(D\)-optimal designs for SEMs is compared with univariate optimal and uniform designs. In each case, the causal relationship changed the optimal designs dramatically and the new \(D\)-optimal designs were more efficient.