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Optimal Design for a Causal Structure
Linear models and mixed models are important statistical tools. But in many natural phenomena, there is more than one endogenous variable involved and these variables are related in a sophisticated way. Structural Equation Modeling (SEM) is often used to model the complex relationships between the endogenous and exogenous variables. It was first implemented in research to estimate the strength and direction of direct and indirect effects among variables and to measure the relative magnitude of each causal factor. Historically, traditional optimal design theory focuses on univariate linear, nonlinear, and mixed models. There is no current literature on the subject of optimal design for a causal structure, therefore this research is the first contribution in the field. There are five objectives for this dissertation research. For a given causal structure, the objectives of this research are to obtain an optimal design: (1) For a completely randomized experiment that produces the most precise estimates for the endogenous and exogenous parameters, (2) For an experiment with random blocks or split-plots that produces the most precise estimates for the endogenous and exogenous parameters, (3) For an experiment with fixed blocks that produces the most precise estimates for the endogenous and exogenous parameters, (4) For an experiment with random blocks or split-plots that produces the most precise estimates for the endogenous parameters, exogenous parameters, and the variance components, and (5) Using the methods above to demonstrate the improvement in efficiency for two applications published in previous research. In each case, the causal relationship dramatically changed the optimal designs. The new optimal designs were more efficient. Even orthogonal designs, which are universally optimal in the univariate case, are not optimal when considering a causal structure.
Kmail, Zaher M, "Optimal Design for a Causal Structure" (2019). ETD collection for University of Nebraska - Lincoln. AAI22615881.