Construction of estimation-equivalent second-order split-split-plot designs
In many experimental settings, some experimental factors are very hard to change or very expensive to change, some factors are hard to change, and some factors are easy to change, which usually leads to a split-split-plot design. In such a case, there are randomization restrictions in our experiments. If the data is analyzed as if it were a completely randomized design, the results could be misleading. The analysis of split-split-plot designs is more complicated relative to the completely randomized design, as generalized least squares (GLS) is recommended for estimating the factor effects, and restricted maximum likelihood (REML) is recommended for estimating the variance components. As an alternative, one can consider estimation-equivalent designs, wherein ordinary least squares (OLS) and GLS estimates of the factor effects are equivalent. These designs provide practical benefits from the perspective of design selection and estimation and are consistent with traditional response surface methods. Although much work has been done with respect to estimation-equivalent second-order split-plot designs, less emphasis has been placed on split-split-plot (and higher strata) designs of this type. My research is to derive the general conditions for achieving OLS-GLS equivalence and use these conditions to construct balanced and unbalanced estimation-equivalent second-order split-split-plot designs from the central composite design (CCD).