| Summary: | The response surface problem is two-fold: to predict values of the response, and to optimize the response. Slope estimation criteria are well suited for the optimization problem. Response prediction capability has been assessed by plotting the average, maximum, and minimum prediction variances on the surface of spheres with radii ranging across the region of interest. Average and maximum prediction bias plots have recently been added to the spherical criteria. Combined with the prediction variance, a graphical MSE criterion results. This research extends these ideas to the slope estimation objective.
A direct relationship between precise slope estimation and the ability to pinpoint the location of the optimum is developed, resulting in a general slope variance measure related to E-optimality in slope estimation. A more specific slope variance measure is defined and analyzed for use in evaluating standard response surface (RS) designs,where slopes parallel to the factor axes are estimated with equal precision. Standard second order RS designs are then studied in light of the prediction and optimization goal distinction. Designs which perform well for prediction of the response do not necessarily estimate the slope precisely.
A spherical measure of bias in slope estimation is developed and used to measure slope bias due to model misspecification and due to the presence of outliers. A study of augmenting saturated orthogonal arrays of strength two to detect lack of fit is included as an application of a combined squared bias and variance measure of MSE in slope.
A study of the designs recommended for precise slope estimation in their robustness to outliers and to missing observations is conducted using the slope bias and general slope variance measures, respectively. === Ph. D.
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