This section provides information about I, D, Bayesian I, Bayesian D, and AliasOptimal designs.
DOptimality
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is the default design type produced by the custom designer except when the RSM button has been clicked to create a full quadratic model.

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has runs whose purpose is to lower the variability of the coefficients of this prestated model. By focusing on minimizing the standard errors of coefficients, a DOptimal design may not allow for checking that the model is correct. It will not include center points when investigating a firstorder model. In the extreme, a DOptimal design may have just p distinct runs with no degrees of freedom for lack of fit.

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maximizes D when

Doptimal split plot designs maximize D when
Bayesian DOptimality
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is a modification of the DOptimality criterion that effectively estimates the coefficients in a model, and at the same time has the ability to detect and estimate some higherorder terms. If there are interactions or curvature, the Bayesian DOptimality criterion is advantageous.

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works best when the sample size is larger than the number of Necessary terms but smaller than the sum of the Necessary and If Possible terms. That is, p + q > n > p. The Bayesian DOptimal design is an approach that allows the precise estimation of all of the Necessary terms while providing omnibus detectability (and some estimability) for the If Possible terms.

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uses the If Possible terms to force in runs that allow for detecting any inadequacy in the model containing only the Necessary terms. Let K be the (p + q) by (p + q) diagonal matrix whose first p diagonal elements are equal to 0 and whose last q diagonal elements are the constant, k. If there are 2factor interactions then k = 4. Otherwise k = 1. The Bayesian DOptimal design maximizes the determinant of (X'X + K2). The difference between the criterion for DOptimality and Bayesian DOptimality is this constant added to the diagonal elements corresponding to the If Possible terms in the X'X matrix.

IOptimality
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is more appropriate than DOptimality if your goal is to predict the response rather than the coefficients, such as in response surface design problems. Using the IOptimality criterion is more appropriate because you can predict the response anywhere inside the region of data and therefore find the factor settings that produce the most desirable response value. It is more appropriate when your objective is to determine optimum operating conditions, and also is appropriate to determine regions in the design space where the response falls within an acceptable range. Precise estimation of the response therefore takes precedence over precise estimation of the parameters.

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minimizes this criterion: If f '(x) denotes a row of the X matrix corresponding to factor combinations x, then

Bayesian IOptimality
Bayesian IOptimality has a different objective function to optimize than the Bayesian Doptimal design, so the designs that result are different. The variance matrix of the coefficients for Bayesian Ioptimality is X'X + K where K is a matrix having zeros for the Necessary model terms and some constant value for the If Possible model terms.
The Bayesian IOptimal design minimizes the average prediction variance over the design region:
where M is defined as before.
Specifically, let X1 be the design matrix corresponding to the model effects, and let X2 be the matrix of alias effects, and let