• D-Optimality
 • Bayesian D-Optimality
 • I-Optimality
 • Bayesian I-Optimality
 • Alias Optimality
 • screening designs
 • experiments that focus on estimating effects or testing for significance
 • designs where identifying the active factors is the experimental goal
Specifically, a D-optimal design maximizes D, where D is defined as follows:
and where X is the model matrix as defined in Simulate Responses.
D-optimal split-plot designs maximize D, where D is defined as follows:
Bayesian D-optimality is a modification of the D-optimality criterion. The Bayesian D-optimality criterion is useful when there are potentially active interactions or non-linear effects. See DuMouchel and Jones (1994) and Jones et al (2008).
 • X is the model matrix as defined in Simulate Responses
 • K is a diagonal matrix with values as follows:
 – k = 0 for Necessary terms
 – k = 1 for If Possible main effects, powers, and interactions involving a categorical factor with more than two levels
 – k = 4 for all other If Possible terms
The prior distribution imposed on the vector of If Possible parameters is multivariate normal, with mean vector 0 and diagonal covariance matrix with diagonal entries . Therefore, a value is the reciprocal of the prior variance of the corresponding parameter.
The values for k are empirically determined. If Possible main effects, powers, and interactions with more than one degree of freedom have a prior variance of 1. Other If Possible terms have a prior variance of 1/16. In the notation of DuMouchel and Jones, 1994, .
To control the weights for If Possible terms, select Advanced Options > Prior Parameter Variance from the red triangle menu. See Advanced Options > Prior Parameter Variance.
 • predict a response
 • determine optimum operating conditions
 • determine regions in the design space where the response falls within an acceptable range
where X is the model matrix as defined in Simulate Responses.
I-optimal designs minimize the integral I of the prediction variance over the entire design space, where I is given as follows:
Here M is the moments matrix:
See Simulate Responses. For further details, see Goos and Jones (2011).
The moments matrix does not depend on the design and can be computed in advance. The row vector f (x)’ consists of a 1 followed by the effects corresponding to the assumed model. For example, for a full quadratic model in two continuous factors, f (x)’ is defined as follows:
 • X is the model matrix, defined in Simulate Responses
 • K is a diagonal matrix with values as follows:
 – k = 0 for Necessary terms
 – k = 1 for If Possible main effects, powers, and interactions involving a categorical factor with more than two levels
 – k = 4 for all other If Possible terms
The prior distribution imposed on the vector of If Possible parameters is multivariate normal, with mean vector 0 and diagonal covariance matrix with diagonal entries . (See Bayesian D-Optimality for more details about the values k.)
where M is the moments matrix. See Simulate Responses.
Specifically, let X1 be the model matrix corresponding to the terms in the assumed model, as defined in Simulate Responses. The design defines the model that corresponds to the alias effects. Denote the matrix of model terms for the alias effects by X2.
The alias matrix is the matrix A, defined as follows:
The sum of squares of the entries in A provides a summary measure of bias. This sum of squares can be represented in terms of a trace as follows:

Help created on 9/19/2017