Let X1 be the model matrix corresponding to the terms in the Model outline. Denote the matrix of model terms for the effects specified in the Alias Terms outline by X2.
The matrix A is called the alias matrix.
where V is the block diagonal covariance matrix of the responses.
where K is a diagonal matrix with these values:
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
In the Custom Design platform, you can control the weights used for If Possible terms by selecting Advanced Options > Prior Parameter Variance from the red triangle menu. There you can set prior variances for all model terms by specifying the diagonal elements of K. The option updates to show the default weights when you click Make Design.