A design is evaluated.
eval.design(frml,design,confounding=FALSE,variances=TRUE,center=FALSE,X=NULL)The formula used to create the design.
The design, which may be the design part of the output of optFederov().
If confounding=TRUE, the confounding patterns will be shown.
If TRUE, the variances each term will be output.
If TRUE, numeric variables will be centered before frml is applied.
X is either the matrix describing the prediction space for I or for G, the the candidate set from which the design was chosen. They are often the same.
A matrix. The columns of which give the regression coefficients of each variable regressed on the others. If \(C\) is the confounding matrix, then \(-ZC\) is a matrix of residuals of the variables regressed on the other variables.
\(|M|^{1/k}\), where \(M=Z'Z/N\), and Z is the model expanded \(N\times k\) design matrix.
The average coefficient variance: \(trace(Mi)/k\), where \(Mi\) is the inverse of \(M\).
The average prediction variance over X, which can be shown to be \(trace((X'X*Mi)/N)\).
The minimax normalized variance over X, expressed as an efficiency with respect to the optimal approximate theory design. It is defined as \(k/max(d)\), where \(max(d)\) is the maximum normalized variance over \(X\) -- i.e. the max of \(x'(Mi)x\), over all rows \(x'\) of \(X\).
A lower bound on D efficiency for approximate theory designs. It is
equal to \(exp(1-1/Ge)\).
The diagonality of the design, excluding the constant, if any. Diagonality is defined as \((|M_1|/\prod{diag(M_1)})^{1/k}\), where \(M_1\) is \(M\) with first column and row deleted when there is a constant.
The geometric mean of the coefficient variances.