AlgDesign (version 1.0-10)

eval.design: Evaluates a design.

Description

A design is evaluated.

Usage

eval.design(frml,design,confounding=FALSE,variances=TRUE,center=FALSE,X=NULL)

Arguments

frml

The formula used to create the design.

design

The design, which may be the design part of the output of optFederov().

confounding

If confounding=TRUE, the confounding patterns will be shown.

variances

If TRUE, the variances each term will be output.

center

If TRUE, numeric variables will be centered before frml is applied.

X

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.

Value

• confounding
  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.
• determinant
  $|M|^{1/k}$, where $M=Z'Z/N$, and Z is the model expanded $N\times k$ design matrix.
• A
  The average coefficient variance: $trace(Mi)/k$, where $Mi$ is the inverse of $M$.
• I
  The average prediction variance over X, which can be shown to be $trace((X'X*Mi)/N)$.
• Ge
  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 $X$.
• Dea
  A lower bound on D efficiency for approximate theory designs. It is equal to $exp(1-1/Ge)$.
• diagonality
  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.
• gmean.variances
  The geometric mean of the coefficient variances.