Statistics Toolbox

candexch

D-optimal design from candidate set using row exchanges

Syntax

• rlist = candexch(C,nrows)
  rlist = candexch(C,nrows,'param1',value1,'param2',value2,...)
  

Description

rlist = candexch(C,nrows) uses a row-exchange algorithm to select a D-optimal design from the candidate set C. C is an n-by-p matrix containing the values of p model terms at each of n points. nrows is the desired number of rows in the design. rlist is a vector of length nrows listing the selected rows.

The candexch function selects a starting design X at random, and uses a row-exchange algorithm to iteratively replace rows of X by rows of C in an attempt to improve the determinant of X'*X.

rlist = candexch(C,nrows,'param1',value1,'param2',value2,...) provides more control over the design generation through a set of parameter/value pairs. Valid parameters are the following:

Parameter	Value
'display'	Either 'on' or 'off' to control display of iteration number The default is 'on'.
'init'	Initial design as an nrows-by-p matrix. The default is a random subset of the rows of C.
'maxiter'	Maximum number of iterations. The default is 10.

Note    The rowexch function also generates D-optimal designs using a row-exchange algorithm, but it accepts a model type and automatically selects a candidate set that is appropriate for such a model.

Examples

Generate a D-optimal design when there is a restriction on the candidate set. In this case, the rowexch function isn't appropriate.

• F = (fullfact([5 5 5])-1)/4;    % Factor settings in unit cube.
  T = sum(F,2)<=1.51;         % Find rows matching a restriction.
  F = F(T,:);                     % Take only those rows.
  C = [ones(size(F,1),1) F F.^2]; % Compute model terms including
                              % a constant and all squared terms.
  R = candexch(C,12);         % Find a D-optimal 12-point subset.
  X = F(R,:);                 % Get factor settings.
  

See Also

candgen, cordexch, rowexch, x2fx

boxplot

candgen