Statistics Toolbox

rowexch

D-optimal design of experiments - row exchange algorithm

Syntax

• settings = rowexch(nfactors,nruns)
  [settings,X] = rowexch(nfactors,nruns)
  [settings,X] = rowexch(nfactors,nruns,'model')
  [settings,X] = rowexch(...,'param1',value1,'param2',value2,...)
  

Description

settings = rowexch(nfactors,nruns) generates the factor settings matrix, settings, for a D-Optimal design using a linear additive model with a constant term. settings has nruns rows and nfactors columns.

[settings,X] = rowexch(nfactors,nruns) also generates the associated matrix X of term settings, often called the design matrix.

[settings,X] = rowexch(nfactors,nruns,'model') produces a design for fitting a specified regression model. The input, 'model', can be one of these strings:

'linear'	Includes constant and linear terms (the default)
'interaction'	Includes constant, linear, and cross product terms.
'quadratic'	Includes interactions plus squared terms.
'purequadratic'	Includes constant, linear and squared terms.

[settings,X] = rowexch(...,'param1',value1,'param2',value2,...) provides more control over the design generation through a set of parameter/value pairs. Valid parameters are:

'display'	Either 'on' or 'off' to control display of iteration counter. The default is 'on'.
'init'	Initial design as an nruns-by-nfactors matrix. The default is a randomly selected set of points.
'maxiter'	Maximum number of iterations. The default is 10.

Example

This example illustrates that the D-optimal design for three factors in eight runs, using an interactions model, is a two level full-factorial design.

• s = rowexch(3,8,'interaction')
  s =
      -1    -1     1
       1    -1    -1
       1    -1     1
      -1    -1    -1
      -1     1     1
       1     1     1
      -1     1    -1
       1     1    -1
  

Algorithm

The rowexch function searches for a D-optimal design using a row-exchange algorithm. It first generates a candidate set of points that are eligible to be included in the design, and then iteratively exchanges design points for candidate points in an attempt to reduce the variance of the coefficients that would be estimated using this design. If you need to use a candidate set that differs from the default one, call the candgen and candexch functions in place of rowexch.

See Also
bbdesign, candexch, candgen, ccdesign, cordexch, x2fx

robustfit

rsmdemo