Statistics Toolbox

cordexch

D-optimal design of experiments - coordinate exchange algorithm

Syntax

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

Description

settings = cordexch(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] = cordexch(nfactors,nruns) also generates the associated design matrix X.

[settings,X] = cordexch(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 and squared terms.
'purequadratic'	Includes constant, linear and squared terms.

Alternatively model can be a matrix of term definitions as accepted by the x2fx function.

[settings,X] = cordexch(...,'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

The D-optimal design for two factors in nine runs using a quadratic model is the 3² factorial as shown below:

• settings = cordexch(2,9,'quadratic')
  settings =
      -1     1
       1     1
       0     1
       1    -1
      -1    -1
       0    -1
       1     0
       0     0
      -1     0
  

Algorithm

The cordexch function searches for a D-optimal design using a coordinate exchange algorithm. It creates a starting design, and then iterates by changing each coordinate of each design point in an attempt to reduce the variance of the coefficients that would be estimated using this design.

See Also
bbdesign, candexch, candgen, ccdesign, daugment, dcovary, rowexch, x2fx

cophenet

corr