Statistics Toolbox

dcovary

D-optimal design with specified fixed covariates

Syntax

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

Description

settings = dcovary(nfactors,covariates) uses a coordinate exchange algorithm to generate a D-optimal design for nfactors factors, subject to the constraint that it also include the fixed covariate values in the input matrix covariates. The number of runs in the design is taken to be the number of rows in the covariates matrix. The output matrix settings is the matrix of factor settings for the design, including the fixed covariates.

[settings,X] = dcovary(nfactors,covariates) also generates the associated design matrix, X.

[settings,X] = dcovary(nfactors,covariates,'model') also controls the order of the regression model. The input, 'model', can be one of these:

'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. The model is applied to the fixed covariates as well as the regular factors. If you want to treat the fixed covariates specially, for example by including linear terms for them but quadratic terms for the regular factors, you can do this by creating the proper 'model' matrix.

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

Example 1. Generate a design for three factors in 2 blocks of 4 runs.

• blk = [-1 -1 -1 -1  1 1 1 1]';
  dsgn = dcovary(3,blk)
  
  dsgn =
      -1     1     1    -1
       1    -1    -1    -1
      -1     1    -1    -1
       1    -1     1    -1
       1     1    -1     1
       1     1     1     1
      -1    -1     1     1
      -1    -1    -1     1
  

Example 2. Suppose we want to block an eight run experiment into 4 blocks of size 2 to fit a linear model on two factors.

• covariates = dummyvar([1 1 2 2 3 3 4 4]);
  settings = dcovary(2,covariates(:,1:3),'linear')
  settings =
       1     1     1     0     0
      -1    -1     1     0     0
      -1     1     0     1     0
       1    -1     0     1     0
       1     1     0     0     1
      -1    -1     0     0     1
      -1     1     0     0     0
       1    -1     0     0     0
  

The first two columns of the output matrix contain the settings for the two factors. The last three columns are dummy variable codings for the four blocks.

Algorithm

The dcovary function creates a starting design that includes the fixed covariate values, and then iterates by changing the non-fixed cordinates of each design point in an attempt to reduce the variance of the coefficients that would be estimated using this design.

See Also
cordexch, daugment, rowexch, x2fx

daugment

dendrogram