Statistics Toolbox™

candexch - Candidate set row exchange

Syntax

treatments = candexch(C,nruns) treatments = candexch(...,param1,val1,param2,val2,...)

Description

treatments = candexch(C,nruns) uses a row-exchange algorithm to select treatments from a candidate design matrix C to produce a D-optimal design with nruns runs. The columns of C represent model terms evaluated at candidate treatments. treatments is a vector of length nruns giving indices of the rows in C used in the D-optimal design. The function selects a starting design at random.

treatments = candexch(...,param1,val1,param2,val2,...) specifies additional parameter/value pairs for the design. Valid parameters and their values are listed in the following table.

Parameter	Value
`'display'`	Either `'on'` or `'off'` to control display of the iteration counter. The default is `'on'`.
`'init'`	Initial design as an `nruns`-by-p matrix, where p is the number of model terms. The default is a random subset of the rows of `C`.
`'maxiter'`	Maximum number of iterations. The default is `10`.
`'start'`	A matrix of treatments as a `nobs`-by-p matrix, where p is the number of model terms, specifying a set of `nobs` fixed treatments to include in the design. The default matrix is empty. `candexch` finds `nruns-nobs` additional rows to add to the `'start'` design. The parameter provides the same functionality as the `daugment` function, using a row-exchange algorithm rather than a coordinate-exchange algorithm.
`'tries'`	Number of times to try to generate a design from a new starting point. The algorithm uses random points for each try, except possibly the first. The default is `1`.

Note The rowexch function automatically generates a candidate set using candgen, and then creates a D-optimal design from that candidate set using candexch. Call candexch separately to specify your own candidate set to the row-exchange algorithm.

Example

The following example uses rowexch to generate a five-run design for a two-factor pure quadratic model using a candidate set that is produced internally:

dRE1 = rowexch(2,5,'purequadratic','tries',10)
dRE1 =
    -1     1
     0     0
     1    -1
     1     0
     1     1

The same thing can be done using candgen and candexch in sequence:

[dC,C] = candgen(2,'purequadratic') % Candidate set
dC =
    -1    -1
     0    -1
     1    -1
    -1     0
     0     0
     1     0
    -1     1
     0     1
     1     1
C =
     1    -1    -1     1     1
     1     0    -1     0     1
     1     1    -1     1     1
     1    -1     0     1     0
     1     0     0     0     0
     1     1     0     1     0
     1    -1     1     1     1
     1     0     1     0     1
     1     1     1     1     1
treatments = candexch(C,5,'tries',10) % D-opt subset
treatments =
     2
     1
     7
     3
     4
dRE2 = dC(treatments,:) % Display design
dRE2 =
     0    -1
    -1    -1
    -1     1
     1    -1
    -1     0

You can replace C in this example with a design matrix evaluated at your own candidate set. For example, suppose your experiment is constrained so that the two factors cannot have extreme settings simultaneously. The following produces a restricted candidate set:

constraint = sum(abs(dC),2) < 2; % Feasible treatments
my_dC = dC(constraint,:)
my_dC =
     0    -1
    -1     0
     0     0
     1     0
     0     1

Use the x2fx function to convert the candidate set to a design matrix:

my_C = x2fx(my_dC,'purequadratic')
my_C =
     1     0    -1     0     1
     1    -1     0     1     0
     1     0     0     0     0
     1     1     0     1     0
     1     0     1     0     1

Find the required design in the same manner:

my_treatments = candexch(my_C,5,'tries',10) % D-opt subset
my_treatments =
     2
     4
     5
     1
     3
my_dRE = my_dC(my_treatments,:) % Display design
my_dRE =
    -1     0
     1     0
     0     1
     0    -1
     0     0

candexch - Candidate set row exchange

Syntax

Description

Example

See Also