candgen

Candidate set generation

Syntax

dC = candgen(nfactors,'model')
[dC,C] = candgen(nfactors,'model')
[...] = candgen(nfactors,'model','Name',value)

Description

dC = candgen(nfactors,'model') generates a candidate set dC of treatments appropriate for estimating the parameters in the model with nfactors factors. dC has nfactors columns and one row for each candidate treatment. model is one of the following strings, specified inside single quotes:

  • linear — Constant and linear terms. This is the default.

  • interaction — Constant, linear, and interaction terms

  • quadratic — Constant, linear, interaction, and squared terms

  • purequadratic — Constant, linear, and squared terms

Alternatively, model can be a matrix specifying polynomial terms of arbitrary order. In this case, model should have one column for each factor and one row for each term in the model. The entries in any row of model are powers for the factors in the columns. For example, if a model has factors X1, X2, and X3, then a row [0 1 2] in model specifies the term (X1.^0).*(X2.^1).*(X3.^2). A row of all zeros in model specifies a constant term, which can be omitted.

[dC,C] = candgen(nfactors,'model') also returns the design matrix C evaluated at the treatments in dC. The order of the columns of C for a full quadratic model with n terms is:

  1. The constant term

  2. The linear terms in order 1, 2, ..., n

  3. The interaction terms in order (1, 2), (1, 3), ..., (1, n), (2, 3), ..., (n – 1, n)

  4. The squared terms in order 1, 2, ..., n

Other models use a subset of these terms, in the same order.

Pass C to candexch to generate a D-optimal design using a coordinate-exchange algorithm.

[...] = candgen(nfactors,'model','Name',value) specifies one or more optional name/value pairs for the design. Valid parameters and their values are listed in the following table. Specify Name inside single quotes.

NameValue
bounds

Lower and upper bounds for each factor, specified as a 2-by-nfactors matrix. Alternatively, this value can be a cell array containing nfactors elements, each element specifying the vector of allowable values for the corresponding factor.

categorical

Indices of categorical predictors.

levels

Vector of number of levels for each factor.

    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.

Examples

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, C
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) % Find 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

See Also

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