Candidate set generation
dC = candgen(nfactors,'
model
')
[dC,C] = candgen(nfactors,'model
')
[...] = candgen(nfactors,'model
','Name
',value
)
dC = candgen(nfactors,'
generates
a candidate set model
')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,'
also
returns the design matrix model
')C
evaluated at the treatments
in dC
. The order of the columns of C
for
a full quadratic model with n terms is:
The constant term
The linear terms in order 1, 2, ..., n
The interaction terms in order (1, 2), (1, 3), ..., (1, n), (2, 3), ..., (n – 1, n)
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,'
specifies
one or more optional name/value pairs for the design. Valid parameters
and their values are listed in the following table. Specify model
','Name
',value
)Name
inside
single quotes.
Name | Value |
---|---|
bounds | Lower and upper bounds for each factor, specified as
a |
categorical | Indices of categorical predictors. |
levels | Vector of number of levels for each factor. |
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