dCE = cordexch(nfactors,nruns)
[dCE,X] = cordexch(nfactors,nruns)
[dCE,X] = cordexch(nfactors,nruns,'
[dCE,X] = cordexch(...,'
dCE = cordexch(nfactors,nruns) uses
a coordinate-exchange algorithm to generate a D-optimal
nruns runs (the
dCE) for a linear additive model with
(the columns of
dCE). The model includes a constant
[dCE,X] = cordexch(nfactors,nruns) also
returns the associated design matrix
X, whose columns
are the model terms evaluated at each treatment (row) of
[dCE,X] = cordexch(nfactors,nruns,' uses
the linear regression model specified in
one of the following:
'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
The order of the columns of
X 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.
model can be a matrix
specifying polynomial terms of arbitrary order. In this case,
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
X3, then a row
[0 1 2] in
(X1.^0).*(X2.^1).*(X3.^2). A row of all
model specifies a constant term,
which can be omitted.
[dCE,X] = cordexch(...,' specifies
one or more optional name/value pairs for the design. Valid parameters
and their values are listed in the following table. Specify
Lower and upper bounds for each factor, specified as
Indices of categorical predictors.
Handle to a function that excludes undesirable runs.
If the function is f, it must support the syntax b = f(S),
where S is a matrix of treatments with
Initial design as a
Vector of number of levels for each factor. Not used
Maximum number of iterations. The default is
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
A structure that specifies whether to run in parallel, and specifies the random stream or streams. This option requires Parallel Computing Toolbox™.
Suppose you want a design to estimate the parameters in the following three-factor, seven-term interaction model:
cordexch to generate a D-optimal
design with seven runs:
nfactors = 3; nruns = 7; [dCE,X] = cordexch(nfactors,nruns,'interaction','tries',10) dCE = -1 1 1 -1 -1 -1 1 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 -1 1 X = 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 -1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1
Columns of the design matrix
X are the model
terms evaluated at each row of the design
The terms appear in order from left to right: constant term, linear
terms (1, 2, 3), interaction terms (12, 13, 23). Use
fit the model, as described in Linear Regression, to response data measured at the design
iterative search algorithms. They operate by incrementally changing
an initial design matrix X to increase D =
at each step. In both algorithms, there is randomness built into the
selection of the initial design and into the choice of the incremental
changes. As a result, both algorithms may return locally, but not
globally, D-optimal designs. Run each algorithm
multiple times and select the best result for your final design. Both
functions have a
'tries' parameter that automates
this repetition and comparison.
Unlike the row-exchange algorithm used by
not use a candidate set. (Or rather, the candidate set is the entire
design space.) At each step, the coordinate-exchange algorithm exchanges
a single element of X with a new element evaluated
at a neighboring point in design space. The absence of a candidate
set reduces demands on memory, but the smaller scale of the search
means that the coordinate-exchange algorithm is more likely to become
trapped in a local minimum.
To run in parallel, set the
'UseParallel' option to
'UseParallel' field of the options structure to
statset and specify the
'Options' name-value pair argument in the call to this function.
For more information, see the
'Options' name-value pair argument.
For more general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).