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D-optimal augmentation


dCE2 = daugment(dCE,mruns)
[dCE2,X] = daugment(dCE,mruns)
[dCE2,X] = daugment(dCE,mruns,model)
[dCE2,X] = daugment(...,param1,val1,param2,val2,...)


dCE2 = daugment(dCE,mruns) uses a coordinate-exchange algorithm to D-optimally add mruns runs to an existing experimental design dCE for a linear additive model.

[dCE2,X] = daugment(dCE,mruns) also returns the design matrix X associated with the augmented design.

[dCE2,X] = daugment(dCE,mruns,model) uses the linear regression model specified in model. model is 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:

  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.

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.

[dCE2,X] = daugment(...,param1,val1,param2,val2,...) specifies additional parameter/value pairs for the design. Valid parameters and their values are listed in the following table.


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


Indices of categorical predictors.


Either 'on' or 'off' to control display of the iteration counter. The default is 'on'.


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 nfactors columns, where nfactors is the number of factors, and b is a vector of Boolean values with the same number of rows as S. b(i) is true if the ith row S should be excluded.


Initial design as an mruns-by-nfactors matrix, where nfactors is the number of factors. The default is a randomly selected set of points.


Vector of number of levels for each factor.


Maximum number of iterations. The default is 10.


The value is a structure that contains options specifying whether to compute multiple tries in parallel, and specifying how to use random numbers when generating the starting points for the tries. Create the options structure with statset. Applicable statset parameters are:

  • 'UseParallel' — If true and if Parallel Computing Toolbox™ is installed, compute in parallel. If the Parallel Computing Toolbox is not installed, or 'UseParallel',false, then computation occurs in serial mode. Default is false, meaning serial computation.

  • UseSubstreams — Set to true to compute in a reproducible fashion. Default is false. To compute reproducibly, set Streams to a type allowing substreams: 'mlfg6331_64' or 'mrg32k3a'.

  • Streams — A RandStream object or cell array of such objects. If you do not specify Streams, daugment uses the default stream or streams. If you choose to specify Streams, use a single object except in the case

    • UseParallel is true

    • UseSubstreams is false

    In that case, use a cell array the same size as the Parallel pool.


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.


The daugment function augments an existing design using a coordinate-exchange algorithm; the 'start' parameter of the candexch function provides the same functionality using a row-exchange algorithm.


The following eight-run design is adequate for estimating main effects in a four-factor model:

dCEmain = cordexch(4,8)
dCEmain =
     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

To estimate the six interaction terms in the model, augment the design with eight additional runs:

dCEinteraction = daugment(dCEmain,8,'interaction')
dCEinteraction =
     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     1     1    -1
     1     1    -1    -1
     1    -1     1     1
     1     1     1    -1

The augmented design is full factorial, with the original eight runs in the first eight rows.

Extended Capabilities

Version History

Introduced before R2006a