Generates central composite designs (R.W. Payne).
Options
PRINT = string token |
Controls printed output (design); if unset in an interactive run AGCENTRALCOMPOSITE will ask whether the design is to be printed, in a batch run the default is not to print anything |
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NCENTRALPOINTS = scalar |
Defines the number of central points to include; default 4 |
NSTARPOINTS = scalar |
Defines the number of star points to include; default 1 |
LFACTORIAL = variate |
Defines the treatment levels in the factorial part of the design; default !(-1,1) |
LSTAR = variate |
Defines the treatment levels for the star points; default is to use the levels defined by LFACTORIAL |
FRACTION = scalar |
Denominator for fractional factorial; default 1 specifies a complete design |
SEED = scalar |
Seed to be used to randomize each design; a negative value implies no randomization |
STATEMENT = text |
Saves a command to recreate the design (useful if the design information has been specified in response to questions from AGCENTRALCOMPOSITE) |
Parameter
TREATMENTFACTOR = factors |
Treatment factors |
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Description
Central composite designs are used for estimating quadratic response surfaces, that is, the model to be fitted to the results is a quadratic function of the various factors. The design is made up of three sets of points.
a) a factorial design: usually this contains all combinations of the factors at a pair of levels (l1,l2), but for five or more factors it is feasible to use a fractional factorial (and still be able to estimate all the parameters of the response surface)
b) star points: this contains a pair of points for each factor where the other factors take the value (l1+l2)/2 and the factor has the values s1 and s2
c) centre points: here all the factors have the value (l1+l2)/2
The treatment factors are listed using the TREATMENTFACTOR parameter. If this is omitted in an interactive run, you will be asked how many factors you want and their names. The number of central points is specified by the NCENTRALPOINTS option; by default this is taken to be four. The LFACTORIAL option can supply a variate to specify the levels to be used in (a); the defaults are 1 and -1 (so the central point is at zero). Similarly, LSTAR specifies the levels for (b), which are taken, by default, to be the same as in (a). The star levels must, however, be equally spaced around the centre point. Option NSTARPOINTS defines how may replicates to have of each star point. The FRACTION option supplies the denominator of a fractional design, if required for (a); the default of one indicates that a complete factorial design is to be used.
The SEED option allows you to specify a seed to be used to randomize the design. In batch the default seed is -1, to suppress randomization. If you do not set SEED when running interactively AGCENTRALCOMPOSITE will ask for a seed, and again a negative value suppresses any randomization. The PRINT option can be set to design to print the plan of the design. By default, if you are running Genstat in batch, the plan is not printed. If you do not set PRINT when running interactively, AGCENTRALCOMPOSITE will ask whether or not you wish to print the design.
The STATEMENT option allows you to save a Genstat text structure containing a command to recreate the design. This is particularly useful if AGCENTRALCOMPOSITE is being used interactively, and the information to define the design has been provided in response to questions from the procedure.
Options: PRINT, NCENTRALPOINTS, NSTARPOINTS, LFACTORIAL, LSTAR, FRACTION, SEED, STATEMENT.
Parameter: TREATMENTFACTOR.
Method
The QUESTION procedure is used to obtain the necessary details of the design and this is then generated by the Genstat manipulation directives and procedure AGFRACTION.
See also
Directive: AFRESPONSESURFACE.
Procedures: AFNONLINEAR, AGBOXBEHNKEN, AGMAINEFFECT, RQUADRATIC.
Commands for: Design of experiments, Regression analysis.
Example
CAPTION 'AGCENTRALCOMPOSITE example',!t(\
'This generates a design for two treatment factors with',\
'factorial levels -1 and +1, star points at -1.5 and +1.5.',\
'and four central points at zero.'); STYLE=meta,plain
AGCENTRALCOMPOSITE [PRINT=design; LSTAR=!(-1.5,1.5)] A,B