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 |
---|---|

`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 |
---|

### 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 (*l*_{1},*l*_{2}), 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 (*l*_{1}+*l*_{2})/2 and the factor has the values *s*_{1} and *s*_{2}

c) centre points: here all the factors have the value (*l*_{1}+*l*_{2})/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