Determines patterns of confounding and aliasing from design keys, and extends the treatment model to incorporate the necessary pseudo-factors.

### Options

`TREATMENTSTRUCTURE` = formula |
Treatment model for the design |
---|---|

`BLOCKSTRUCTURE` = formula |
Block model for the design |

`FACTORIAL` = scalar |
Limit on the number of factors in each treatment term |

`LROWS` = factors or scalars |
Numbers of levels of factors, or factors, corresponding to the rows of the key matrices |

`LCOLUMNS` = factors or scalars |
Numbers of levels of factors, or factors, corresponding to the columns of the key matrices |

`NEWTREATMENTSTRUCTURE` = identifier |
Store the extended treatment model |

`PSEUDOFACTORS` = pointer |
Pseudo-factors required for the keys |

`NPSEUDOFACTORS` = scalar |
Number of pseudo-factors required for the keys |

`KEYPSEUDOFACTORS` = matrix |
Key to generate the pseudo-factors from the treatment factors |

`KEYCONTRASTS` = matrix |
Key partitioning the treatment terms into orthogonal sets of contrasts |

### Parameters

`KEY` = matrices |
Design keys |
---|---|

`KEYINVERSE` = matrices |
Store the inverses of the design keys |

`ALIASSETS` = variates |
Stores aliasing information about the orthogonal sets of treatment contrasts |

`RESOLUTION` = scalars |
Saves the resolution number of the design constructed by each key |

### Description

The `FPSEUDOFACTORS`

directive examines a list of design keys, specified using the `KEY`

parameter, and forms pseudo-factors to allow the `ANOVA`

directive to cope with partial confounding or aliasing in the design generated by the keys. The factors corresponding to the rows of the keys are specified by the `LROWS`

option, and those for the columns are specified by the `LCOLUMNS`

option. If you merely want to save the inverses of the keys, using the `KEYINVERSE`

parameter, you can specify scalars defining the numbers of levels of the factors instead of the factors themselves. If `LROWS`

is not specified, `FPSEUDOFACTORS`

will take the factors from the formula specified by the `TREATMENTSTRUCTURE`

parameter, in the order that they occur there. Similarly, the `BLOCKSTRUCTURE`

option can provide a default for `LCOLUMNS`

.

`FPSEUDOFACTORS`

assumes that the design is formed by generating a replicate using each design key. The `BLOCKSTRUCTURE`

option defines the block structure within each replicate, so the full block structure would be `Rep/(#BLOCKSTRUCTURE)`

where `Rep`

is a factor for the replicates. The `TREATMENTSTRUCTURE`

option specifies the treatment terms to be estimated using the design, and the `FACTORIAL`

option allows a limit to be set on the number of factors in the terms that are generated as, for example, in the `ANOVA`

directive. `FPSEUDOFACTORS`

examines the keys to see whether any treatment terms are partially aliased or partially confounded. Provided the factors of each such term all have the same (prime) number of levels it can then extend the treatment formula, inserting pseudo-factors for these terms, so that the `ANOVA`

directive can produce a correct analysis. The extended formula can be saved using the `NEWTREATMENTSTRUCTURE`

option, and the `NPSEUDOFACTORS`

option saves the number of pseudo-factors that are needed. The pseudo-factors themselves are represented by the elements of a pointer specified by the `PSEUDOFACTORS`

option, and the `KEYPSEUDOFACTORS`

option can save the key matrix required to generate their values from the values of the treatment factors.

`FPSEUDOFACTORS`

can also determine the aliasing relationships of treatment terms in fractional factorial designs. The `KEYCONTRASTS`

option can save a design key that partitions the treatment terms into orthogonal sets of contrasts. (The matrix thus has a row for each set of contrasts, and a column for each treatment factor.) The `ALIASSETS`

parameter saves a variate, for each design key, with length equal to the number of rows in the `KEYCONTRASTS`

matrix. The variate stores integers indicating the alias group of each set of contrasts so, if two elements of the variate are equal, this indicates that the corresponding sets of contrasts are aliased in the replicate generated by the design key concerned. The `RESOLUTION`

parameter saves the resolution number for the replicate generated by each design key. This is the minimum number of factors involved in any pair of aliased terms.

Options: `TREATMENTSTRUCTURE`

, `BLOCKSTRUCTURE`

, `FACTORIAL`

, `LROWS`

, `LCOLUMNS`

, `NEWTREATMENTSTRUCTURE`

, `PSEUDOFACTORS`

, `NPSEUDOFACTORS`

, `KEYPSEUDOFACTORS`

, `KEYCONTRASTS`

.

Parameters: `KEY`

, `KEYINVERSE`

, `ALIASSETS`

, `RESOLUTION`

.

### See also

Directives: `AFMINABERRATION`

, `GENERATE`

, `FKEY`

.

Procedures: `AGFACTORIAL`

, `AKEY`

, `ARANDOMIZE`

, `FACDIVIDE`

, `FBASICCONTRASTS`

.

Commands for: Design of experiments, Analysis of variance.