FPSEUDOFACTORS directive

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.