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CDNROWCOLUMNDESIGN procedure

Constructs a row-column design using CycDesigN (R.W. Payne).

Options

PRINT = strings Controls printed output (design, report, factors); default * i.e. none
LEVELS = scalar or variate Numbers of levels of the treatment factors; if unset, takes the numbers of levels declared for the factors in the TREATMENTSTRUCTURE model
NREPLICATES = scalar Number of replicates
NROWS = scalar Number of rows
NCOLUMNS = scalar Number of columns
NGROUPS = variate Group sizes for a two-factor nested treatment structure
TREATMENTFACTORS = factors Up to four factors to use in the treatment model: one factor for a one-way treatment model, two factors for a nested structure when NGROUPS is set, or two to four factors for a factorial treatment structure when NGROUPS is not set
REPLICATES = factor Replicate factor
ROWS = factor Row factor
COLUMNS = factor Column factor
RESOLVABLE = string Whether the design is resolvable (yes, no); default no
METHOD = string How to construct the design (onestage, twostage, unrestrictedtwostage); default ones
NRLATIN = scalar Number of contiguous rows to latinize; default 0 i.e. not latinized
NCLATIN = scalar Number of contiguous columns to latinize; default 0 i.e. not latinized
REPLATINGROUPS = variate Specifies the number of replicates in each column when constructing latinized designs; default * i.e. all in one column
SPATIALMODEL = string Spatial model to use with a single-treatment-factor resolvable design (integer, linearvariance, seconddifference, ev); default * i.e. none
EVDECAY = scalar Decay parameter to use when SPATIALMODEL=ev; default 0.5
WEIGHTS = variate Variate with two values specifying weightings for the main effects and for the interactions in factorial treatment structures; default !(1, 0.25)
RCWEIGHTS = variate Variate with three values specifying weightings for the within-row-and-column, between-row and between-column information; default has weight one for the within-row-and-column information, and the reciprocal of their numbers of levels for the rows and columns
SEED = scalar or variate Scalar or variate with two values specifying seeds for the random numbers used by CycDesigN to search for the best design and to randomize it – if a scalar is specified the same seed is used for both purposes; default 0 i.e. set automatically
SPREADSHEET = string Whether to put the design factors into a spreadsheet (design); default *
TIMELIMITS = scalar or variate A scalar or a variate containing up to three numbers defining the time in minutes to spend on the first phase, the second phase and the spatial phase of the search (if the 2nd or 3rd numbers are omitted they default to the maximum of those specified); default 1
NRANDOMIZATIONS = scalar
Number of randomizations to generate from the best design; default 1
TRIALS = factor Trials factor

No parameters

Description

CycDesigN is a package for the computer generation of experimental designs, which constructs optimal or near-optimal block and row-column designs; see the book Cyclic and Computer Generated Designs by John & Williams (1995). CycDesigN can also operate as a batch program, that can be called from within Genstat. This program is distributed with Genstat, and there are procedures to call the program, read its output back into Genstat, and form the relevant design factors. There are also Genstat add-in and resource files to define user menus, which can be downloaded from the VSNi website. However, before CycDesigN can be used, a license must be obtained; see vsni.co.uk/software/cycdesign for details.

This procedure, CDNROWCOLUMNDESIGN, uses the CycDesigN algoriths to form a row-column design. The treatment factors, whose values are to be formed, are specified by the TREATMENTFACTORS option. This can be set to a single factor if you want a one-way treatment structure. Alternatively, if option NGROUPS is set, you can supply two factors to define a nested model

factor_1 / factor_2

The group sizes (i.e. the number of levels of the second factor within each level of the first factor) are supplied by NGROUPS, in a variate. Otherwise, if option NGROUPS is not set, you can supply from two to four factors, to define a factorial model.

The LEVELS option can be used to define the numbers of levels of the factors, as a scalar if there is only one factor, or as a variate if there are several. The levels specified in the variate are assumed to be in the same order as the order in which the factors occur in the TREATMENTFACTORS list. LEVELS can be omitted if the factors have already been been declared with the right numbers of levels. Alternatively, if you want only a single treatment factor, and do not want to save its generated levels, you can specify its number of levels using LEVELS, and leave TREATMENTFACTORS unset.

The NROWS option can define the number of rows, and the ROWS option can supply a factor to save the levels generated for the row factor. You can omit NROWS if ROWS is set to a factor that has already been defined with the correct number of levels. Similarly, the NCOLUMNS option can define the number of columns, and the COLUMNS option can supply a factor to save the levels generated for the column factor. Finally, the NREPLICATES option can define the number of replicates of each treatment combination, and the REPLICATES option can supply a factor to save the levels generated for a replication factor.

Printed output is controlled by the PRINT option, with settings:

    design to print the design,
    report to print a report by CycDesigN on the design, and
    factors to print the factor values.

The RESOLVABLE option controls whether or not the design is resolvable i.e. whether the rows and columns can be grouped into replicates, each of which contains a single replicate of each treatment combination. Suppose that there are v treatment combinations, k rows, s columns and r replicates of each treatment combination. Then in a non-resolvable design these numbers must satisfy the condition

v × r = k × s

whereas in a resolvable design the condition is

v = k × s.

By default the design search has a single stage. However, you can use the METHOD option to request that two stages are used. The first constructs the column component design, and second forms the row-column design. (At the second stage the column component design is not changed; this is achieved by allowing only treatment interchanges to take place within columns.) If METHOD=unrestrictedtwostage, there is no restriction on the way in which the design is constructed during the first stage. Alternatively, if METHOD=twostage, an alpha design is constructed during the first stage for a resolvable design, or a cyclic design is constructed during the first stage for a non-resolvable design.

You can set option NRLATIN to request that the design is latinized by rows. If NRLATIN=1, the replication of each treatment combination is equalized as far as possible within each row. Alternatively, setting NRLATIN to n, say, aims to equalize the occurrence of the treatment combinations within each set of n contiguous rows. Similarly option NCLATIN can request that the design is latinized by columns. By default, the replicates in a latinized design are assumed to be in a single row, side by side. The REPLATINGROUPS option allows you to to define an alternative layout. For example, setting REPLATINGROUPS=!(1,2) when you have three replicates, defines two columns of replicates, the first with one replicate (replicate 1), and the second with two replicates (replicate 2 alongside replicate 1, and replicate 3 below replicate 2).

The SPATIALMODEL option lets you request that the construction of a resolvable design should take account of the separation of different treatments in rows and columns. The principle is that plots close together are assumed to be correlated more than plots further apart; a spatial model attempts to model this correlation decay. The criterion used to generate spatial designs is the neighbour efficiency factor of Williams (1985), which has been extended to two-dimensional blocking structures by Williams, John & Whitaker (2005) and to cater for different decay functions. The available settings are

    integer integer,
    linearvariance linear variance,
    seconddifference modified second difference, and
    ev modified exponential variance.

The weights used with the first three settings are described by Williams (1985). The fourth setting, ev, is appropriate for a model specifying an autoregressive variance matrix. Its decay parameter is specified by the EVDECAY option; default 0.5. However, the spatial designs generated by CycDesigN are usually quite robust to the choice of weight function. Spatial models cannot be used with latinized designs.

The WEIGHTS option and the RCWEIGHTS option specify how to weight the importance of the information in the design. WEIGHTS is used when the design has a factorial treatment structure, and RCWEIGHTS is used when there is a single treatment factor or a nested treatment structure.

The WEIGHTS option specifies a variate with two values to define how to weight the efficiencies of the terms when there is a factorial treatment structure. The first value defines a weight for the main effects (default 1), and the second defines a weight for the interactions (default 0.25) These defaults are the same as those used in the stand-alone CycDesigN system.

For designs without a factorial treatment structure, the RCWEIGHTS option specifies a variate with three values to define the weightings to use for the within-row-and-column, between-row and between-column information. By default, the within-row-and-column information is given a weight of one, the between-row information has a weight equal to the reciprocal of the number of levels of the row factor, and the between-column information has a weight equal to the reciprocal of the number of levels of the column factor. These defaults are again the same as those in the stand-alone CycDesigN system.

The SEED option lets you supply seeds for the random numbers to be used within CycDesigN to search for the best design and to randomize it. You can specify a variate with two values to supply a different seed for each purpose, or a scalar to use the same one for both. If a zero value is specified, the corresponding seed is set automatically. The default is the scalar zero.

By default only one randomization is done with the best design. However, you can use the NRANDOMIZATION option to provide several randomizations of that design, for use in different trials. The TRIALS option can save a factor to identify the trials.

You can set option SPREADSHEET=design to put the design factors into a Genstat spreadsheet.

The TIMELIMITS option can be set to a scalar or a variate containing up to three numbers to define the time in minutes to spend on the first phase, the second phase and the spatial phase of the design search. If the second or third numbers are omitted, they default to the maximum of those specified. The default is 1.

Options: PRINT, LEVELS, NREPLICATES, NROWS, NCOLUMNS, NGROUPS, TREATMENTFACTORS, REPLICATES, ROWS, COLUMNS, RESOLVABLE, METHOD, NRLATIN, NCLATIN, REPLATINGROUPS, SPATIALMODEL, EVDECAY, SEED, WEIGHTS, RCWEIGHTS, SPREADSHEET, TIMELIMITS, NRANDOMIZATION, TRIALS.

Parameters: none.

Method

The batch program CycDesRun is called using the SUSPEND directive.

References

John, J.A. & Williams, E.R. (1995). Cyclic and Computer Generated Designs. London: Chapman and Hall.

Williams, E.R. (1985). A criterion for the construction of optimal neighbour designs. J.R. Statist. Soc. B, 47, 487-497.

Williams, E.R., John, J.A. & Whitaker, D. (2005). Construction of resolvable spatial row-column designs. Biometrics, 62, 103-108.

See also

Procedures: CDNPREP, CDNBLOCKDESIGN.

Commands for: Design of experiments.

Example

CAPTION            'CDNROWCOLUMNDESIGN example'; STYLE=meta
FACTOR             [LEVELS=25] treat
FACTOR             [LEVELS=5] row
FACTOR             [LEVELS=10] column
FACTOR             [LEVELS=2] rep
CDNROWCOLUMNDESIGN [PRINT=design; TREATMENT=treat;\
                   REPLICATES=rep; ROWS=row; COLUMNS=column;\
                   RESOLVABLE=no; SEED=38417; TIMELIMITS=0.2]
Updated on September 2, 2019

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