GR(ID, digits=2)
GRind(design, digits=3, arft=TRUE, scft=TRUE, cancors=FALSE, with.blocks=FALSE)
SCFTs(design, digits = 3, all = TRUE, resk.only = TRUE, kmin = NULL, kmax = ncol(design),
regcheck = FALSE, arft = TRUE, cancors = FALSE, with.blocks = FALSE)
## S3 method for class 'GRind':
print(x, quote=FALSE, ...)oa;
can also be a character string containing the name of an array listed in data frame oacatdesign, which may also includesign
is not of class design.
Per default, an existing block factor is ignored.
For desiall is TRUE, should only full resolution projections be considered?
Choosing FALSE may cause very long run times.TRUE, the function stops after the first projection size
that included squared canonical correlation different from 0 or 1.GRind, as created by function GRindprintGR returns a list with elements GR (the generalized resolution of the array, a not necessarily integer
number between 3 and 5) and RPFT (the relative projection frequency table).
GR values smaller than 5 are exact, while the number five
stands for GR.
The RPFT element is the relative projection frequency table for 4-factor projections
for GR=5. For unconfounded three- and four-column designs, GR takes the
value Inf (used to be 5 for package versions up to 0.23-4).
Function GRind works on designs with resolution at least 3 and
returns a list with elements
GRs (the two versions of
generalized resolution described in Groemping and Xu 2014),
the matrix GR.i with rows GRtot.i and GRind.i for the
factor wise generalized resolutions (also in Groemping and Xu 2014),
and optionally
the ARFT (Groemping 2013),
the SCFT (Groemping 2013),
and/or the canonical correlations.
The latter are held in an
nfac x choose(nfac-1, R-1) x max(nlev)-1 array
and are supplemented with 0es,
if there are fewer of them than the respective dfi.
The factor wise generalized resolutions are in the closed interval between
resolution and resolution + 1. In the latter case, their meaning is "at least
resolution + 1". (The print method ensures that they are printed accordingly,
but the list elements themselves are just the numbers.)
Function SCFTs returns a list of lists with a component for
each projection size considered. Each such component contains the following entries:GR, GRind, and SCFTs work for factors only and are not intended
for quantitative variables. Nevertheless it is possible to apply them to class design plans with quantitative
variables in them in some situations.
Function GR calculates the generalized resolution according to Deng and Tang (1999)
for 2-level designs or a generalization thereof according to Groemping (2011) and
Groemping and Xu (2014) for general
orthogonal arrays. It returns a value between 3 and 5, where the numeric value 5 stands for
GRind (newer than GR, and recommended) calculates the generalized
resolution, together with factor wise generalized resolution values, squared canonical correlations
and average R-squared values, as introduced in Groemping and Xu (2014) and detailed in Gr�mping (2013).
The print method for class Grind objects prints the individual factor components of GRind.i such that they
do not mislead:
Because of the shortest word approach for GR, SCFT and ARFT, a GRind.i component
can be at most one larger than the resolution. For example, if GR is 3.5 so that the
resolution is 3, the largest possible numeric value of a GRind.i component is 4, but it means ">=4".
Function SCFTs does more extensive SCFT and ARFT calculations than function GRind:
in particular, the function allows to do such calculations for more projection sizes,
either restricting attention to full resolution projections or going for ALL projections
with non-zero word lengths.
These capabilities have been introduced in relation to regularity checking based on SCFTs
(see Groemping and Bailey 2016):
Defining a factorial design as regular if all main effects are orthogonal in some sense
to effects including other factors of any order, it is conjectured that a regularity check on full resolution
projections only will suffice for identifying non-regularity (work in progress).
However, this is a conjecture only; as long as it is not proven, a definite check for this type of regularity requires checking ALL projections,
i.e. setting resk.only to FALSE. With this setting, the function may run for a very long time
(depends in particular on the number of factors)!GWLP and generalized.word.lengthoa24.bad <- oa.design(L24.2.13.3.1.4.1, columns=c(1,2,14,15))
oa24.good <- oa.design(L24.2.13.3.1.4.1, columns=c(3,10,14,15))
## generalized resolution differs (resolution is III in both cases)
GR(oa24.bad)
GR(oa24.good)
## and analogously also GRind and ARFT and SCFT
GRind(oa24.bad)
GRind(oa24.good)
## SCFTs
plan <- L24.2.12.12.1[,c(1:5,13)]
GRind(plan) ## looks regular (0/1 SCFT only)
SCFTs(plan)
SCFTs(plan, resk.only=FALSE)Run the code above in your browser using DataLab