check.regular {fechner} | R Documentation |
check.regular
is used to check whether the data satisfy
regular minimality/maximality.
check.regular(X, type = c("probability.different", "percent.same", "reg.minimal", "reg.maximal"))
X |
a required square matrix or data frame of numeric
data. No NA , NaN , Inf , or -Inf
values are allowed. |
type |
an optional character string giving the type of check to
be performed. This must be one of "probability.different" ,
"percent.same" , "reg.minimal" , or
"reg.maximal" , with default "probability.different" ,
and may be abbreviated to a unique prefix. |
The type
argument specifies whether regular minimality or
regular maximality is to be checked. "probability.different"
and "percent.same"
are for datasets in the
probability-different and percent-same formats, and imply regular
minimality and regular maximality checks, respectively.
"reg.minimal"
and "reg.maximal"
can be specified to
force checking for regular minimality and regular maximality,
respectively, independent of the used dataset. In particular,
"reg.minimal"
and"reg.maximal"
are to be used for
datasets that are properly in the general format.
check.regular
calls check.data
. In
particular, the rows and columns of the canonical
representation matrix (see ‘Value’) are canonically
relabeled based on the labeling provided by
check.data
. That is, using the
check.data
labeling, the pairs of points of subjective
equality (PSEs) are assigned identical labels, leaving intact the
labeling of the rows and relabeling the columns with their
corresponding PSEs. If the data X
do not satisfy regular
minimality/maximality, check.regular
produces respective
messages. The latter give information about parts of X
violating that condition.
Regular minimality/maximality is a fundamental property of discrimination and means that
X
which is
minimal/maximal in the ith row is also minimal/maximal
in the jth column, and vice versa.
If p\_ij is the entry which is minimal/maximal in the ith row and in the jth column, the ith row object (in one, the first, observation area) and the jth column object (in the other, the second, observation area) are called each other's PSEs. In psychophysical applications, for instance, observation area refers to the two fixed and perceptually distinct areas in which the stimuli are presented pairwise; for example, spatial arrangement (left versus right) or temporal order (first versus second).
If the data do satisfy regular minimality/maximality,
check.regular
returns a named list consisting of the
following four components:
canonical.representation |
a matrix giving the
representation of X in which regular
minimality/maximality is satisfied in the canonical form.
That is, the single minimal/maximal entries of the rows and
columns lie on the main diagonal (of the canonical
representation). In addition, the rows and columns are
canonically relabeled. |
canonical.transformation |
a data frame giving the
permutation of the columns of X used to produce the
canonical representation of X . The first and second
variables of this data frame, observation.area.1 and
observation.area.2 , respectively, represent the pairs
of PSEs. The third variable, common.label , lists the
identical labels assigned to the pairs of PSEs. |
check |
a character string giving the check that was
performed. This is either "regular minimality" or
"regular maximality" . |
in.canonical.form |
logical. If TRUE , the
permutation of the columns used to obtain the canonical
representation of X is the identity; that is, the
original data X are already in the canonical form. |
Thomas Kiefer thomas.kiefer@student.uni-augsburg.de, Ali Uenlue ali.uenlue@math.uni-augsburg.de. Based on original MATLAB source by Ehtibar N. Dzhafarov.
Dzhafarov, E. N. and Colonius, H. (2006) Reconstructing distances among objects from their discriminability. Psychometrika, 71, 365–386.
Dzhafarov, E. N. and Colonius, H. (2007) Dissimilarity cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290–304.
Uenlue, A. and Kiefer, T. and Dzhafarov, E. N. (2009) Fechnerian scaling in R: The package fechner. Journal of Statistical Software, 31(6), 1–24. URL http://www.jstatsoft.org/v31/i06/.
check.data
for checking data format;
fechner
, the main function for Fechnerian scaling.
See also fechner-package
for general information
about this package.
## dataset \link{wish} satisfies regular minimality in canonical form check.regular(wish) ## dataset \link{regMin} satisfies regular minimality in non-canonical ## form and so is canonically transformed and relabeled regMin check.regular(regMin) ## dataset \link{noRegMin} does satisfy neither regular minimality nor ## regular maximality check.regular(noRegMin, type = "probability.different") check.regular(noRegMin, type = "reg.maximal") ## dataset \link{morse} satisfies regular maximality in canonical form check.regular(morse, type = "percent.same") ## part of \link{morse} data satisfies regular maximality check.regular(morse[c(2, 27:36), c(2, 27:36)], type = "reg.maximal")