check.regular function

Check for Regular Minimality/Maximality

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"))

Arguments

• 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.

Details

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

1. every row contains a single minimal/maximal entry;
2. every column contains a single minimal/maximal entry;
3. an entry $p\_ij$ of X which is minimal/maximal in the $i$th row is also minimal/maximal in the $j$th column, and vice versa.

If $p\_ij$ is the entry which is minimal/maximal in the $i$th row and in the $j$th column, the $i$th row object (in one, the first, observation area) and the $j$th 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).

Returns

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.

Author(s)

Thomas Kiefer, Ali Uenlue. Based on original MATLAB source by Ehtibar N. Dzhafarov.

References

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 : The package fechner. Journal of Statistical Software, 31 (6), 1--24. URL http://www.jstatsoft.org/v31/i06/.

See Also

check.data for checking data format; fechner, the main function for Fechnerian scaling. See also fechner-package for general information about this package.

Examples

## 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")