fechner (version 1.0-3)

summary.fechner: Summary Method for Objects of Class fechner

Description

S3 method to summarize objects of the class fechner.

Usage

"summary"(object, level = 2, ...)

Arguments

object

a required object of class fechner, obtained from a call to the function fechner.

level

an optional numeric, integer-valued and greater than or equal to $2$, giving the level of comparison of the $S$-index and the overall Fechnerian distance $G$.

...

further arguments to be passed to or from other methods. They are ignored in this function.

Value

If the arguments object and level are of required types, and if there are (off-diagonal) pairs of stimuli with geodesic loops containing at least level links, summary.fechner returns a named list, of the class summary.fechner, consisting of the following four components:

pairs.used.for.comparison

a data frame giving the pairs of stimuli (first variable stimuli.pairs) and their corresponding $S$-index (second variable S.index) and $G$ (third variable Fechnerian.distance.G) values used for comparison.

Pearson.correlation

a numeric giving the value of the Pearson correlation coefficient if it exists, or a character string saying “Pearson's correlation coefficient is not defined” if it does not exist.

C.index

a numeric giving the value of the $C$-index.

comparison.level

a numeric giving the level of comparison used.

Details

The summary method outlines the results obtained from Fechnerian scaling analyses. It computes the Pearson correlation coefficient and the $C$-index (see Uenlue, Kiefer, and Dzhafarov (2009)) $$C = \frac{2\sum (S - G)^2}{\sum S^2 + \sum G^2}$$ for specific (controlled by the argument level) stimuli pairs with their corresponding $S$-index and $G$ values.

The level of comparison refers to the minimum number of links in geodesic loops. That is, choosing level $n$ means that comparison involves only those $S$-index and $G$ values that have geodesic loops containing not less than $n$ links.

If there are no (off-diagonal) pairs of stimuli with geodesic loops containing at least level links (in this case a summary is not possible), summary.fechner stops with an error message.

The function summary.fechner returns an object of the class summary.fechner (see ‘Value’), for which a print method, print.summary.fechner, is provided. Specific summary information details such as individual stimuli pairs and their corresponding $S$-index and $G$ values can be accessed through assignment (see ‘Examples’).

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

See Also

plot.fechner, the S3 method for plotting objects of the class fechner; print.fechner, the S3 method for printing objects of the class fechner; print.summary.fechner, the S3 method for printing objects of the class summary.fechner; fechner, the main function for Fechnerian scaling, which creates objects of the class fechner. See also fechner-package for general information about this package.

Examples

## Fechnerian scaling of dataset \link{wish}
f.scal.wish <- fechner(wish)

## results are summarized for comparison levels 2 and 5
summary(f.scal.wish)
summary(f.scal.wish, level = 5)

## accessing detailed summaries through assignment
str(detailed.summary.l1 <- summary(f.scal.wish))
detailed.summary.l5 <- summary(f.scal.wish, level = 5)
detailed.summary.l5$pairs.used.for.comparison[1, ]

## to verify the obtained summaries
f.scal.wish$geodesic.loops
f.scal.wish$S.index
f.scal.wish$overall.Fechnerian.distances