strans {eba}R Documentation

Stochastic Transitivity

Description

Checks the weak, moderate, and strong stochastic transitivity.

Usage

strans(M)

Arguments

M a square matrix or a data frame consisting of absolute choice frequencies

Details

The weak (WST), moderate (MST), and strong (SST) stochastic transitivity hold for a set of choice probabilities P, whenever if P_{ij} >= 0.5 and P_{jk} >= 0.5, then

P_{ik} >= 0.5 (WST),

P_{ik} >= min(P_{ij}, P_{jk}) (MST),

P_{ik} >= max(P_{ij}, P_{jk}) (SST).

Value

A table displaying the number of violations of the weak, moderate, and strong stochastic transitivity, the number of tests, the error ratio (violations/tests), and the mean and maximum deviation from the minimum probability for which the corresponding transitivity would hold.

weak number of violations of WST
moderate number of violations of MST
strong number of violations of SST
n.tests number of transitivity tests performed
wst.violations a vector containing 0.5 - P_{ik} for all triples that violate WST
mst.violations a vector containing min(P_{ij}, P_{jk}) - P_{ik} for all triples that violate MST
sst.violations a vector containing max(P_{ij}, P_{jk}) - P_{ik} for all triples that violate SST
pcm the square matrix of relative choice frequencies

References

Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48.

See Also

eba, circular, kendall.u.

Examples

data(celebrities)  # absolute choice frequencies
strans(celebrities)  # WST and MST hold, but not SST
strans(celebrities)$pcm  # relative frequencies

[Package eba version 1.5-2 Index]