eba (version 1.4-2)

strans: 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

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.
• 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

Details

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

$P_{ik} \ge 0.5$ (WST),

$P_{ik} \ge \min(P_{ij}, P_{jk})$ (MST),

$P_{ik} \ge \max(P_{ij}, P_{jk})$ (SST).

References

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

See Also

eba, kendall.u.

Examples

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