trineq {eba} R Documentation

## Trinary Inequality

### Description

Checks if binary choice probabilities fulfill the trinary inequality.

### Usage

trineq(M, A = 1:I)

### Arguments

 M a square matrix or a data frame consisting of absolute choice frequencies; row stimuli are chosen over column stimuli A a list of vectors consisting of the stimulus aspects; the default is 1:I, where I is the number of stimuli

### Details

For any triple of stimuli x, y, z, the trinary inequality states that, if P(x, y) > 1/2 and (xy)z, then

R(x, y, z) > 1,

where R(x, y, z) = R(x, y) R(y, z) R(z, x), R(x, y) = P(x, y)/P(y, x), and (xy)z denotes that x and y share at least one aspect that z does not have (Tversky and Sattath, 1979, p. 554).

inclusion.rule checks if a family of aspect sets is representable by a tree.

### Value

Results checking the trinary inequality.

 n number of tests of the trinary inequality prop proportion of triples confirming the trinary inequality quant quantiles of R(x, y, z) n.tests number of transitivity tests performed chkdf data frame reporting R(x, y, z) for each triple where P(x, y) > 1/2 and (xy)z

### References

Tversky, A., & Sattath, S. (1979). Preference trees. Psychological Review, 86, 542–573. doi: 10.1037/0033-295X.86.6.542

eba, inclusion.rule, strans.

### Examples

data(celebrities)             # absolute choice frequencies
A <- list(c(1,10), c(2,10), c(3,10),
c(4,11), c(5,11), c(6,11),
c(7,12), c(8,12), c(9,12))  # the structure of aspects
trineq(celebrities, A)        # check trinary inequality for tree A
trineq(celebrities, A)\$chkdf  # trinary inequality for each triple


[Package eba version 1.10-0 Index]