trineq function

Trinary Inequality

Checks if binary choice probabilities fulfill the trinary inequality.

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

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.

Returns

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. tools:::Rd_expr_doi("10.1037/0033-295X.86.6.542")

See Also

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