trineq: Trinary Inequality
In eba: Elimination-by-Aspects Models

Description Usage Arguments Details Value References See Also Examples

Checks if binary choice probabilities fulfill the trinary inequality.

1	trineq(M, A = 1:I)

`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

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.

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

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

eba, inclusion.rule, strans.

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

Trinary Inequality

Number of Tests: 54 
% triples confirming trinary inequality: 0.87 
Quantiles of R(xyz):
 25%  50%  75% 
1.14 1.39 1.69 

         triple       Pxy      Rxyz trineq
1    (LBJ,HW)JU 0.6794872 1.6745404   TRUE
2    (LBJ,HW)CY 0.6794872 1.6390481   TRUE
3   (LBJ,HW)AJF 0.6794872 1.4084252   TRUE
4    (LBJ,HW)BB 0.6794872 1.4950289   TRUE
5    (LBJ,HW)ET 0.6794872 1.0680446   TRUE
6    (LBJ,HW)SL 0.6794872 1.4961569   TRUE
7   (LBJ,CDG)JU 0.6965812 1.2610178   TRUE
8   (LBJ,CDG)CY 0.6965812 1.3045396   TRUE
9  (LBJ,CDG)AJF 0.6965812 1.0140206   TRUE
10  (LBJ,CDG)BB 0.6965812 1.2056276   TRUE
11  (LBJ,CDG)ET 0.6965812 1.1565990   TRUE
12  (LBJ,CDG)SL 0.6965812 1.5656877   TRUE
13   (HW,CDG)JU 0.5897436 0.9996317  FALSE
14   (HW,CDG)CY 0.5897436 1.0565256   TRUE
15  (HW,CDG)AJF 0.5897436 0.9557129  FALSE
16   (HW,CDG)BB 0.5897436 1.0704787   TRUE
17   (HW,CDG)ET 0.5897436 1.4375000   TRUE
18   (HW,CDG)SL 0.5897436 1.3891286   TRUE
19   (JU,CY)LBJ 0.7521368 2.5083596   TRUE
20    (JU,CY)HW 0.7521368 2.5626761   TRUE
21   (JU,CY)CDG 0.7521368 2.4246762   TRUE
22    (JU,CY)BB 0.7521368 1.8397740   TRUE
23    (JU,CY)ET 0.7521368 2.3209481   TRUE
24    (JU,CY)SL 0.7521368 3.0344828   TRUE
25  (AJF,JU)LBJ 0.5085470 1.1354119   TRUE
26   (AJF,JU)HW 0.5085470 0.9549741  FALSE
27  (AJF,JU)CDG 0.5085470 0.9130172  FALSE
28   (AJF,JU)BB 0.5085470 0.8705091  FALSE
29   (AJF,JU)ET 0.5085470 0.9280821  FALSE
30   (AJF,JU)SL 0.5085470 0.8376491  FALSE
31  (AJF,CY)LBJ 0.6709402 1.8493468   TRUE
32   (AJF,CY)HW 0.6709402 1.5891337   TRUE
33  (AJF,CY)CDG 0.6709402 1.4375000   TRUE
34   (AJF,CY)BB 0.6709402 1.0399511   TRUE
35   (AJF,CY)ET 0.6709402 1.3987076   TRUE
36   (AJF,CY)SL 0.6709402 1.6505243   TRUE
37   (ET,BB)LBJ 0.7136752 1.9002628   TRUE
38    (ET,BB)HW 0.7136752 1.3575426   TRUE
39   (ET,BB)CDG 0.7136752 1.8229858   TRUE
40    (ET,BB)JU 0.7136752 1.2848411   TRUE
41    (ET,BB)CY 0.7136752 1.6208781   TRUE
42   (ET,BB)AJF 0.7136752 1.2051368   TRUE
43   (SL,BB)LBJ 0.7948718 2.1088998   TRUE
44    (SL,BB)HW 0.7948718 2.1104911   TRUE
45   (SL,BB)CDG 0.7948718 2.7387218   TRUE
46    (SL,BB)JU 0.7948718 1.2120665   TRUE
47    (SL,BB)CY 0.7948718 1.9991558   TRUE
48   (SL,BB)AJF 0.7948718 1.2596145   TRUE
49   (SL,ET)LBJ 0.6282051 1.2061750   TRUE
50    (SL,ET)HW 0.6282051 1.6896552   TRUE
51   (SL,ET)CDG 0.6282051 1.6327988   TRUE
52    (SL,ET)JU 0.6282051 1.0252861   TRUE
53    (SL,ET)CY 0.6282051 1.3404923   TRUE
54   (SL,ET)AJF 0.6282051 1.1359765   TRUE