strans {eba}  R Documentation 
Checks the weak, moderate, and strong stochastic transitivity.
strans(M)
M 
a square matrix or a data frame consisting of absolute choice frequencies; row stimuli are chosen over column stimuli 
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).
See Suppes, Krantz, Luce, and Tversky (1989/2007, chap. 17) for an introduction to the representation of choice probabilities.
If WST holds, a permutation of the indices of the matrix exists such that
the proportions in the upper triangular matrix are \ge 0.5
. This
rearranged matrix is stored in pcm
. If WST does not hold, cells in
the upper triangular matrix that are smaller than 0.5 are replaced by 0.5.
The deviance resulting from this restriction is reported in wst.fit
.
The approximate likelihood ratio test for significance of the WST violations is according to Tversky (1969); for a more exact test of WST see Iverson and Falmagne (1985).
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

mst.violations 
a vector containing

sst.violations 
a vector containing

pcm 
the permuted square matrix of relative choice frequencies 
ranking 
the ranking of the objects, which corresponds to the colnames of pcm 
chkdf 
data frame reporting the choice proportions for each triple in each permutation 
violdf 
data frame reporting for each triple which type of transitivity holds or does not hold 
wst.fit 
likelihood ratio test of WST (see Details) 
wst.mat 
restricted matrix that satisfies WST 
Iverson, G., & Falmagne, J.C. (1985). Statistical issues in measurement. Mathematical Social Sciences, 10, 131–153. doi: 10.1016/01654896(85)900319
Suppes, P., Krantz, D.H., Luce, R.D., & Tversky, A. (1989/2007). Foundations of measurement. Volume II. Mineola, N.Y.: Dover Publications.
Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48. doi: 10.1037/h0026750
eba
, circular
, kendall.u
,
trineq
.
data(celebrities) # absolute choice frequencies
strans(celebrities) # WST and MST hold, but not SST
strans(celebrities)$pcm # reordered relative frequencies
strans(celebrities)$violdf # transitivity violations