strans {eba} | R Documentation |
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; row stimuli are chosen over column stimuli |
Details
Weak (WST), moderate (MST), and strong (SST) stochastic transitivity hold
for a set of choice probabilities , whenever if
and
, then
(WST),
(MST),
(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 . 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).
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 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 |
References
Iverson, G., & Falmagne, J.-C. (1985). Statistical issues in measurement. Mathematical Social Sciences, 10, 131–153. doi: 10.1016/0165-4896(85)90031-9
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
See Also
eba
, circular
, kendall.u
,
trineq
.
Examples
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