
KENDALL TAU DISSIMILARITYName:
\( \frac{Y_j  Y_i}{X_j  X_i} \) < 0  pair is discordant \( \frac{Y_j  Y_i}{X_j  X_i} \) = 0  pair is considered a tie X_{i} = X_{j}  pair is not compared Kendall's tau is computed as
with N_{c} and N_{d} denoting the number of concordant pairs and the number of discordant pairs, respectively, in the sample. Ties add 0.5 to both the concordant and discordant counts. There are \( \left( \begin{array}{c} n \\ 2 \end{array} \right) \) possible pairs in the bivariate sample. Kendall's tau is an alternative to the Spearman's rho rank correlation. A perfect linear relationship yields a correlation coefficient of +1 (or 1 for a negative relationship) and no linear relationship yields a correlation coefficient of 0. In some applications, such as clustering, it can be useful to transform Kendall's tau coefficient to a dissimilarity measure. The transformation used here is
This converts Kendall's tau coefficient with values between 1 and 1 to a score between 0 and 1. High positive correlation (i.e., very similar) results in a dissimilarity near 0 and high negative correlation (i.e., very dissimilar) results in a dissimilarity near 1. If a similarity score is preferred, you can use
where d is defined as above.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the computed Kendall's tau dissimilarity is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = KENDALL TAU DISSIMILARITY Y1 Y2 SUBSET TAG > 2
SKIP 25 READ BERGER1.DAT Y X LET CORR = KENDALL TAU Y X LET D = KENDALL TAU DISSIMILARITY Y X SET WRITE DECIMALS 3 PRINT CORR DThe following output is generated Program 2: SKIP 25 READ IRIS.DAT Y1 Y2 Y3 Y4 SET WRITE DECIMALS 3 . LET M = GENERATE MATRIX KENDALL TAU DISSIMILARITY Y1 Y2 Y3 Y4 PRINT MThe following output is generated Program 3: SKIP 25 READ IRIS.DAT Y1 Y2 Y3 Y4 TAG . TITLE CASE ASIS TITLE OFFSET 2 CASE ASIS TIC MARK OFFSET UNITS DATA YLIMITS 0 1 MAJOR YTIC MARK NUMBER 6 MINOR YTIC MARK NUMBER 1 Y1TIC MARK LABEL DECIMAL 1 XLIMITS 1 3 MAJOR XTIC MARK NUMBER 3 MINOR XTIC MARK NUMBER 0 XTIC MARK OFFSET 0.3 0.3 CHARACTER X BLANK LINES BLANK SOLID . MULTIPLOT CORNER COORDINATES 5 5 95 95 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 3 . TITLE Sepal Length vs Sepal Width KENDALL TAU DISSIMILARITY Y1 Y2 TAG . TITLE Sepal Length vs Petal Length KENDALL TAU DISSIMILARITY Y1 Y3 TAG . TITLE Sepal Length vs Petal Width KENDALL TAU DISSIMILARITY Y1 Y4 TAG . TITLE Sepal Width vs Petal Length KENDALL TAU DISSIMILARITY Y2 Y3 TAG . TITLE Sepal Width vs Petal Width KENDALL TAU DISSIMILARITY Y2 Y4 TAG . TITLE Petal Length vs Petal Width KENDALL TAU DISSIMILARITY Y3 Y4 TAG . END OF MULTIPLOT X1LABEL Species . JUSTIFICATION CENTER MOVE 50 5 TEXT Species DIRECTION VERTICAL MOVE 5 50 TEXT Kendall Tau Dissimilarity Coefficient DIRECTION HORIZONTAL  
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Date created: 09/20/2017 