Characteristics of measures of directional dependence - Monte Carlo studies
by Alexander von Eye and Richard P. DeShon .
In the context of linear models, the response variable will always have less skew than
the explanatory variable. Based on this result, one can use third and fourth order moments, and
information concerning the deviation of variables from normality, to ascertain which of two
variables is the response and which is the explanatory variable. In this article, the ratio of two
skewness measures, the ratio of two kurtosis measures, and one omnibus test of deviation from
normality are examined. Results from simulation studies show that all three measures (1) are
sensitive to various data distributions, (2) sample size, and (3) a simple correlation structure. The
ratio of two kurtosis measures is sensitive in particular to the correlation structure. It is concluded
that (1) decisions about directional dependence can be based on various types of deviation from
normality, (2) measures that respond to deviations based on skewness and kurtosis have
characteristics that make them prime candidates for determining directional dependence, and (3)
each of the measures proposed thus far is sensitive to either specific or omnibus deviations from
directional dependence, simulation, skewness, kurtosis, normality
Alexander von Eye, firstname.lastname@example.org
Richard P. DeShon, email@example.com
Richard G. Graf, firstname.lastname@example.org
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