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Characteristics of measures of directional dependence
"... Recent results (Dodge & Rousson, 2000; von Eye & DeShon, 2008) show that, in the context of linear models, the response variable will always have less skew than the explanatory variable. This applies accordingly to the kurtosis of the two variables. These facts can be used to determine the d ..."
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Recent results (Dodge & Rousson, 2000; von Eye & DeShon, 2008) show that, in the context of linear models, the response variable will always have less skew than the explanatory variable. This applies accordingly to the kurtosis of the two variables. These facts can be used to determine the direction of dependence. Specifically, using third and fourth order moments, and information concerning the deviation of variables from normality, it can be ascertained 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. Simulation studies are reported that allow one to answer the question whether, these measures (1) are sensitive to various data distributions, (2) sample size, and (3) a simple correlation structure. Results suggest that all three measures are highly sensitive to these factors. The ratio of two kurtosis measures is sensitive in particular to the correlation structure. It is concluded that (1) 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
Methods and measures Directional dependence in developmental research
"... In this article, we discuss and propose methods that may be of use to determine direction of dependence in nonnormally distributed variables. First, it is shown that standard regression analysis is unable to distinguish between explanatory and response variables. Then, skewness and kurtosis are dis ..."
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In this article, we discuss and propose methods that may be of use to determine direction of dependence in nonnormally distributed variables. First, it is shown that standard regression analysis is unable to distinguish between explanatory and response variables. Then, skewness and kurtosis are discussed as tools to assess deviation from normality. Deviation from normality can be used to assess direction of dependence. This proposition is based on the fact that the response variable will always have less skew than the independent variable (Dodge & Rousson, 2000). It has been shown that the cube of the Pearson correlation coefficient can be calculated as the ratio of the skewness measures of the correlated variables. Because correlations cannot exceed the interval (1.0; þ1.0), directional dependence of the two correlated variables can be determined by the ratio that results in a correlation that stays within this interval. It is also proposed that other measures of deviation from normality can be used to determine directional dependence; for example, kurtosis. Recommendations are given for making decisions concerning directional dependence. Empirical data examples from developmental research on violence against women and on attention deficit hyperactivity disorder (ADHD) illustrate the use of the methodology. Crosssectional and temporal directional dependence are discussed, and the effects of onset of a causal agent and termination of a causal agent are illustrated. Keywords causality, development, directional dependency, research Does money make us happy, or do happier people make more