Coefficients of Structural Association
40 Pages Posted: 10 Apr 2012
Date Written: April 9, 2012
Estimation of a variable’s dependence against another one is considered in a new approach based on a Coefficient of Structural Association (CSA). This method profiles the distribution of one variable along the segments formed by another one, and yields a gauge similar to the coefficient of determination in regression modeling, or in analysis of variance. Constructing CSA requires finding a targeted value of a structure which corresponds to the maximum possible variance or the equidistant variance in the given conditions, and we consider the cases of independent and dependent shares of the segments. The CSA relations to other measures of dependence are shown too, particularly, for binary variables CSA reduces to the Loevinger’s coefficient of association. Numerical simulations performed with the variables in nominal-numerical and numerical-numerical scales indicate that CSA presents a powerful tool for data analysis where traditional measures fail. This method can enrich both theoretical consideration and practical estimations for identifying hidden patterns in the data, and help decision-makers in taking appropriate decisions.
Keywords: correlation, association, correlation ratio, median, targeted structure, maximum variance, equidistant variance, Loevinger’s coefficient.
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