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Exploring and Comparing Pairwise Nonlinear Association Measures for Continuous
Variables Exploración y comparación de medidas de asociación no lineal por pares para variables continuas
DOI:
https://doi.org/10.15446/rce.v48n3.123662Keywords:
Correlation coefficient, Maximum correlation, Permutation test. (en)Coeficiente de correlación, Correlación máxima, Prueba de permutación. (es)
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There are many linear and nonlinear measures of association between two continuous pairwise variables. They are used to indicate the strength of the relationship between the two variables. The question thus arises as to which of these measures should be used to explore relationships between two variables in general. The identification of linear and/or nonlinear relationship between two variables can help to avoid problems within a regression framework. The objective of this paper is to examine alternative measures of association that could be employed as a replacement or in conjunction with, standard linear correlation coefficients. The results lead us to conclude that the maximum correlation measure is particularly useful, and capable of detecting linear and nonlinear associations between two continuous variables, while also being relatively computationally efficient. It can be utilized in exploratory analysis and in a modern regression framework.
Existen numerosas medidas de asociación, tanto lineales como no lineales, entre pares de variables continuas. Estas medidas se utilizan para indicar la fuerza de la relación entre las dos variables. Surge entonces la pregunta de cuál de estas medidas debería emplearse para explorar, en general, las relaciones entre dos variables. La identificación de relaciones lineales o no lineales puede ayudar a evitar problemas en modelos de regresión. El objetivo de este trabajo es examinar medidas alternativas de asociación que podrían utilizarse como reemplazo o en conjunto con los coeficientes de correlación lineal estándar. Los resultados nos llevan a concluir que la medida de correlación máxima es particularmente útil y capaz de detectar asociaciones no lineales entre variables continuas, además de ser relativamente eficiente desde el punto de vista computacional. Puede emplearse tanto en análisis exploratorios como en un marco de regresión moderno.
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