An extended study to measure dependence with grouped-ordinal variables generated by unobserved non-normal variables

Abstract

In the last decades, the availability of attitudinal surveys generating data of ordinal (discrete) nature has increasingly risen. Such kind of data may be also associated with responses expressed through grouped-continuous scales. This article proposes the use of a recent new dependence measure, called MDC ${}_{\text{go}}$, suitable to all the scenarios where the independent variable is ordinal and the dependent variable is “grouped” into classes. The promising results of the MDC ${}_{\text{go}}$ coefficient behavior in the case of normally and t-Student distributed variables lead us to extend the investigation to the non-normally distributed variables. A Monte Carlo simulation study is built with the aim of assessing the performance of the MDC ${}_{\text{go}}$ coefficient in comparison with the most common dependence coefficients. Additional evidence on the effectiveness of the MDC ${}_{\text{go}}$ coefficient arises from a real application to data on heart diseases.

Keywords:

• Dependency
• ordinal variable
• “grouped” variables
• unobserved non-normally distributed variables

Acknowledgments

Acknowledgments go to the two anonymous reviewers for their helpful comments and suggestions that allowed to improve the article.

Notes

1 Given two variables Y and X, from the notion of monotonic dependence relationship, it derives that Y and X are linked according to a monotonic functional relationship up to a random noise, i.e., $Y=f(X)+ϵ$, with $ϵ\sim N(0,{\sigma }^2)$. In the case of a perfect monotonically dependence relationship between Y and X, ${\sigma }^2=0$.