The subjective assessment of quality of life, personal skills and the agreement with a certain opinion are common issues in clinical, social, behavioral and marketing research. A wide set of surveys providing ordinal data arises. Beside such variables, other common surveys generate responses on a continuous scale, where the variable actual point value cannot be observed since data belong to certain groups. This paper introduces a re-formalization of the recent “Monotonic Dependence Coefficient” (MDC) suitable to all frameworks in which, given two variables, the independent variable is expressed in ordinal categories and the dependent variable is grouped. We denote this novel coefficient with \(\mathrm{MDC}\mathrm{go}\). The \(\mathrm{MDC}\mathrm{go}\) behavior and the scenarios in which it presents better performance with respect to the alternative correlation/association measures, such as Spearman’s \(r_\mathrm{S}\), Kendall’s \(\tau _b\) and Somers’ \(\varDelta \) coefficients, are explored through a Monte Carlo simulation study. Finally, to shed light on the usefulness of the proposal in real surveys, an application to drug-expenditure data is considered.

中文翻译：

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MDCgo应对组合序数据的关联/相关性挑战

生活质量，个人技能的主观评估以及持有一定意见的协议是临床，社会，行为和市场研究中的常见问题。产生了一系列提供序数数据的调查。除了这些变量外，其他常见调查还产生连续规模的响应，由于数据属于某些组，因此无法观察到可变的实际点值。本文介绍了适用于所有框架的最新“单调相依系数”（MDC）的重新形式化，其中，给定两个变量，自变量以有序类别表示，因变量被分组。我们用\（\ mathrm {MDC} \ mathrm {go} \）表示这个新颖系数。该\（\ mathrm {MDC} \ mathrm {去} \）行为以及在其他相关/关联度量（例如Spearman的\ {r_ \ mathrm {S} \），Kendall的\ {\ tau _b \）和Somers的\（\ varDelta \ ）系数，是通过蒙特卡洛模拟研究探索的。最后，为了阐明该建议在实际调查中的有用性，考虑将其应用于药物支出数据。