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MDCgo takes up the association/correlation challenge for grouped ordinal data

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Abstract

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.

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Notes

  1. Boxplots referring to \(n=50\) may be provided upon request.

  2. Even if the JT test is typically used when three or more populations are considered, it can be used for just two populations.

  3. The JT test was led by resorting to the R package “clinfun” which uses the statistic \(JT=\sum _{k<l}\sum _{ij}I(X_{ik}<X_{jl})+0.5I(X_{ik}=X_{jl})\), where i, j are observations in groups k and l, respectively, and \(I(\psi )\) equals one if \(\psi \) is true and zero otherwise. Since the JT test refers to a large sample size (i.e., the values obtained by the indices in 10,000 iterations), the p values provided here are based on normal approximation of the standardized test statistic \(Z=(JT-E(JT))/\sqrt{\mathrm{var}(JT)}\).

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Acknowledgements

The authors gratefully acknowledge the ASL CN1 of Cuneo (Italy) for making available the dataset representing the case study illustrated and discussed in the paper. A special thanks goes to the Associate Editor and the two anonymous reviewers for their helpful comments and suggestions that allowed to improve the paper.

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Authors and Affiliations

  1. Department of Economics, Management and Quantitative Methods, Università degli Studi di Milano, Via Conservatorio 7, 20122, Milan, Italy

    Emanuela Raffinetti

  2. School of Management and Economics, University of Turin, C.so Unione Sovietica 218 Bis, 10134, Turin, Italy

    Fabio Aimar

  3. ASL CN1, Via C. Boggio 12, 12100, Cuneo, Italy

    Fabio Aimar

Authors
  1. Emanuela Raffinetti
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  2. Fabio Aimar
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Correspondence to Emanuela Raffinetti.

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Raffinetti, E., Aimar, F. MDCgo takes up the association/correlation challenge for grouped ordinal data. AStA Adv Stat Anal 103, 527–561 (2019). https://doi.org/10.1007/s10182-018-00341-1

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