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

Emanuela Raffinetti () and Fabio Aimar ()
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Emanuela Raffinetti: Università degli Studi di Milano
Fabio Aimar: University of Turin

AStA Advances in Statistical Analysis, 2019, vol. 103, issue 4, No 4, 527-561

Abstract: 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 $$\mathrm{MDC}\mathrm{go}$$ MDC go . The $$\mathrm{MDC}\mathrm{go}$$ MDC go behavior and the scenarios in which it presents better performance with respect to the alternative correlation/association measures, such as Spearman’s $$r_\mathrm{S}$$ r S , Kendall’s $$\tau _b$$ τ b and Somers’ $$\varDelta $$ Δ 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.

Keywords: Grouped ordinal data; Dependence; Correlation coefficients; Association coefficients; Monte Carlo simulations; 62-07; 62H20; 62P25 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10182-018-00341-1

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