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A dependence measure flow tree through Monte Carlo simulations

Author

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  • Emanuela Raffinetti

    (University of Milan)

  • Pier Alda Ferrari

    (University of Milan)

Abstract

In applied psychological, behavioral and sociological research the majority of data are typically mixed (continuous and discrete) or, if continuous, they violate the normality condition. Given a dependent and an independent variables: (a) both the variables may appear with distinct values (continuous variables); (b) the dependent variable may present distinct values (continuous variable) and the independent variable tied values (discrete variable); (c) the dependent variable may present tied values (discrete variable) and the independent variable distinct values (continuous variable). The dependence relationship between the variables could be assessed through the common correlation coefficients, i.e., the Pearson’s, Spearman’s and Kendall’s coefficients, jointly with a recently revisited monotonic dependence coefficient, called “Monotonic Dependence Coefficient”. But, the choice of the most suitable dependence measure in different scenarios may become problematic. The aim of the paper is to show which dependence measure to use to discover dependence relationships. A flow tree displaying how to find the best dependence measures is proposed by means of a Monte Carlo simulation study. Both Normal and non-Normal distributions producing continuous and discrete data, together with the possibility of transforming discrete data into continuous ones, are considered. Finally, validation of simulation findings on real data is also introduced.

Suggested Citation

  • Emanuela Raffinetti & Pier Alda Ferrari, 2021. "A dependence measure flow tree through Monte Carlo simulations," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(2), pages 467-496, April.
    • Handle: RePEc:spr:qualqt:v:55:y:2021:i:2:d:10.1007_s11135-020-01010-9
    DOI: 10.1007/s11135-020-01010-9
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    References listed on IDEAS

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    1. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    2. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    3. Nadia Solaro & Alessandro Barbiero & Giancarlo Manzi & Pier Alda Ferrari, 2017. "A sequential distance-based approach for imputing missing data: Forward Imputation," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 395-414, June.
    4. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    5. Emanuela Raffinetti, 2019. "A Note on the Dependence Measurement for Ordinal-Continuous Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 9(5), pages 129-134, October.
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