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Methods for quantifying ordinal variables: a comparative study

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  • Sara Casacci
  • Adriano Pareto

Abstract

The solution to the problem of ‘quantification’ or scoring, i.e., assigning real numbers to the qualitative modalities (categories) of an ordinal variable, is of primary relevance in data analysis. The literature offers a wide variety of quantification methods, all with their pros and cons. In this work, we present a comparison between an univariate and a multivariate approach. The univariate approach allows to estimate the category values of an ordinal variable from the observed frequencies on the basis of a distributional assumption. The multivariate approach simultaneously transforms a set of observed qualitative variables into interval scales through a process called optimal scaling. As an example of application, we consider the Bank of Italy data coming from the “Survey on Household Income and Wealth” in order to ‘quantify’ a self-rating item of happiness. A simulation study to compare the performance of the two approaches is also presented. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Sara Casacci & Adriano Pareto, 2015. "Methods for quantifying ordinal variables: a comparative study," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(5), pages 1859-1872, September.
  • Handle: RePEc:spr:qualqt:v:49:y:2015:i:5:p:1859-1872
    DOI: 10.1007/s11135-014-0063-2
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    References listed on IDEAS

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    1. Forrest Young, 1981. "Quantitative analysis of qualitative data," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 357-388, December.
    2. Wim Kalmijn, 2013. "From Discrete 1 to 10 Towards Continuous 0 to 10: The Continuum Approach to Estimating the Distribution of Happiness in a Nation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(2), pages 549-557, January.
    3. Easterlin, Richard A, 2001. "Income and Happiness: Towards an Unified Theory," Economic Journal, Royal Economic Society, vol. 111(473), pages 465-484, July.
    4. Jarl Kampen & Marc Swyngedouw, 2000. "The Ordinal Controversy Revisited," Quality & Quantity: International Journal of Methodology, Springer, vol. 34(1), pages 87-102, February.
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    Cited by:

    1. Sara Casacci & Adriano Pareto, 2018. "Subjective Indicators Construction by Distance Indices: An Application to Life Satisfaction Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 137(3), pages 831-846, June.
    2. Dennis A. Perry & Bill Olson & Paul Blessner & Timothy D. Blackburn, 2016. "Evaluating the Systems Engineering Problem Management Process for Industrial Manufacturing Problems," Systems Engineering, John Wiley & Sons, vol. 19(2), pages 133-145, March.
    3. Nurith Epstein & Daniel Lachmann, 2018. "Gender Inequity during the Ph.D.: Females in the Life Sciences Benefit Less from Their Integration into the Scientific Community," Social Sciences, MDPI, vol. 7(8), pages 1-15, August.
    4. Kamal, Mustafa & Blacklow, Paul, 2021. "Attitudes to gender and personality in the Australian gender wage gap," Working Papers 2021-07, University of Tasmania, Tasmanian School of Business and Economics.

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