Methods for quantifying ordinal variables: a comparative study

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.