Emanuela Raffinetti

On the Gini coefficient normalization when attributes with negative values are considered

Typically, inequality indices appear both as basic concepts in the analysis of welfare economics and as technical tools applied to income or other transferable attributes. Several findings in such research fields are provided by the standard Gini coefficient, traditionally introduced for incomes taking non-negative values. Even if negative income can appear as an unfamiliar concept, it can arise in real surveys, especially when assessing families’ financial assets. The main troubles associated with the treatment of negative income regards the violation of the normalization principle. The inclusion of income taking negative values can yield for the standard Gini coefficient achieving values

New perspectives for the MDC index in social research fields

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The Combined Median Rank-Based Gini Index for Customer Satisfaction Analysis

>1. The Gini coefficient then has to be adjusted in order to ensure that its range is bounded between 0 and 1. In this paper, a reformulation of the Gini coefficient with respect to that proposed in the literature is presented and discussed in light of the negative income issue. In particular, a new definition of the Gini coefficient normalization term, revealing more coherence with the classical situation of maximum inequality, is provided. Finally, an empirical application based on the Survey of Household Income and Wealth data of the Bank of Italy (2012) further validates the actual attitude of the new Gini coefficient in catching inequality in the distribution of the attribute.

Lorenz Zonoids and Dependence Measures: A Proposal

This article focuses on a statistical tool for dependence analysis in scientific research. Starting from a recent index of concordance for a multiple linear regression model, a coefficient suitable in catching any monotonic dependence relationship between a dependent variable and an independent variable is derived and discussed. Given its interpretation in terms of monotonic dependence, it is called monotonic dependence coefficient (MDC). It is appropriate to all contexts where the dependent variable is quantitative (continuous or discrete) and the independent variable is at least of ordinal nature; tied data are also allowed. MDC’s adequacy is validated through Monte Carlo simulations led by taking into account different scenarios of dependence. Finally, an application to real data is provided to stress MDC’s capability of detecting dependence relationships between two variables, even if some pieces of information about original data are lost.

An extension and a new interpretation of the rank-based concordance index

The great interest in quantitative social research has led to the development of specific statistical techniques suitable in dealing with dependence between variables also in the presence of ordinal data. A specific index, hereafter called monotonic dependence coefficient (MDC), was provided as a monotonic dependence measure. Due to its properties and specific features, MDC overcomes the Pearson’s correlation coefficient, since it captures not only linear dependence relationships but also any general monotonic one. The MDC adequacy is validated by a simulation study assessing its performance with respect to the traditional Pearson’s correlation coefficient. Finally, a real application of MDC to real data is also illustrated.

School tracking and equality of opportunity in a multilevel perspective

In this paper a statistical interpretation of a recent measure, called “Rank-based Concordance Index” (RCI), in terms of monotonic dependence relationship between a non-negative dependent variable and a quantitative independent one is provided. Due to its rank-based construction, the measure presents properties and features that make it suitable also in an ordinal context of analysis. In applied research many data sets contain observations from ordinal variables rather than continuous ones. In such situations, the study of dependence relationship among variables represents an interesting issue, since ordinal variables are not specified according to a metric scale. The proposal discussed here can thus contribute to solve this problem.

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

The quality assessment represents a relevant topic especially with regard to several real contexts. Currently, firms and services suppliers pay particular attention to customer satisfaction surveys in order to investigate about the “perceived quality” feature. Typically, a useful tool to obtain information about the customer satisfaction degree is represented by the quality questionnaires. The use of quality questionnaires implies that the collected data mostly assume ordinal nature.A contribution in dealing with ordinal data is provided by this paper. Here, we propose a novel Gini measure built on ranks. By combining it with the median index, one can depict the customer satisfaction degree by exploiting information coming from the responses given to the quality questionnaires items.

Analyzing the Effects of Negative and Non-negative Values on Income Inequality : Evidence from the Survey of Household Income and Wealth of the Bank of Italy (2012)

Recently, the analysis of ordered and non-ordered categorical variables has assumed a relevant role, especially with regard to the evaluation of customer satisfaction, health and educational effectiveness. In such real contexts, the study of dependence relations among the involved variables represents an attractive research field. However, the categorical nature of variables does not always successfully allow the application of the existing standard dependence measures, since categorical data are not specified according to a metric scale. In fact, the aforementioned statistical methods are more appropriate in a purely quantitative setting, because based on the Euclidean distance. Our purpose aims at overcoming these restrictions by extending the dependence study in a quali–quantitative perspective. The idea is focused on employing specific statistical tools, such as the Lorenz curves and the so-called Lorenz zonoids. A novel Lorenz zonoids-based relative dependence measure is proposed as an alternative to the partial correlation coefficient to establish each categorical covariate contribution in a multiple linear regression model.