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An interpretation of the Pearson’s correlation coefficient is presented that describes the coefficient as the difference-sum ratio between the sum of squared errors for the geometric mean regressio...

In the last years, there has been a growing interest in composite indices, whether they be social, socio-economic or environmental indices. In this paper, we propose a new approach to the composite indices construction which consists in computing an interval of possible values, for each statistical unit, rather than a single value. The interval is called ‘performance interval’ and it is constructed depending on the level of compensability of individual indicators. As an example of application, we considered a set of indicators of well-being in Italy and we constructed the performance intervals for the Italian Regions. Finally, we compared the midpoint of the performance intervals with the geometric mean, a classic partially compensatory aggregation function.

The construction of subjective indicators for measuring phenomena expressed in an ordinal scale is a central issue in social sciences, particularly in sociology and psychology. In this paper, we propose the use of a subjective indicator by groups of units (for example, by geographical area) based on the ‘distance’ between the empirical cumulative distribution and a hypothetical cumulative distribution of reference. This approach allows to avoid the awkward question of the ‘quantification’ of an ordinal variable, i.e., the conversion of an ordinal variable into an interval variable. As an example of application, we consider life satisfaction data coming from the annual multipurpose survey on “Aspects of Daily Life”, carried out by the Italian National Institute of Statistics, and we present a comparison with some classical methods.

Most of the socio-economic phenomena such as development, well-being, and quality of life have a multidimensional nature and require the definition of a set of individual indicators to be properly assessed. Often, individual indicators are summarized and a composite index is created. One of the main problems in constructing composite indices is the choice of a method which allows time comparisons. In this paper, we consider the Adjusted Mazziotta–Pareto Index, a non-compensatory composite index used by the Italian National Institute of Statistics for measuring “Equitable and Sustainable Well-being” in Italy. An empirical comparison with some traditional non-compensatory indices is presented and an Influence Analysis is, for the first time, performed in order to assess the robustness of the index.

Composite indices for measuring multidimensional phenomena have become very popular in a variety of economic, social and policy domains. The literature offers a wide range of aggregation methods, all with their pros and cons. The most used are additive methods, but they imply requirements and properties which are often not desirable or difficult to meet. For example, they assume a full substitutability among the components of the index: a deficit in one dimension can be compensated by a surplus in another. In this paper, we consider a non-compensatory composite index for spatial comparisons and its variant for spatio-temporal comparisons. A study of the aggregation function is, for the first time, presented and its main properties are formally defined. As an example of application, a set of individual indicators of well-being for OECD countries is considered and a comparison between the two approaches is provided, in order to show what they offer and how they work.

Composite indices are being more and more used to measure multidimensional phenomena in social sciences. Considerable attention has been devoted in recent years to the methodological issues associated with index construction, such as non-compensability and comparability of the data over time. The aim of this paper is to compare two non-additive approaches: the Mazziotta–Pareto Index (MPI) and the Weighted Product (WP) method. The MPI is a nonlinear composite index that rewards the units with ‘balanced’ values of the individual indicators. The WP method implicitly penalizes the ‘unbalance’ and allows building, for each unit, two closely interrelated composite indices: a ‘static’ index for space comparisons and a ‘dynamic’ index for time comparisons. The MPI entails an equal weighting of the indicators, and only relative time comparisons are allowed. The indices based on the WP method give more weight to low values, and allow for both absolute and relative time comparisons. An application to indicators of w...

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.

In this paper, we consider a non-compensatory composite index, denoted as MPI (Mazziotta–Pareto Index) and propose an original method for visualizing the index value for a set of statistical units. The MPI is characterized by two elements: “mean” and “penalty”. The idea is to represent each unit as a particular graphical object, a “stickman with a sack”, where the value of the “mean” is assigned to the size of the “stickman” and the value of the “penalty” is assigned to the size of the “sack”. The assignment is such that the overall appearance of the object changes as a function of the MPI values.