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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.

Il libro descrive e affronta alcune questioni tutt’ora aperte nel campo della costruzione di indicatori compositi. Si propone come complemento a riferimenti consolidati quali OECD handbook of composite indicators, e approfondisce temi che saranno certo oggetto di ampio sviluppo nel prossimo futuro, soprattutto nell’ambito degli indicatori di benessere e progresso umano. La prima parte del libro illustra lo stato dell’arte delle metodologie per la costruzione di indicatori compositi mentre la seconda parte affronta specifici nodi critici piu’ recenti. Il libro fornisce strumenti utili sia a ricercatori con una conoscenza limitata degli indicatori compositi, che a studiosi interessati ad un aggiornamento su temi più avanzati.

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.

The Italian wine industry is going through, during a general economic crisis, a period of strong growth and expansion in the world markets. The quality of products, characterized by tradition and innovation, has defeated the involution of the Italian entrepreneurial system. The variety of wines produced represents the peculiarities of the Italian territory. The aim of this paper is to measure a multidimensional phenomenon, the “Enological vocation” of the Italian provinces, through the use of a composite index. The results highlight both areas of the territory for which it is known the strong vocation and less known areas where you need to do further investigation.

The measurement of well-being of people is very difficult because it is characterized by a multiplicity of aspects or dimensions. Principal Components Analysis (PCA) is probably the most popular multivariate statistical technique for reducing data with many dimensions and, often, well-being indicators are reduced to a single index of well-being by using PCA. However, PCA is implicitly based on a reflective measurement model that is not suitable for all types of indicators. In this paper, we discuss the use and misuse of PCA for measuring well-being, and we show some applications to real data.

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...

In recent years, the debate on the measurement of multidimensional phenomena has caused, within the worldwide scientific Community of developed countries, a renewed interest. It is common awareness that a number of socio-economic phenomena cannot be measured by a single descriptive indicator and that, instead, they should be represented with a multiplicity of aspects or dimensions. Phenomena such as development, progress, poverty, social inequality, well-being, quality of life, etc., require, to be measured, the ‘combination’ of different dimensions, to be considered together as components of the phenomenon (Mazziotta and Pareto 2013). In fact, the complex and multidimensional nature of these phenomena requires the definition of intermediate objectives whose achievement can be observed and measured by individual indicators. The mathematical combination (or aggregation as it is termed) of a set of indicators that represent the different dimensions of a phenomenon to be measured can be obtained by applying methodologies known as composite indicators or composite indices (Saisana and Tarantola 2002; Salzman 2003; OECD 2008).

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.

It has long been accepted that the GDP per capita cannot alone explain the well-being in a geographical area. Several have been the attempts to construct alternative, non-monetary, indices of well-being by aggregating a variety of individual indicators that represent different dimensions of well-being. The most famous, in Italy, are the Index of Regional Quality of Development and the “Il Sole 24 Ore” Quality of Life Index. An issue often not solved, from a methodological point of view, concerns the comparability of the data over time. In this work, we propose a ‘static’ and a ‘dynamic’ well-being measure based on the application of the Jevons index to the socio-economic indicators. The obtained indices are closely related and allow synthetic spatial and temporal comparisons of the level of well-being.

The aim of this work is to provide a tool for the measurement of the health infrastructure endowment based on the assumption of “non-substitutability” of the indicators (a compensation among them is not allowed). The proposed approach, called “Method of Penalties by Coefficient of Variation”, normalizes the indicators by a specific criterion that deletes the unit of measurement and the variability effect and uses, as aggregation function, an adjusted mean by a penalty coefficient that is function, for each unit, of the indicators’ variability in relation to the mean. The obtained index is easily computable, interpretable and comparable over time. As an example of application, we consider a set of indicators of endowment of advanced medical equipment.

Questo lavoro nasce dall'esigenza di sviluppare un sistema per la produzione di stime preliminari, a livello di ripartizione geografica, nelle statistiche giudiziarie rilasciate dall'ISTAT, con particolare riferimento alle separazioni e ai divorzi. La prima parte č dedicata all'esposizione del quadro normativo e del contesto operativo di riferimento. Quindi, vengono illustrati le fonti, il processo produttivo e le serie storiche utilizzate. Infine, viene proposta e sperimentata una metodologia per la produzione delle stime anticipate dei dati annuali basata sull'applicazione del metodo di Holt-Winters a serie storiche trimestrali. Tale metodologia puň essere applicata con successo anche nei casi in cui la numerositŕ delle serie storiche non consente l'applicazione di modelli sofisticati, come i modelli ARIMA. La positiva performance riscontrata sui dati delle separazioni e dei divorzi apre lo scenario all'eventuale applicazione della metodologia proposta ad altre indagini della statistica giudiziaria.

Il tema della sintesi di diversi indicatori in un indicatore rappresentativo dell’insieme dei fenomeni considerati è un tema ben noto in letteratura, soprattutto nel campo delle statistiche sociali. Spesso, tuttavia, la sintesi viene effettuata senza l’introduzione di alcuna ponderazione, dunque assumendo implicitamente che i diversi fenomeni considerati abbiano tutti lo stesso rilievo e possano quindi “entrare” nel procedimento di sintesi in termini paritetici. Questa assunzione, pur comprensibile per la difficoltà di evitare il rischio dell’arbitrarietà, potrebbe tuttavia condurre a risultati distorti, o quanto meno non completamente affidabili, dato che nella realtà difficilmente i fenomeni da sintetizzare possono essere posti su un livello paritetico. La questione, peraltro, si complica quando si è in presenza di una doppia dimensione da sintetizzare: quella settoriale (nel lavoro qui presentato, le diverse categorie infrastrutturali) e quella territoriale (qui, le province italiane). Al problema  in particolare, a quello della costruzione di un indicatore di sintesi della dotazione infrastrutturale a livello di diverse unità territoriali  sono state date soluzioni diverse, tutte più o meno basate sulla variabilità, settoriale e/o territoriale, quale elemento da assumere per la determinazione dei pesi da introdurre eventualmente nell’algoritmo di sintesi. Il lavoro che qui si presenta si pone l’obiettivo di mettere a confronto alcuni degli approcci a tal fine utilizzati e di verificare sia l’eventuale convergenza sia il grado di robustezza (e dunque di affidabilità) dei risultati ottenuti. The synthesis of different indicators expressed in only one representative measure of a set of phenomena is a subject known in literature, especially in the social statistics. Frequently the synthesis is calculated without weighting, or rather it is assumed, implicitly, that the phenomena considered have the same importance and they can be considered on the same level. This assumption reduces the risk of the arbitrariness but it could lead biased, or not completely reliable, results. However the issue is more complicated when there are two dimensions to summarize: the sectorial dimension (in this paper, the different infrastructural categories) and the territorial dimension (the Italian provinces). The problem  in particular, computing composite indicators of infrastructural endowment  is dealt with different approaches based on the sectorial and territorial variability in order to determine the weights for a set of elementary indicators. The aim of this paper is to compare some approaches, to verify the convergence and the robustness (reliability) of the results obtained.

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.

Composite indices for ranking territorial units are widely used by many international organizations in order to measure economic, social and environmental phenomena. The literature offers a great variety of aggregation methods, all with their pros and cons. In this chapter, we propose an alternative composite index which, starting from a linear aggregation, introduces penalties for the units with “unbalanced” values of the indicators. As an example of application, we consider the set of individual indicators of the Technology Achievement Index (TAI) and present a comparison between some traditional methods and the proposed index.

Assessing the quality of life (QoL) at different levels (neighbourhood, city or country) requires the definition of intermediate objectives whose achievement can be observed and measured by individual indicators. In this chapter, we consider the QoL data in Italy, at provincial level, used by the Italian economic newspaper Il Sole 24ore in 2010. The set of indicators gives complete information about the phenomenon, but the multidimensionality and the different units of measurement of the indicators can complicate the reading and the analysis of the results. Il Sole 24ore normalizes the indicators using a ‘distance to a reference’ and summarizes them by simple arithmetic mean. Nevertheless, this method does not make the indicators independent of the variability and assumes a full substitutability among the components of the index: a deficit in one dimension may be compensated by a surplus in another. To overcome these limitations, we propose a non-compensatory composite index which normalizes the indicators by a traditional ‘standardization’ and summarizes the indices of each dimension using a penalty for the provinces showing ‘unbalanced’ values of the indicators. A comparison between the approach adopted by Il Sole 24ore and the proposed method is finally presented.

The measurement of development or poverty as multidimensional phenomena is very difficult because there are several theoretical, methodological and empirical problems involved. The literature of composite indicators offers a wide variety of aggregation methods, all with their pros and cons. In this paper, we propose a new, alternative composite index denoted as MPI (Mazziotta-Pareto Index) which, starting from a linear aggregation, introduces penalties for the countries or geographical areas with ‘unbalanced’ values of the indicators. As an example of application of the MPI, we consider a set of indicators in order to measure the Millennium Development Goals (MDGs) and we present a comparison between HDI (Human Development Index) methodology, HPI (Human Poverty Index) methodology and MPI.