Abstract
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).
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Notes
- 1.
Some authors describe a greater number of steps (e.g., imputation of missing data). We report only the fundamental steps.
- 2.
The ‘complement with respect to 1’ is the number to add to make 1.
- 3.
Note that the equal weighting approach may give extra weight to certain performance aspects if several individual indicators are in effect measuring the same attribute. As a remedy, indicators could be tested for statistical correlations, and lower weights could be given to variables strongly correlated with each other. On the other hand, correlations may merely show that unit performance on these indicators is similar (Freudenberg 2003).
- 4.
Although PCA has a number of excellent mathematical properties, its use in weighting components of social indices is dubious. For example, it may lead to indicators which have little variation being assigned small weights, irrespective of their possible contextual importance (Salzman 2003).
- 5.
Note that compensability/non-compensability does not imply dependence/independence and vice-versa. For example, “Hospital beds (per 1000 people)” and “Hospital doctors (per 1000 people)” are two dependent (positively correlated) indicators but they are non-substitutable, because a deficit in beds cannot be compensated by a surplus in doctors and vice-versa (Mazziotta and Pareto 2015a).
- 6.
Note that a ‘partially compensatory’ approach can be considered ‘non-compensatory’, since it is not full compensatory.
- 7.
Note that a simple non-compensatory approach uses the minimum (maximum) value of the normalized indicators so that the other values cannot increase (decrease) the value of the index. This function realizes the maximum penalization for unbalanced values of the indicators (Casadio Tarabusi and Guarini 2013).
- 8.
Normalized indicators have a mean of 100 and standard deviation of 10.
- 9.
Normalized indicators range approximately between 70 and 130.
- 10.
Point (a) can be verified by applying the traditional approaches of statistical hypothesis testing, whereas specific coefficients were proposed for evaluating (b) (Guilford 1954). Receiver operating characteristic (ROC) analysis allows to identify discriminant cut-points in (c).
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Mazziotta, M., Pareto, A. (2017). Synthesis of Indicators: The Composite Indicators Approach. In: Maggino, F. (eds) Complexity in Society: From Indicators Construction to their Synthesis. Social Indicators Research Series, vol 70. Springer, Cham. https://doi.org/10.1007/978-3-319-60595-1_7
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