Synthesis of Indicators: The Non-aggregative Approach

Abstract

The need for new tools in synthetic indicators construction in the social sciences is deeply related to the problem of describing and understanding increasingly complex societal facts. On the one hand, official surveys, administrative data, web data, open data, to say a few, are now easily available to social scientists in the form of wide and complex multidimensional indicator systems. On the other hand, as data complexity grows, the need to get effective synthetic views, capable to enhance decision-making, increases as well. New procedures for data treatment are necessary, to overcome the limitations of older approaches that are designed for simpler data systems, are based on the “synthesis-as-aggregation” paradigm and employ composite indicators as their main statistical tool. To make a concrete example, consider the “beyond GDP” perspective to well-being and to societal evaluation. Going “beyond GDP” invariably requires dealing with multidimensional systems of ordinal data (e.g. pertaining to ownership of goods, access to services, self-perception of health and economic status…), ruling out the possibility to directly apply the composite indicator approach to measurement (Fattore 2015). In this and similar contexts, two main issues arise.

• 1. Ordinal attributes cannot be aggregated through linear combinations, averages or other functionals, designed for numerical variables. In fact, ordinal scores cannot be summed, multiplied by scalars or composed in other ways. For this reason, they are often transformed into numerical scores, through more or less sophisticated scaling tools, before aggregation. Unfortunately, there are evidences that such procedures may lead to controversial results (Madden 2010). Moreover, one could legitimately ask why concepts naturally conceived in ordinal terms should be forced into numerical settings. Is the idea of ordinal scores as rough manifestations of underlying continuous traits always well founded? Or is it actually motivated by the lack of consistent and effective procedures for the treatment of ordinal data? Such problems go beyond the setting of well-being measurement and arise in many other fields as well. For example, in marketing and customer segmentation, in ecological and environmental studies, in risk management and, more generally, in ordinal multi-criteria decision-making (Bruggemann et al. 1999; Annoni and Bruggemann 2009; Bruggemann and Patil 2010, 2011; Bruggemann and Voigt 2012; Bruggemann and Carlsen 2014; Carlsen and Bruggemann 2014). It is in fact a feature of modern information society that most of data we deal with are of a discrete and qualitative kind. The absence of statistical tools and procedures to manage such data types consistently may well turn into severe limitations in our capability to exploit the great amount of information they convey.

• 2. Independently of their nature, it is a matter of fact that many data systems available to social scientists often comprise weakly interdependent attributes. The absence of strong interconnections in a multi-indicator system prevents from achieving effective dimension reductions through aggregation procedures. Consequently, and independently of the models or of the procedures they are computed from (e.g. latent variables or structural equation models, PLS path modeling or other formative aggregation tools), composite indicators are inherently inappropriate in these situations, being aggregative and compensative. This leads to a fundamental question: is attribute aggregation the only road to synthesis? The answer to this question motivates most of the present chapter.