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.
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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.
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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.
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References
Alkire, S., & Foster, J. (2011). Counting and multidimensional poverty measurement. Journal of Public Economics, 95(7–8), 476–487.
Annoni, P., & Bruggemann, R. (2009). Exploring partial order of European countries. Social Indicators Research, 92, 471–487.
Annoni, P., Fattore, M., & Bruggemann, R. (2011). A multi-criteria fuzzy approach for analyzing poverty structure. Statistica & Applicazioni – Special Issue, 2011, 7–30.
Arcagni, A., & Fattore, M. (2014). PARSEC: An R package for poset-based evaluation of multidimensional poverty. In R. Bruggemann, L. Carlsen, & J. Wittmann (Eds.), MultiIndicator systems and modelling in partial order. Berlin: Springer.
Bruggemann, R., & Carlsen, L. (2014). Incomparable-what now? MATCH Communications in Mathematical and in Computer Chemistry, 71, 699–714.
Bruggemann, R., & Patil, G. P. (2010). Multicriteria prioritization and partial order in environmental sciences. Environmental and Ecological Statistics, 17, 383–410.
Bruggemann, R., & Patil, G. P. (2011). Ranking and prioritization for multi-indicator systems – introduction to partial order applications. New York: Springer.
Bruggemann, R., & Voigt, K. (2012). Antichains in partial order, example: Pollution in a German region by lead, cadmium, zinc and sulfur in the herb layer. MATCH Communications in Mathematical and in Computer Chemistry, 67, 731–744.
Bruggemann, R., Pudenz, S., Voigt, K., Kaune, A., & Kreimes, K. (1999). An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetics. Chemosphere, 38, 2263–2279.
Bubley, R., & Dyer, M. (1999). Faster random generation of linear extensions. Discrete Mathematics, 201, 81–88.
Carlsen, L., & Bruggemann, R. (2014). The “failed state index”: Offers more than just a simple ranking. Social Indicators Research, 115, 525–530.
Cerioli, A., & Zani, S. (1990). A fuzzy approach to the measurement of poverty. In C. Dagum & M. Zenga (Eds.), Income and wealth distribution, inequality and poverty. Berlin: Springer.
Davey, B. A., & Priestley, B. H. (2002). Introduction to lattices and order. Cambridge: CUP.
Fattore, M. (2008). Hasse diagrams, poset theory and fuzzy poverty measures. Rivista INternazionale di Science Sociali, 1, 63–75.
Fattore, M. (2015). Partially ordered sets and the measurement of multidimensional ordinal deprivation. Social Indicators Research, 128(2), 835. doi:10.1007/s11205-015-1059-6.
Fattore, M., & Arcagni, A. (2016). A reduced posetic approach to the measurement of multidimensional ordinal deprivation. Social Indicators Research (to be published)
Fattore, M., & Maggino, F. (2014). Partial orders in socio-economics: A practical challenge for poset theorists or a cultural challenge for social scientists? In R. Bruggemann, L. Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order. Berlin: Springer.
Fattore, M., Bruggemann, R., & Owsinski, J. (2011). Using poset theory to compare fuzzy multidimensional material deprivation across regions. In S. Ingrassia, R. Rocci, & M. Vichi (Eds.), New perspectives in statistical modeling and data analysis. Berlin: Springer.
Fattore, M., Maggino, F., & Colombo, E. (2012). From composite indicators to partial order: Evaluating socio-economic phenomena through ordinal data. In F. Maggino & G. Nuvolati (Eds.), Quality of life in Italy: Research and reflections, Social indicators research series 48. New York: Springer.
Lemmi, A., & Betti, G. (Eds.). (2006). Fuzzy set approach to multidimensional poverty measurement. New York: Springer.
Madden, D. (2010). Ordinal and cardinal measures of health inequality: An empirical comparison. Health Economics, 19, 243–250.
Neggers, J., & Kim, S. H. (1998). Basic posets. Singapore: World Scientific.
Patil, G. P., & Taillie, C. (2004). Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization. Environmental and Ecological Statistics, 11, 199–228.
Qizilbash, M. (2006). Philosophical accounts of vagueness, fuzzy poverty measures and multidimensionality. In A. Lemmi & G. Betti (Eds.), Fuzzy set approach to multidimensional poverty measurement. New York: Springer.
R Core Team. (2012). R: A language and environment for statistical computing, R Foundation for Statistical Computing. Vienna, Austria. http://www.R-project.org/
Schroeder, B. (2002). Ordered set. An introduction. Boston: Birkhauser.
Sen, A. (1992). Inequality reexamined. Cambridge: Harvard University Press.
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Fattore, M. (2017). Synthesis of Indicators: The Non-aggregative 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_8
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