Abstract
Indicators play an increasing role in characterizing complex systems and – to some degree – in decision problems, when a ranking is thought of as an intermediate step for a selection of optimal – or depending on external constraints – suboptimal options. When ranking is the aim, we cannot usually describe it by a single indicator. We need a set of indicators, called a Multi-Indicator system (MIS). Typically, an analysis of MIS is confronted with the following problems: • Scaling level: What to do, if the indicators are on a nominal, ordinal, or metric level • Relevance of indicators: Are we confronted with somewhat which may be called information noise? • Role of the inherent characteristic of partial orders, the incomparability. Is incomparability an unavoidable disadvantage? Methods to check these points are presented and critically discussed.
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Notes
- 1.
For the main characteristics of these two different approaches, see Maggino (2017a). The literature about the difference between these two tipes of models is rich. As shown by Alaimo and Maggino (2020), the state of the theory on formative models has been in intense discussion for some years. Several authoritative scholars (for instance, Edwards 2011; Aguirre-Urreta et al. 2016) have questioned the validity of this method and published appeals to no longer host its applications in scientific journals. The debate seems to be far from being resolved. We would like to point out that the choice between the two types of model does not depend directly on the researcher, but exclusively on the nature and direction of relationships between constructs and measures.
- 2.
For more information, see Maggino 2017a.
- 3.
- 4.
For instance, in two papers on sustainable development and regional differences in Italy, Alaimo and Maggino show how similar values in composite indicators assumed by different regions can represent similar or even completely different combinations in basic indicators (Alaimo and Maggino 2018, 2020).
- 5.
In particular, the computations performed to assign numerical scores to the statistical units involve only the ordinal features of data, avoiding any scaling procedure or any other transformation of the kind.
References
Aguirre-Urreta, M. I., Rönkkö, M., & Marakas, G. M. (2016). Omission of causal indicators: Consequences and implications for measurement. Measurement: Interdisciplinary Research and Perspectives, 14(3), 75–97.
Alaimo, L. S. (2020). Complexity of social phenomena: Measurements, analysis, representations and synthesis. Unpublished Doctoral Dissertation, University of Rome “La Sapienza”, Rome, Italy.
Alaimo, L. S., & Maggino, F. (2018). Sviluppo sostenibile e differenze regionali. In E. di Bella, F. Maggino, & M. Trapani (Eds.), AIQUAV 2018. V Convegno dell’Associazione Italiana per gli Studi sulla Qualità della Vita. Libro dei Contributi Brevi (pp. 199–206). Genova: Genova University Press.
Alaimo, L. S., & Maggino, F. (2020). Sustainable development goals indicators at territorial level: Conceptual and methodological issues—The Italian perspective. Social Indicators Research, 147, 383–419. https://doi.org/10.1007/s11205-019-02162-4.
Bruggemann, R., & Annoni, P. (2014). Average heights in partially ordered sets. MATCH Communications in Mathematical and in Computer Chemistry, 71, 101–126.
Bruggemann, R., & Carlsen, L. (2011). An improved estimation of averaged ranks of partially orders. MATCH Communications in Mathematical and in Computer Chemistry, 65, 383–414.
Bruggemann, R., & Carlsen, L. (2014). Incomparable-what now? MATCH Communications in Mathematical and in Computer Chemistry, 71, 699–714.
Bruggemann, R., & Kerber, A. (2018). Fuzzy logic and partial order; first attempts with the new PyHasse-program L_eval. MATCH Communications in Mathematical and in Computer Chemistry, 80, 745–768.
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. (2011). A new tool to analyze partially ordered sets – Application: Ranking of polychlorinated biphenyls and alkanes/alkenes in river main, Germany. MATCH Communications in Mathematical and in Computer Chemistry, 66, 231–251.
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., Sørensen, P. B., Lerche, D., & Carlsen, L. (2004). Estimation of averaged ranks by a local partial order model. Journal of Chemical Information and Computer Sciences, 44, 618–625.
Bubley, R., & Dyer, M. (1999). Faster random generation of linear extensions. Discrete Mathematics, 201, 81–88.
Carlsen, L. (2018). Happiness as a sustainability factor. The world happiness index: A posetic-based data analysis. Sustainability Science, 13, 549–571.
Carlsen, L., & Bruggemann, R. (2017). Fragile state index: Trends and developments, a partial order data analysis. Social Indicators Research, 133, 1–14.
Davey, B. A., & Priestley, H. A. (1990). Introduction to lattices and order. Cambridge: Cambridge University Press.
De Loof, K., De Meyer, K. H., & De Baets, B. (2006). Exploiting the lattice of ideals representation of a poset. Fundamenta Informaticae, 71, 309–321.
Edwards, J. R. (2011). The fallacy of formative measurement. Organizational Research Methods, 14(2), 370–388.
Erdi, P. (2008). Complexity explained. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-540-35778-0.
Fattore, M. (2016). Partially ordered sets and the measurement of multidimensional ordinal deprivation. Social Indicators Research, 128, 835–858.
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 (pp. 197–214). New York: Springer.
Fattore, M., Maggino, F., & Greselin, F. (2011). Socio-economic evaluation with ordinal variables: Integrating and poset approaches. Statistica & Applicazioni, Special Issue, 2011, 31–42.
Gorban, A. N., & Yablonsky, G. S. (2013). Grasping complexity. Computers & Mathematics with Applications, 65(10), 1421–1426.
Kerber, A. (2017). Evaluation, considered as problem orientable mathematics over lattices. In R. Bruggemann & M. Fattore (Eds.), Partial order concepts in applied sciences (pp. 87–103). Cham: Springer.
Kerber, A., & Bruggemann, R. (2015). Problem driven evaluation of chemical compounds and its exploration. MATCH Communications in Mathematical and in Computer Chemistry, 73, 577–613.
Lazarsfeld, P. F. (1958). Evidence and inference in social research. Daedalus, 87(4), 99–130.
Lima, M. (2013). Visual complexity: Mapping patterns of information. New York: Princeton Architectural Press.
Luther, B., Bruggemann, R., & Pudenz, S. (2000). An approach to combine cluster analysis with order theoretical tools in problems of environmental pollution. Match, 42, 119–143.
Maggino, F. (2009). The state of the art in indicators construction in the perspective of a comprehensive approach in measuring Well-being of societies. Firenze: Firenze University Press, Archivio E-Prints.
Maggino, F. (2017a). Developing indicators and managing the complexity. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis (pp. 87–114). Cham: Springer.
Maggino, F. (2017b). Dealing with synthesis in a system of indicators. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis (pp. 115–137). Cham: Springer.
Mazziotta, M., & Pareto, A. (2017). Synthesis of indicators: The composite indicators approach. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis (pp. 161–191). Cham: Springer.
Meadows, D. H. (2009). Thinking in systems: A primer. London: Earthscan.
Morin, E. (1984). Le vie della complessità. In G. Bocchi & M. Cerruti (Eds.), La sfida della complessità (pp. 49–60). Milano: Feltrinelli.
Porter, T. M. (2001). Trust in numbers: The pursuit of objectivity in science and public life. Princeton: Princeton University Press.
Restrepo, G. (2014). Quantifying complexity of partially ordered sets. In R. Bruggemann, L. Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order (pp. 85–103). New York: Springer.
Sacconaghi, R. (2017). Building Knowledge. Between Measure and Meaning: A Phenomenological Approach. In Complexity in Society: From Indicators Construction to their Synthesis, ed. F. Maggino, 51–68. Cham: Springer.
Tufte, E. R. (2015). The visual display of quantitative information. Cheshire: Graphics Press.
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Maggino, F., Bruggemann, R., Alaimo, L.S. (2021). Indicators in the Framework of Partial Order. In: Bruggemann, R., Carlsen, L., Beycan, T., Suter, C., Maggino, F. (eds) Measuring and Understanding Complex Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-030-59683-5_2
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