Skip to main content
SpringerLink
Log in

Modeling “Equitable and Sustainable Well-being” (BES) Using Bayesian Networks: A Case Study of the Italian Regions

  • Original Research
  • Published:
Social Indicators Research Aims and scope Submit manuscript

Abstract

Measurement of well-being has been a highly debated topic since the end of the last century. While some specific aspects are still open issues, a multidimensional approach as well as the construction of shared and well-rooted systems of indicators are now accepted as the main route to measure this complex phenomenon. A meaningful effort, in this direction, is that of the Italian “Equitable and Sustainable Well-being” (BES) system of indicators, developed by the Italian National Institute of Statistics (ISTAT) and the National Council for Economics and Labour (CNEL). The BES framework comprises a number of atomic indicators measured yearly at regional level and reflecting the different domains of well-being (e.g. Health, Education, Work & Life Balance, Environment,...). In this work we aim at dealing with the multidimensionality of the BES system of indicators and try to answer three main research questions: (I) What is the structure of the relationships among the BES atomic indicators; (II) What is the structure of the relationships among the BES domains; (III) To what extent the structure of the relationships reflects the current BES theoretical framework. We address these questions by implementing Bayesian Networks (BNs), a widely accepted class of multivariate statistical models, particularly suitable for handling reasoning with uncertainty. Implementation of a BN results in a set of nodes and a set of conditional independence statements that provide an effective tool to explore associations in a system of variables. In this work, we also suggest two strategies for encoding prior knowledge in the BN estimating algorithm so that the BES theoretical framework can be represented into the network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. According to this distance, given a set of continuous variable (or features) and two observations x and y, the contribution of each feature to a measure of closeness between x and y is set to 1 if the feature exhibits missing values in either x or y while, if values are not missing, it corresponds to their difference normalized by the feature range. To come up with a final distance between x and y, all features’ contributions are then aggregated by means of the euclidean distance.

References

  • Blalock, H. M, Jr. (2018). Causal inferences in nonexperimental research. Chapel Hill: UNC Press Books.

    Google Scholar 

  • Bollen, K. A., & Diamantopoulos, A. (2017). In defense of causal-formative indicators: A minority report. Psychological Methods, 22(3), 581.

    Article  Google Scholar 

  • Ceriani, L., Gigliarano, C et al. (2016). Multidimensional well-being: A Bayesian Networks approach. Tech. rep.

  • Checchi, D., & Peragine, V. (2010). Inequality of opportunity in Italy. The Journal of Economic Inequality, 8(4), 429–450.

    Article  Google Scholar 

  • Chelli, F. M., Ciommi, M., Emili, A., Gigliarano, C., & Taralli, S. (2015). Comparing equitable and sustainable well-being (BES) across the Italian provinces. A factor analysis-based approach. Rivista Italiana di Economia Demografia e Statistica, 69(3), 61–72.

    Google Scholar 

  • Chelli, F. M., Ciommi, M., Emili, A., Gigliarano, C., & Taralli, S. (2016). Assessing the equitable and sustainable well-being of the Italian provinces. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 24(Suppl. 1), 39–62.

    Article  Google Scholar 

  • Claeskens, G., & Hjort, N. L. (2008). Model selection and model averaging. Cambridge: Cambridge University Press.

    Google Scholar 

  • Cowell, R. G., Dawid, P., Lauritzen, S. L., & Spiegelhalter, D. J. (2006). Probabilistic networks and expert systems: Exact computational methods for Bayesian networks. New York: Springer Science & Business Media.

    Google Scholar 

  • D’Agostino, R. B. (1986). Goodness-of-fit-techniques (Vol. 68). Boca Raton: CRC Press.

    Google Scholar 

  • Davino, C., Dolce, P., & Taralli, S. (2017). Quantile composite-based model: A recent advance in PLS-PM. In M. Ronkko (Ed.), Partial least squares path modeling (pp. 81–108). New York: Springer.

    Chapter  Google Scholar 

  • De Muro, P., Mazziotta, M., Pareto, A. (2009). Composite indices for multidimensional development and poverty: An application to MDG indicators. In: Wye City Group Meeting.

  • Diamantopoulos, A., & Siguaw, J. A. (2006). Formative versus reflective indicators in organizational measure development: A comparison and empirical illustration. British Journal of Management, 17(4), 263–282.

    Article  Google Scholar 

  • Diamantopoulos, A., & Winklhofer, H. M. (2001). Index construction with formative indicators: An alternative to scale development. Journal of Marketing Research, 38(2), 269–277.

    Article  Google Scholar 

  • Duda, R. O., Hart, P. E., & Stork, D. G. (2012). Pattern classification. Hoboken: Wiley.

    Google Scholar 

  • Ebert-Uphoff, I., & Deng, Y. (2012a). A new type of climate network based on probabilistic graphical models: Results of boreal winter versus summer. Geophysical Research Letters, 39(19), 1–7.

    Article  Google Scholar 

  • Ebert-Uphoff, I., & Deng, Y. (2012b). Causal discovery for climate research using graphical models. Journal of Climate, 25(17), 5648–5665.

    Article  Google Scholar 

  • Ebert-Uphoff, I., & Deng, Y. (2015). Using causal discovery algorithms to learn about our planet’s climate. In V. Lakshmanan, E. Gilleland, A. McGovern, & M. Tingley (Eds.), Machine learning and data mining approaches to climate science (pp. 113–126). New York: Springer.

    Chapter  Google Scholar 

  • Ferrara, A.R., Nisticò, R. (2019). Does institutional quality matter for multidimensional well-being inequalities? Insights from Italy. Social Indicators Research pp. 1–43.

  • Franzin, A., Sambo, F., & Di Camillo, B. (2016). bnstruct: An R package for Bayesian Network structure learning in the presence of missing data. Bioinformatics, 33(8), 1250–1252.

    Google Scholar 

  • Friedman, N., Goldszmidt, M., Wyner, A. (1999a). Data analysis with Bayesian networks: A bootstrap approach. In: Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence, Morgan Kaufmann Publishers Inc., pp 196–205.

  • Friedman, N., Nachma, I., Pe’er, D. (1999b). Learning Bayesian network structure from massive datasets: The “sparse candidate” algorithm. In: Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence, Morgan Kaufmann Publishers Inc., pp 206–215.

  • Friedman, N., Linial, M., Nachman, I., & Pe’er, D. (2000). Using Bayesian networks to analyze expression data. Journal of Computational Biology, 7(3–4), 601–620.

    Article  Google Scholar 

  • Frydenberg, M. (1990). The chain graph Markov property. Scandinavian Journal of Statistics, 17, 333–353.

    Google Scholar 

  • Gardiner, S. M. (2011). A perfect moral storm: The ethical tragedy of climate change. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Hall, J., Giovannini, E., Morrone, A., Ranuzzi, G. (2010). A framework to measure the progress of societies.

  • Helldin, T., Riveiro, M. (2009). Explanation Methods for Bayesian Networks: review and application to a maritime scenario. In: Proceedings of the 3rd Annual Skövde Workshop on Information Fusion Topics (SWIFT 2009), pp 11–16.

  • Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Reconsidering formative measurement. Psychological Methods, 12(2), 205.

    Article  Google Scholar 

  • Hradsky, B. A., Penman, T. D., Ababei, D., Hanea, A., Ritchie, E. G., York, A., et al. (2017). Bayesian networks elucidate interactions between fire and other drivers of terrestrial fauna distributions. Ecosphere, 8(8), e01926.

    Article  Google Scholar 

  • ISTAT. (2015). Il benessere equo e sostenibile in italia (2015). Retrieved from https://www.istatit/it/files//2015/12/Rapporto_BES_2015pdf.

  • ISTAT. (2018). Il benessere equo e sostenibile in italia (2018). Retrieved from https://www.istatit/it/files//2018/12/Bes_2018pdf.

  • Jordan, M. I. (1998). Learning in graphical models (Vol. 89). New York: Springer Science & Business Media.

    Book  Google Scholar 

  • Kitov, I., Kitov, O. (2011). Employment, unemployment and real economic growth. Unemployment and Real Economic Growth (July 24, 2011).

  • Kolar, M. (2013). Uncovering structure in high-dimensions: Networks and multi-task learning problems. PhD thesis, figshare.

  • Koller, D., Friedman, N., & Bach, F. (2009). Probabilistic graphical models: principles and techniques. London: MIT Press.

    Google Scholar 

  • Kreyenfeld, M., & Hank, K. (2000). Does the availability of child care influence the employment of mothers? Findings from western germany. Population Research and Policy Review, 19(4), 317–337.

    Article  Google Scholar 

  • Lappenschaar, M., Hommersom, A., Lucas, P. J., Lagro, J., & Visscher, S. (2013). Multilevel Bayesian networks for the analysis of hierarchical health care data. Artificial Intelligence in Medicine, 57(3), 171–183.

    Article  Google Scholar 

  • Lauritzen, S. L. (1996). Graphical models (Vol. 17). Oxford: Clarendon Press.

    Google Scholar 

  • Lauritzen, S. L., & Wermuth, N. (1989). Graphical models for associations between variables, some of which are qualitative and some quantitative. The Annals of Statistics, 17, 31–57.

    Google Scholar 

  • Maggino, F. (2017). Developing indicators and managing the complexity. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis (pp. 87–114). New York: Springer.

    Chapter  Google Scholar 

  • Maggino, F., & Zumbo, B. D. (2012). Measuring the quality of life and the construction of social indicators. In K. C. Land, A. C. Michalos, & M. J. Sirgy (Eds.), Handbook of social indicators and quality of life research (pp. 201–238). New York: Springer.

    Chapter  Google Scholar 

  • Maitah, M., Toth, D., & Kuzmenko, E. (2015). Exploring the relationship between economic growth and employment in the Czech Republic and Belgium. European Studies Review, 7, 115.

    Google Scholar 

  • Mazziotta, M., & Pareto, A. (2016). On a generalized non-compensatory composite index for measuring socio-economic phenomena. Social Indicators Research, 127(3), 983–1003.

    Article  Google Scholar 

  • Mazziotta, M., & Pareto, A. (2019). Use and misuse of PCA for measuring well-being. Social Indicators Research, 142(2), 451–476.

    Article  Google Scholar 

  • Milns, I., Beale, C. M., & Smith, V. A. (2010). Revealing ecological networks using Bayesian network inference algorithms. Ecology, 91(7), 1892–1899.

    Article  Google Scholar 

  • Molina, J. L., Pulido-Velázquez, D., García-Aróstegui, J. L., & Manuel, P. V. (2013). Dynamic Bayesian networks as a decision support tool for assessing climate change impacts on highly stressed groundwater systems. Journal of Hydrology, 479, 113–129.

    Article  Google Scholar 

  • Monte, A., Schoier, G. (2017). Il benessere economico e la sua evoluzione nelle regioni italiane: un’analisi attraverso indicatori.

  • Neapolitan, R. E., et al. (2004). Learning bayesian networks (Vol. 38). Upper Saddle River, NJ: Pearson Prentice Hall.

    Google Scholar 

  • Oposa, A. A. (1994). In defense of future generations. Phil LJ, 69, 164.

    Google Scholar 

  • Panzera, D., & Postiglione, P. (2019). Measuring the spatial dimension of regional inequality: An approach based on the gini correlation measure. Social Indicators Research, 148, 379–394.

    Article  Google Scholar 

  • Pearl, J. (2014). Probabilistic reasoning in intelligent systems: Networks of plausible inference. Amsterdam: Elsevier.

    Google Scholar 

  • Penny, R.N., Reale, M. (2004). Using graphical modelling in official statistics.

  • Peterson, R. (2018). bestNormalize: Normalizing transformation functions. R package version, 1(2).

  • Peterson, R.A., Cavanaugh, J.E. (2019). Ordered quantile normalization: A semiparametric transformation built for the cross-validation era. Journal of Applied Statistics. https://doi.org/10.1080/02664763.2019.1630372.

  • Rodin, A., Mosley, T. H, Jr., Clark, A. G., Sing, C. F., & Boerwinkle, E. (2005). Mining genetic epidemiology data with Bayesian networks application to APOE gene variation and plasma lipid levels. Journal of Computational Biology, 12(1), 1–11.

    Article  Google Scholar 

  • Russell, S. J., & Norvig, P. (2016). Artificial intelligence: A modern approach. Malaysia: Pearson Education Limited.

    Google Scholar 

  • Scutari, M., & Denis, J. B. (2014). Bayesian networks: With examples in R. Boca Raton: Chapman and Hall/CRC.

    Book  Google Scholar 

  • Scutari, M., Howell, P., Balding, D. J., & Mackay, I. (2014). Multiple quantitative trait analysis using Bayesian networks. Genetics, 198(1), 129–137.

    Article  Google Scholar 

  • Scutari, M., Ness, R. (2012). bnlearn: Bayesian network structure learning, parameter learning and inference. R package version 3.

  • Sebastiani, P., & Ramoni, M. (2001). On the use of Bayesian networks to analyze survey data. Research in Official Statistics, 4(1), 53–64.

    Google Scholar 

  • Sen, A., et al. (1999). Commodities and capabilities. Oxford: OUP Catalogue.

    Google Scholar 

  • Stiglitz, J.E., Sen, A., Fitoussi, J.P., on the Measurement of Economic Performance C, Progress S (2009). Report by the commission on the measurement of economic performance and social progress.

  • Van der Heijden, M., Velikova, M., & Lucas, P. J. (2014). Learning Bayesian networks for clinical time series analysis. Journal of Biomedical Informatics, 48, 94–105.

    Article  Google Scholar 

  • Verma, T., & Pearl, J. (1991). Equivalence and synthesis of causal models. Computer Science Department: UCLA.

  • Vitolo, C., Scutari, M., Ghalaieny, M., Tucker, A., & Russell, A. (2018). Modeling air pollution, climate, and health data using Bayesian Networks: A case study of the English regions. Earth and Space Science, 5(4), 76–88.

    Article  Google Scholar 

  • Wainwright, M. J., Jordan, M. I., et al. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends in Machine Learning, 1(1–2), 1–305.

    Article  Google Scholar 

  • Wesselink, B., Bakkes, J., Best, A., Hinterberger, F., ten Brink, P. (2007). Measurement beyond GDP. Beyond GDP 304.

  • Whittaker, J. (2009). Graphical models in applied multivariate statistics. Hoboken: Wiley Publishing.

    Google Scholar 

  • Wilcox, J. B., Howell, R. D., & Breivik, E. (2008). Questions about formative measurement. Journal of Business Research, 61(12), 1219–1228.

    Article  Google Scholar 

  • Wilson, D. R., & Martinez, T. R. (1997). Improved heterogeneous distance functions. Journal of Artificial Intelligence Research, 6, 1–34.

    Article  Google Scholar 

  • Zhou, Y. (2011). Structure learning of probabilistic graphical models: a comprehensive survey. arXiv:11116925.

Download references

Author information

Authors and Affiliations

  1. Department of Statistical Sciences, University of Rome La Sapienza, Rome, Italy

    Federica Onori & Giovanna Jona Lasinio

Authors
  1. Federica Onori
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giovanna Jona Lasinio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federica Onori.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Tables 2, 3, 4, 5, 6, 7, 8and 9.

Table 2 BES dataset: BES domains and corresponding atomic indicators (Outcome domains) (ISTAT 2018)
Full size table
Table 3 BES dataset: BES domains and corresponding atomic indicators (Context domains) (ISTAT 2018)
Full size table
Table 4 Pearson P test statistic for Gaussianity and the corresponding used transformation for each atomic indicator (Outcome domains)
Full size table
Table 5 Pearson P test statistic for Gaussianity and the corresponding used transformation for each atomic indicator (Context domains)
Full size table
Table 6 Prior blacklist: list of the edges \(X \rightarrow Y\) not allowed to be present in the network structure
Full size table
Table 7 Network estimated by adopting prior Strategy 1 with NUTS 1 level areas (NW-NE-C-S-I): in-degree, out-degree and Markov blanket size of the nodes (Outcome domains)
Full size table
Table 8 Network estimated by adopting prior Strategy 1 with NUTS 1 level areas (NW-NE-C-S-I): in-degree, out-degree and Markov blanket size of the nodes (Context domains)
Full size table
Table 9 Network estimated by adopting prior Strategy 1 with NUTS 1 level areas (NW-NE-C-S-I): direct connections among domains
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Onori, F., Jona Lasinio, G. Modeling “Equitable and Sustainable Well-being” (BES) Using Bayesian Networks: A Case Study of the Italian Regions. Soc Indic Res 161, 1003–1037 (2022). https://doi.org/10.1007/s11205-020-02406-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11205-020-02406-8

Keywords

Search

Navigation