Bayesian Networks Model Averaging for Bes Indicators
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Bayesian Networks Model Averaging for Bes Indicators Pierpaolo D’Urso1 · Vincenzina Vitale1 Accepted: 31 May 2020 © Springer Nature B.V. 2020
Abstract The measure of the equitable and sustainable well-being (Bes) is of growing interest in the last years. The National Institute of Statistics (Istat) provides, for Italy, a wide set of indicators describing each domain of well-being that is, by definition, a multidimensional concept. In this study, we propose the use of Bayesian networks to deal with basic and composite Bes indicators. Its capability to model very complex multivariate dependence structures is useful to describe the relationships between indicators belonging to different domains and, being a probabilistic expert system, the estimated network could be also useful for probabilistic inference and what-if analysis. In this study, all the Bayesian networks structures have been estimated by means of the hill climbing algorithm based on bootstrap resampling and model averaging in order to prevent bias due to deviations from the normality assumption. Keywords Bayesian networks · Equitable and sustainable well-being · Structural learning · Bootstrap resampling
1 Introduction The equitable and sustainable well-being (Bes) is a measure of the progress of the society, focusing not only on the economic aspects but also on the social and environmental ones. As other social and economic phenomena (i.e. development, poverty), as highlighted in the seminal papers of Sen (1980, 1985), the Bes has a multidimensional nature. Therefore, the definition of a global indicator framework is needed. In Italy, Istat developed a multidimensional approach to measure the “Equitable and Sustainable Well-being”, taking into account 130 basic indicators, grouped into 12 dimensions of well-being (for further insights see Stiglitz et al. 2009; Cnel and Istat 2015; OECD 2015): Health, Education and training, Work and life balance, Economic well-being, Social relationships, Politics and institutions, Safety, Subjective well-being, Landscape and cultural heritage, Environment, Innovation, research and creativity * Vincenzina Vitale [email protected] Pierpaolo D’Urso [email protected] 1
Dipartimento di Scienze Sociali ed Economiche, Sapienza Università di Roma, Rome, Italy
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and Quality of services. Synthetic indicators for each domain are also computed by the aggregation of some basic indicators. In this regard, the interest, in literature, on composite indicators and their aggregation methods is growing rapidly in the last decade; to give some important examples of composite indexes we cite the World Economic Forum’s Global Competitiveness Index, the United Nations’ Human Development Index (HDI) and Human Poverty Index. As pointed out by Alaimo and Maggino (2020), all proposed methods for constructing composites indexes, in literature, have their strengths and weaknesses and there is no “such thing as the best method”. The choice of the aggregation function surely
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