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Posetic Tools in the Social Sciences: A Tutorial Exposition

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Measuring and Understanding Complex Phenomena

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Abstract

In this chapter, we provide a brief outline of the main motivations why partial order theory is of key importance in the statistical analysis of socio-economic data, presenting some of the more recent tools available for practical applications. We focus in particular on four typical problems in the analysis of socio-economic data, namely: (i) the construction of rankings, (ii) the evaluation of multidimensional latent traits, like deprivation, (iii) the comparison of statistical populations scored on multi-indicator systems and (iv) the measurement of multidimensional ordinal inequality. The exposition has a didactic aim; statistical procedures are sketched avoiding technical details, but discussing simple examples and providing the relevant software code, in the R language.

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Notes

  1. 1.

    Let A be a square matrix; a vector x is called eigenvector of A relative to the eigenvalue a if it holds A x = a x, where a is a real number. Eigenvectors, when they exist, provide deep information on the structure of the input matrix and are often used in multivariate statistics, to produce optimal data synthesis.

  2. 2.

    ORIM stands for “Osservatorio regionale per l’integrazione e la multietnicità” (“Regional observatory on integration and multiethnicity”).

  3. 3.

    Given two cumulative distributions F(t) and G(t), defined on the same totally ordered set T (which can be either continuous or discrete), we say that G first-order dominates F, if G(t) ≤ F(t), ∀t ∈ T. As described in Fattore and Arcagni (2018), the notion of stochastic dominance can be made fuzzy, computing a degree of dominance in [0,  1].

  4. 4.

    Dimension 1: Subjective and self-reported health. Dimension 2: Pain or discomfort in shoulder, back, arms, legs…; headaches; sleeping problems, depression, anxiety…Dimension 3: Asthma, allergy; migraine; diabetes; hypertension; chronic bronchitis. Dimension 4: Tobacco use; excessive alcohol consumption, obesity; unhealthy life style…

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Author information

Authors and Affiliations

  1. Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy

    Marco Fattore

  2. Department MEMOTEF, Sapienza University of Rome, Rome, Italy

    Alberto Arcagni

Authors
  1. Marco Fattore
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  2. Alberto Arcagni
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Corresponding author

Correspondence to Marco Fattore .

Editor information

Editors and Affiliations

  1. Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany

    Rainer Bruggemann

  2. Awareness Center, Trekroner, Roskilde amt, Denmark

    Lars Carlsen

  3. Institut de Sociologie, Université de Neuchâtel, Neuchâtel, Neuchatel, Switzerland

    Tugce Beycan

  4. Institut de Sociologie, Universite de Neuchatel, Neuchatel, Switzerland

    Christian Suter

  5. Dipartimento di Scienze Statistiche, Sapienza University of Rome, Roma, Italy

    Filomena Maggino

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Fattore, M., Arcagni, A. (2021). Posetic Tools in the Social Sciences: A Tutorial Exposition. 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_15

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