Abstract
The aim of this work is to propose a tool for measuring a complex concept, and to apply it to big sets of data measured on ordinal and/or dichotomous scales. An important field of application are subjective data, that are often based on opinions or personal evaluations. Many national and international surveys employ this kind of data, measured among thousand of individuals. Thanks to the use of the “average rank” as a synthetic measure of a complex concept, we believe that poset theory could be a very useful approach for dealing with ordinal data avoiding the use of scaling procedures. Because classic poset approaches are at their best when applied to few data at a time, our idea is based on a procedure for sampling units from a big population using a simple criterion to summarize the resulting values appropriately. Applying the central limit theorem enables a comparison of the results obtained from different groups using statistical tests on the means. We used our Height of Groups by Sampling (HOGS) method to compare the average rank among groups that are defined by one or more socio-demographic variables influencing the level of the complex concept we wish to measure. The application of the HOGS procedure to life satisfaction in Italy generated convincing results, revealing significant differences between regions, genders and levels of formal education. We compared the results given by HOGS with the non linear principal component analysis and obtain an easy readable output with convincing precision and accuracy; we are confident that the HOGS procedure can be applied to many other concepts investigated in the social sciences.
Similar content being viewed by others
References
Brüggemann, R., & Carlsen, L. (2011). An improved estimation of averaged ranks of partial orders. MATCH Communications in Mathematical and in Computer Chemistry, 65, 383–414.
Brüggemann, R., & Patil, G. P. (2011). Ranking and prioritization for multi-indicator systems (Vol. 5). New York: Springer.
Brüggemann, 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(2), 618–625.
Brüggemann, R., & Voigt, K. (2009). Analysis of partial orders in environmental systems applying the new software pyhasse. In J. Wittmann, M. Flechsig (Eds.), Simulation in Umwelt-und Geowissenschaften, Workshop Potsdam (pp. 43–55), ShakerVerlag.
Caperna, G. (2016). Partial order theory for synthetic indicators. Ph.D. thesis, University of Padova.
Cummins, R. A. (1996). The domains of life satisfaction: An attempt to order chaos. Social Indicators Research, 38(3), 303–328.
Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order. New York: Cambridge University Press.
De Leeuw, J., & Mair, P. (2009). Gifi methods for optimal scaling in r: The package homals. Journal of Statistical Software, 31(4), 1–30.
De Loof, K. (2009). Efficient computation of rank probabilities in posets. Ph.D. thesis, University of Ghent.
De Loof, K., De Baets, B., & De Meyer, H. (2011). Approximation of average ranks in posets. MATCH Communications in Mathematical and in Computer Chemistry, 66, 219–229.
Fattore, M. (2015). Partially ordered sets and the measurement of multidimensional ordinal deprivation. Social Indicators Research, 1–24. doi:10.1007/s11205-015-1059-6.
Fattore, M., & Arcagni, A. (2014). Parsec: an r package for poset-based evaluation of multidimensional poverty. In R. Brüggeman, L. Carlsen & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order (pp. 317–330). New York: Springer.
Flanagan, J. C. (1978). A research approach to improving our quality of life. American Psychologist, 33(2), 138–147.
Gifi, A. (1990). Nonlinear multivariate analysis. Chicester: Wiley.
Gupta, D. K., Jongman, A. J., & Schmid, A. P. (1994). Creating a composite index for assessing country performance in the field of human rights: Proposal for a new methodology. Human Rights Quarterly, 6(1), 131–162.
Krupinski, J. (1980). Health and quality of life. Social Science and Medicine Part A: Medical Psychology and Medical Sociology, 14(3), 203–211.
Lerche, D., & Sørensen, P. B. (2003). Evaluation of the ranking probabilities for partial orders based on random linear extensions. Chemosphere, 53(8), 981–992.
Loewe, N., Bagherzadeh, M., Araya-Castillo, L., Thieme, C., & Batista-Foguet, J. M. (2014). Life domain satisfactions as predictors of overall life satisfaction among workers: Evidence from chile. Social Indicators Research, 118(1), 71–86.
Maggino, F., & Fattore, M. (2011). New tools for the construction of ranking and evaluation indicators in multidimensional systems of ordinal variables. In Proceedings of the: New techniques and technologies for statistics, Brussels. https://ec.europa.eu/eurostat/cros/sites/crosportal/files/S16P4.pdf-20/02/2016.
Maggino, F., & Nuvolati, G. (2012). Quality of life in Italy: Research and reflections (Vol. 48). Dordrecht: Springer Science & Business Media.
Polya, G. (1920). Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem. Mathematische Zeitschrift, 8(3), 171–181.
Rojas, M. (2006). Life satisfaction and satisfaction in domains of life: Is it a simple relationship? Journal of Happiness Studies, 7(4), 467–497.
Schröder, B. (2012). Ordered sets: An introduction. New York: Springer Science & Business Media.
Veenhoven, R. (2012). Happiness: Also known as life satisfaction and subjective well-being. In K. C. Land, A. C. Michalos, & J. Sirgy (Eds.), Handbook of social indicators and quality of life research (pp. 63–77). Dordrecht: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Caperna, G., Boccuzzo, G. Use of Poset Theory with Big Datasets: A New Proposal Applied to the Analysis of Life Satisfaction in Italy. Soc Indic Res 136, 1071–1088 (2018). https://doi.org/10.1007/s11205-016-1482-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11205-016-1482-3