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Comparing Latent Subgroups

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Multilateral Wellbeing Comparison in a Many Dimensioned World

Part of the book series: Global Perspectives on Wealth and Distribution ((GPWD))

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Abstract

Frequently, the groupings of interest in a society are not directly observed; they are latent and unknown in number. In this chapter, a technique for determining the number of groups and partially determining an agents’ group membership is explored. The determination is partial in the sense that only the probability of an individual’s membership of a group can be determined. The technique is based upon mixture distributions, for which a good reference is McLachlan and Peel (Finite Mixture Models. Wiley, New York, 2000). After outlining the nature of mixture distributions, estimation, calculation of the probability of class membership and determining the optimal number of classes are discussed. Ultimately, possibilities for examining the determinants of group membership are outlined.

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Notes

  1. 1.

    Examples of disputed boundaries are not hard to find; determining the poor has probably been the most contentious (e.g. Sen 1982; Foster 1998). Things are not different when the focus of the analysis is on the middle or rich class (Atkinson and Brandolini 2013; Banerjee and Duflo 2008; Easterly 2001; Saez and Veall 2005). The most recent disputation as to the value of this type of classification argues that “wellness” is in general a many dimensioned concept so that income of itself is but a reflection of societal wellness (Stiglitz et al. 2010). Sen and others (e.g. papers in Grusky and Kanbur, 2006; Kakwani and Silber 2008; Nussbaum, 1997 2011; Alkire and Foster 2011) have forcibly argued that limitations to individual’s functionings and capabilities should be considered the determining factors in her/his poorness or wellness, again implying that an individual’s income will only partially reflect her/his poverty status.

  2. 2.

    Indeed, this is generally assumed in practice in elementary wellbeing measurement.

  3. 3.

    The law is basically a central limit theorem (see Chap. 2) using the idea that averages of things will be normally distributed in the limit.

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  1. Department of Economics, University of Toronto, Toronto, ON, Canada

    Gordon Anderson

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Anderson, G. (2019). Comparing Latent Subgroups. In: Multilateral Wellbeing Comparison in a Many Dimensioned World. Global Perspectives on Wealth and Distribution. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-21130-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-21130-1_5

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