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Abstract

Abstract. Building upon the ideas first exposed by Theil and Finizza (1971) and Fuchs (1975), this paper presents an additively decomposable segregation index based on the entropy concept used in information theory. For any pair of classification variables in a given year, the index is decomposed into a between-group and a within-group term. To analyze intertemporal changes in gender segregation for a given partition, the index is decomposed into two terms that capture, respectively, gender composition effects, and changes in the groups' demographic importance. These decompositions are illustrated with Spanish data on occupations and human capital levels for 1977 and 1992. It is found that, in both years, the higher the educational level, the smaller is gender segregation for most age groups. Moreover, gender segregation decreases with age in all educational categories. However, most gender segregation takes place within, rather than between, age/education categories. Lastly, changes in gender composition across occupations, nearly offset by occupational mix changes, account for a decline of 2% in total gender segregation over this period.

Computing decomposable multigroup indices of segregation

“…On other occasions, segregation stems from different levels of social organization (Mora and Ruiz-Castillo 2011). School racial segregation is a telling illustration.…”

“…In this article, we introduce the command dseg for computing eight indices of multigroup segregation. As explained in detail in section 3.3, these are 1) the mutual information index, M , and a normalized version, N M , that rescales segregation as a proportion of maximum segregation (we refer to this as "weak normalization"; see Mora and Ruiz-Castillo [2011]); 2) one version of the symmetric Atkinson's index that is group decomposable and one that is unit decomposable; 3) one version of the relative diversity index that is group decomposable and one that is unit decomposable; and 4) one ver-sion of Theil's H index that is group decomposable and one that is unit decomposable. These are the only multigroup segregation indices that satisfy the group decomposability property, the unit decomposability property, or both.…”

“…Then the index is strongly unit decomposable (SUD). If segregation changes by the same amount ∆ in all clusters, an index that is SUD has the desirable property of changing its within term by ∆ (see Mora and Ruiz-Castillo [2011] for a more detailed discussion of the advantages of SUD over WUD indices in the context of entropy-based indices).…”

“…Reardon and Firebaugh (2002) study the properties of H group|unit and R group|unit (as well as those of other multigroup indices that are not decomposable). Mora and Ruiz-Castillo (2011) (1992) dseg, seg…”

Extracting directed information flow networks: An application to genetics and semantics

“…There are many indexes in literature to measure geographical segregation [19]. A popular one is the Theil's segregation index [20,21] and it is based on information theory.…”