2. Measures of Multigroup Segregation

TLDR

The paper derives and evaluates measures of multigroup segregation. The authors conceptualize multigroup segregation in four ways, derive six indices (D, G, H, C, R, P), and evaluate them against seven desirable properties. The information theory index H is identified as the most satisfactory multigroup segregation index, uniquely satisfying the principle of transfers and allowing decomposition into between‑ and within‑group components.

Abstract

In this paper we derive and evaluate measures of multigroup segregation. After describing four ways to conceptualize the measurement of multigroup segregation—as the disproportionality in group (e.g., race) proportions across organizational units (e.g., schools or census tracts), as the strength of association between nominal variables indexing group and organizational unit membership, as the ratio of between-unit diversity to total diversity, and as the weighted average of two-group segregation indices—we derive six multigroup segregation indices: a dissimilarity index (D), a Gini index (G), an information theory index (H), a squared coefficient of variation index (C), a relative diversity index (R), and a normalized exposure index (P). We evaluate these six indices against a set of seven desirable properties of segregation indices. We conclude that the information theory index H is the most conceptually and mathematically satisfactory index, since it alone obeys the principle of transfers in the multigroup case. Moreover, H is the only multigroup index that can be decomposed into a sum of between- and within-group components.