Decomposition analysis is a critical tool for understanding the social and spatial dimensions of segregation and diversity. In this paper, I highlight the conceptual, mathematical, and empirical distinctions between segregation and diversity and introduce the Divergence Index as a decomposable measure of segregation. Scholars have turned to the Information Theory Index as the best alternative to the Dissimilarity Index in decomposition studies, however it measures diversity rather than segregation. I demonstrate the importance of preserving this conceptual distinction with a decomposition analysis of segregation and diversity in U.S. metropolitan areas from 1990 to 2010, which shows that the Information Theory Index has tended to decrease, particularly within cities, while the Divergence Index has tended to increase, particularly within suburbs. Rather than being a substitute for measures of diversity, the Divergence Index complements existing measures by enabling the analysis and decomposition of segregation alongside diversity.

翻译：分解分析是理解隔离与多样性的社会及空间维度的关键工具。本文强调了隔离与多样性在概念、数学及实证上的区别，并引入分歧指数作为一种可分解的隔离度量。学者们已转向将信息论指数视为分解研究中差异指数的最佳替代，然而它衡量的是多样性而非隔离。我通过对1990年至2010年美国大都市区隔离与多样性的分解分析，论证了保留这一概念区别的重要性。该分析表明，信息论指数呈下降趋势（尤其是在城市内部），而分歧指数呈上升趋势（尤其是在郊区）。分歧指数并非多样性度量的替代，而是通过实现隔离与多样性的并行分析与分解，对现有度量形成补充。