In the construction of composite or summary social indicators/indices, a recurrent methodological issue pertains to how to weight each of the quality-of-life/well-being components of the indices. Two methods of composite index construction that have been widely applied empirically in recent decades are Data Envelopment Analysis (DEA), which is based on an optimization principle, and the equal weights/minimax (EW/MM) method, which has been shown to have minimax statistical properties in the sense that it minimizes maximum possible disagreements among individuals on weights. This paper applies both of these methods to two empirical datasets of social indicators: 1) data on 25 well-being indicators used in the construction of state-level Child and Youth Well-being Indices for each of the 50 U.S. states, and 2) data on indicators of life expectancy, educational attainment, and income used in the construction of the United Nations Human Development Programme’s Human Development Index (HDI) for 188 countries. In these empirical contexts, we study issues of measurement sensitivity of the EW/MM and DEA methods to the numbers of indictors used in the construction of the composite indices and corresponding issues of robustness. We find that the DEA method is more sensitive to the numbers of component indicators than the EW/MM method. In addition, the composite indicators formed by the EW/MM and DEA methods become more similar as the numbers of indicators in the composites decreases. We also apply Chance-Constrained DEA method to reclassify countries in the HDI dataset by levels of human development. The resulting human development groupings of the DEA composite indices have a large overlap with those of the HDI in the Human Development Reports , which are based on fixed cut-off points derived from the quartiles of distributions of the HDI component indicators.

中文翻译：

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综合社会指标构建的数据包络分析和等权/最小极大值方法：数据敏感性和鲁棒性的方法论研究

在构建综合或汇总的社会指标/指数时，一个反复出现的方法学问题涉及如何对指数的生活质量/福祉组成部分进行加权。最近几十年来，两种在经验上得到广泛应用的复合指标构建方法是：基于优化原理的数据包络分析（DEA）和等重/极小值（EW / MM）方法，已证明它们具有以下优点：从某种意义上说，它最大程度地减少了个体之间在权重上的最大分歧，从而具有最小最大统计特性。本文将这两种方法都应用于两个社会指标的经验数据集：1）美国50个州中的每个州在构建州级儿童和青少年幸福指数时使用的25个幸福指标的数据； 2）有关预期寿命指标的数据，受教育程度，以及用于188个国家的联合国人类发展计划的人类发展指数（HDI）构建的收入。在这些经验背景下，我们研究了EW / MM和DEA方法对用于构建综合指数的指标数量的测量敏感性问题以及相应的鲁棒性问题。我们发现DEA方法比EW / MM方法对组件指标的数量更为敏感。此外，通过EW / MM和DEA方法形成的复合指标随着复合物中指标数量的减少而变得越来越相似。我们还应用机会约束DEA方法按人类发展水平对HDI数据集中的国家进行重新分类。