Composite Index Construction with Expert Opinion
Composite Index Construction with Expert Opinion
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DOI：
10.1080/07350015.2021.2000418
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发表时间：
2021-11
影响因子：
3
通讯作者：
Rong Chen;Yuanyuan Ji;Guolin Jiang;Han Xiao;Ruoqing Xie;Pingfang Zhu
中科院分区：
文献类型：
--
作者：
Rong Chen;Yuanyuan Ji;Guolin Jiang;Han Xiao;Ruoqing Xie;Pingfang Zhu
摘要综合指数是一种强有力的和普遍使用的工具，它通过总结一组测量（成分指数）的不同方面的主题，提供了一个整体的措施。它广泛应用于经济、金融、政策评估、绩效排名等诸多领域。人们已经广泛地研究了如何有效地构建一个综合指数。最广泛使用的方法是使用成分指数的线性组合，其中组合权重通过优化目标函数来确定。为了最大化综合指数的整体变化，可以通过主成分分析来获得组合权重。本文提出将专家意见纳入综合指数的构建中。人们注意到，专家意见往往提供有用的信息，以评估哪些组成指数对该主题的总体衡量更为重要。我们考虑的情况下，一组专家进行了咨询，每个提供了一组的重要性分数的组成部分指数，沿着一组的信心分数，反映了专家自己的信心，在他/她的评估。此外，综合指数的构建者还可以提供对每个专家的专门知识水平的评估。我们使用线性组合来构建综合指数，其中组合权重通过最大化所产生的综合指数变化和所使用的组合权重与专家评分之间的偏差平方的负加权和的总和来确定。数据驱动的方法用于在两种信息来源之间找到最佳平衡。的过程的理论性质进行了研究。最后，以科技发展指数的构建为例进行了仿真分析和经济应用。
Abstract Composite index is a powerful and popularly used tool in providing an overall measure of a subject by summarizing a group of measurements (component indices) of different aspects of the subject. It is widely used in economics, finance, policy evaluation, performance ranking, and many other fields. Effective construction of a composite index has been studied extensively. The most widely used approach is to use a linear combination of the component indices, where the combination weights are determined by optimizing an objective function. To maximize the overall variation of the resulting composite index, the combination weights can be obtained through principal component analysis. In this article, we propose to incorporate expert opinions into the construction of the composite index. It is noted that expert opinion often provides useful information in assessing which of the component indices are more important for the overall measure of the subject. We consider the case that a group of experts have been consulted, each providing a set of importance scores for the component indices, along with a set of confidence scores which reflects the expert’s own confidence in his/her assessment. In addition, the constructor of the composite index can also provide an assessment of the expertise level of each expert. We use linear combinations to construct the composite index, where the combination weights are determined by maximizing the sum of resulting composite index variation and the negative weighted sum of squares of deviation between the combination weights used and the experts’ scores. A data-driven approach is used to find the optimal balance between the two sources of information. Theoretical properties of the procedure are investigated. Simulation examples and an economic application on constructing science and technology development index is carried out to illustrate the proposed method.