Composite Index Construction with Expert Opinion

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.