Principal component analysis for constructing socio-economic composite indicators: theoretical and empirical considerations

Composite indicators for measuring multidimensional phenomena have become very popular in various social, economic and political fields. This increasing popularity has led to the frequent use of Principal Component Analysis (PCA) to aggregate a set of socio-economic indicators into a composite index. However, a PCA-based composite index must be supported by an appropriate measurement model to function adequately, and this aspect is almost always ignored, both by those teaching PCA and by manuals for constructing composite indicators. In this paper, we discuss the importance of the measurement model for the proper construction of a PCA-based composite index and show that PCA can lead to serious problems in the construction of composite indicators in formative models. A simple numerical example and an application to real data are also shown, where a formative model is required, and the PCA-based composite index produces incorrect results.