Partial Least Squares and Principal Component Analysis with Non-metric Variables for Composite Indices

Abstract

A composite index is an aggregated variable comprising individual indicators and weights that commonly represent the relative importance of each indicator. Composite indices are often used to measure latent phenomena or to summarize complex information in a small number of variables. It is crucial to choose correct weights for the variables that build a composite index. Principal Component Analysis (PCA) is a popular approach to derive weights, but it may not work when informative variations account for only small variances in the variables in a composite index. Therefore, this study proposes to use Partial Least Squares (PLS), which takes advantages of the relationship between outcome variables and the variables in a composite index. Our simulation study shows that PLS performs either as good as PCA or significantly outperforms it. Additionally, in practice variables that enter a composite index are often non-metric, which require special treatments to apply PCA or PLS. This study reviews various PCA and PLS algorithms for non-metric variables available in the literature and compares them by means of extensive simulation studies to make recommendations for practitioners. Dummy coding shows often satisfactory performance compared to more sophisticated methods. As our applications wealth, globalization, gender inequality and corruption are quantified using composite indices based on PCA and PLS, by which PLS generates composite indices tailored to each respective outcome variable showing often better performance compared to PCA. A comparison between PCA and PLS weights and coefficients shows which variables are particularly relevant for each respective outcome variable.