On the use of Structural Equation Models and PLS Path Modeling to build composite indicators

Nowadays there is a pre-eminent need to measure very complex phenomena like poverty, progress, well-being, etc. As is well known, the main feature of a composite indicator is that it summarizes complex and multidimensional issues. Thanks to its features, Structural Equation Modeling seems to be a useful tool for building systems of composite indicators. Among the several methods that have been developed to estimate Structural Equation Models we focus on the PLS Path Modeling approach (PLS-PM), because of the key role that estimation of the latent variables (i.e. the composite indicators) plays in the estimation process. In this work, first we present Structural Equation Models and PLS-PM. Then we provide a suite of statistical methodologies for handling categorical indicators in PLS-PM. In particular, in order to take categorical indicators into account, we propose to use a modified version of the PLS-PM algorithm recently presented by Russolillo [2009]. This new approach provides a quantification of the categorical indicators in such a way that the weight of each quantified indicator is coherent with the explicative ability of the corresponding categorical indicator. To conclude, an application involving data taken from a paper by Russet [1964] will be presented.