Quantile Composite-Based Model: A Recent Advance in PLS-PM

The aim of the present chapter is to discuss a recent contribution in the partial least squares path modeling framework: the quantile composite-based path modeling. We introduce this recent contribution from both a methodological and an applicative point of view. The objective is to provide an exploration of the whole dependence structure and to highlight whether and how the relationships among variables (both observed and unobserved) change across quantiles. We use a real data application, measuring the equitable and sustainable well-being of Italian provinces. Partial least squares path modeling is first applied to study the relationships among variables assuming homogeneity among observations. Afterwards, a multi-group analysis is performed, assuming that a specific factor (the geographic area) causes heterogeneity in the population. Finally, the quantile approach to composite-based path modeling provides a more in-depth analysis. Some relevant results are selected and described to show that the quantile composite-based path modeling can be very useful in this real data application, as it allows us to explore territorial disparities in depth.