Assessing item contribution on unobservable variables’ measures with hierarchical data

This paper aims at measuring the contribution of each item used to construct composite indicators of unobservable variables when data come from multi-item scales and have a hierarchical structure. To this end, we combine the MultiLevel NonLinear Principal Components Analysis with the CRAGGING algorithm, and then extracting its MultiLevel Mean Decrease in Accuracy measure of variable importance. The first algorithm is used to realize a composite indicator of the latent variable, while the second is an ensemble method suitable for hierarchical data and able to provide a variable importance measure. The proposed procedure takes account of the data structure, thus offering a new way to assess the items’ contribution on the hierarchical-based unobservable variables’ measure.