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 MultiLevel Mean Decrease in Accuracy. The first algorithm is used to realize a composite indicator of the latent variable, while the second is a variable importance measure, introduced in the context of CRAGGING, which is an ensemble method able to deal with hierarchical data. The two techniques are combined in such an extent to take account of the data structure, thus offering a new way to assess the items' contribution on the hierarchical-based unobservable variables' measure