On the use of bootstrap in factor analysis

Within several research fields (sociology, economics, demography and health), it is likely to deal with hierarchical structure phenomenon, with multi-level data: individual, familiar, territorial and social. In such circumstances it is necessary to proceed with the analysis of the relation between individuals and the society, where naturally, can be observed at different hierarchical levels, and variables may be defined at each level. This leads to research into the interaction between variables characterizing individuals and variables characterizing groups. The measurement of this interaction has been defined “moderating effect”. This has been carried out by considering a non-parametric regression analysis (Giordano and Aria, 2010), that is based on a generalization of Classification and Regression Trees algorithm (Breiman et al., 1984) that takes into account the different role played by variables belonging to higher levels. This paper points out how ensemble procedure in a regression tree methodology can be implemented that considers the relationships among variables belonging to different levels of a data matrix which is characterized by a hierarchical structure.