Optimal Scaling Trees for Three-Way Data

The framework of this paper is developed on tree-based models for three-way data. Three-way data are measurements of variables on a sample of objects in different occasions (i.e. space, time, factor categories) and they are obtained when prior information play a role in the analysis.

Three way data can be analyzed by exploratory methods, i.e., the factorial approach (TUCKER, PARAFAC, CANDECOMP, etc.) as well as confirmatory methods, i.e., the modelling approach (log-trilinear association models, simultaneous latent budget models, etc.).

Recently, we have introduced a methodology for classification and regression trees in order to deal specifically with three-way data. Main idea is to use a stratifying variable or instrumental variable to distinguish either groups of variables or groups of objects. As a result, prior information plays a role in the analysis providing a new framework of classification and regression trees for three-way data.

In this paper we introduce a tree-based method based on optimal scaling in order to account of the presence of non-linear correlated groups of variables. The results of a real world application on Tourist Satisfaction Analysis in Naples will be also presented.