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In this work we speak about the problem of the treatment of qualitative variables in the SEM models, and in particular in the PLS-PM. In the contest of PLS-PM we propose an algorithm, called Alternating Least Squares Path Modeling (ALS-PM), that allows us to use the qualitative indicators: the algorithm computes the optimal quantification of qualitative indicators, taking into account the relation between variables (manifest and latent). We discuss in this work also about the validation of the model, in particular we propose some indexes that measure the variability explained by the relation of model between manifest and latent variables. We present some real cases of models in which we have qualitative indicators that with the classical approach of PLS-PM can not be included in the model.

Invited talk in the Specialized Session "Statistical Methods for the Assessment of Scientific Research Communities"

In many real datasets, the same variables are measured on objects from different groups, and the covariance structure may vary from group to group. Oftentimes, the underlying population covariance matrices are not identical, yet they still have a common basic structure, e.g. there exists some rotation that diagonalizes simultaneously all covariance matrices in the groups, or all covariances can be made congruent by some translation and/or dilation. The purpose of this paper is to show how a test of homoscedasticity can be made more informative by performing a separate check for equality between shapes and equality between orientations of the concentration ellipsoids. This approach, combined with parsimonious parametrization in mixture data modeling, provides a formal hypothesis testing procedure for model assessment.