The study of complex multi-block systems, as the ones relevant for sensometrics, may imply the analysis of a network of hypothesized, but often hidden, « causal » or predictive relationships between blocks of manifest variables summarized by latent variables. PLS Path Modeling (PLS-PM) is classically regarded as a component-based approach to Structural Equation Models (SEM) and has been more recently revisited as a general framework for multi-block data analysis. Both the measurement model (manifest-latent links) and the structural model (latent-latent links) are usually specified by theoretical hypotheses of the researcher and can be eventually (but only slightly) modified in case the statistical modeling of empirical data provides a different evidence. A PLS regression-based approach integrated within PLS-PM allows estimating outer weights and path coefficients in presence of multidimensional blocks (with uni-dimensionality and full-dimensionality as special cases), multicollinearity, missing data or landscape tables (e.g., few products as compared to the multitude of judges expressing preferences). Causal or predictive modeling based on SEM or PLS-PM may be limited for diagnosis by the theoretically hypothesized causal network. Bayesian probabilistic networks are instead limited in differentiating between manifest and latent variables as well as between causal and spurious relationships. These two approaches can be combined with the objective of discovering and validating a hidden network of relationships between manifest variables based on probabilistic causation. Such unsupervised learning approach can be applied to manifest variables prior to PLS-PM or to latent variable scores yielded by PLS-PM with different insights for both theory and practice in terms of diagnosis and prediction.
ESPOSITO VINZI, V., JOUFFE, L., RUSSOLILLO, G., TRINCHERA, L. et ZARGOUSH, M. (2010). Integrated Approaches for PLS Path Modeling: PLS Regression Estimation Modes and Probabilistic Networks. Dans: 10th SENSOMETRICS Meeting.