Structural equation models (SEMs) make it possible to estimate the causal relationships, defined according to a theoretical model, linking two or more latent complex concepts, each measured through a number of observable indicators, usually called manifest variables. Traditionally, the component-based estimation of SEMs by means of partial least squares (PLS path modelling, PLS-PM) assumes homogeneity over the observed set of units: all units are supposed to be well represented by a unique model estimated on the overall data set. In many cases, however, it is reasonable to expect classes made of units showing heterogeneous behaviours to exist.Two different kinds of heterogeneity could be affecting the data: observed and unobserved heterogeneity. The first refers to the case of a priori existing classes, whereas in unobserved heterogeneity no information is available either on the number of classes or on their composition.If a group structure for the statistical units is given, the aim of the analysis is to search for any differences in the behaviours of the a priori given classes. In PLS-PM this would mean studying the effect of directly observed moderating variables, i.e. estimating as many (local) models as there are classes.Unobserved heterogeneity, instead, implies identifying classes of units (a priori unknown) having similar behaviours. Such heterogeneity is captured by an unobserved (latent) discrete moderating variable defining both the number of classes and the class membership.A new method for unobserved heterogeneity detection in PLS-PM is proposed in this paper: responsebased procedure for detecting unit segments in PLS-PM (REBUS-PLS). REBUS-PLS, according to PLS-PM features, does not require distributional hypotheses and may lead to local models that are different in terms of both structural and measurement models. An application of REBUS-PLS on real data will be shown.

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Partial least squares (PLS) regression, Preference data, External information, L-structures,

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