This paper introduces structural equation modeling for imprecise data, which enables evaluations with different types of uncertainty. Coming under the framework of variance-based analysis, the proposed method called Partial Possibilistic Regression Path Modeling (PPRPM) combines the principles of PLS path modeling to model the network of relations among the latent concepts, and the principles of possibilistic regression to model the vagueness of the human perception. Possibilistic regression defines the relation between variables through possibilistic linear functions and considers the error due to the vagueness of human perception as reflected in the model via interval-valued parameters. PPRPM transforms the modeling process into minimizing components of uncertainty, namely randomness and vagueness. A case study on the motivational and emotional aspects of teaching is used to illustrate the method
