Handling Uncertainty in Structural Equation Modeling

This paper attempts to propose an overview of a recent method named partial possibilistic regression path modeling (PPRPM), which is a particular structural equation model that combines the principles of path modeling with those of possibilistic regression to model the net of relations among variables. PPRPM assumes that the randomness can be referred to the measurement error, that is the error in modeling the relations among the observed variables, and the vagueness to the structural error, that is the uncertainty in modeling the relations among the latent variables behind each block. PPRPM gives rise to possibilistic regressions that account for the imprecise nature or vagueness in our understanding phenomena, which is manifested by yielding interval path coefficients of the structural model. However, possibilistic regression is known to be a model sensitive to extreme values. That is way recent developments of PPRPM are focused on robust procedures for the detection of extreme values to omit or lessen their effect on the modeling. A case study on the motivational and emotional aspects of teaching is used to illustrate the procedure.