Use of non-normality in structural equation modeling: Application to direction of causation

Structural equation modeling (SEM) typically utilizes first- and second-order moment structures. This limits its applicability since many unidentified models and many equivalent models that researchers would like to distinguish are created. In this paper, we relax this restriction and assume non-normal distributions on exogenous variables. We shall provide a solution to the problems of underidentifiability and equivalence of SEM models by making use of non-normality (higher-order moment structures). The non-normal SEM is applied to finding the possible direction of a path in simple regression models. The method of (generalized) least squares is employed to estimate model parameters. A test statistic for examining a fit of a model is proposed. A simulation result and a real data example are reported to study how the non-normal SEM approach works empirically.