A comparison between the Bayesian parametric and the semiparametric approach in estimating nonpolynomial instantaneous indirect effect in the Structural Equation Model with ordinal data

A Bayesian parametric and the semiparametric approach are compared to estimate the nonpolynomial direct and the instantaneous indirect effect among latent factors in the Structural Equation Model (SEM). Nonpolynomial indirect relationships are especially common in the psychological, biometrical, and physical fields. However, the assumption of normality within the parametric framework limits the statistical inferences of the nonlinear direct and indirect estimates. The semiparametric Bayesian approach is applied using the truncated Dirichlet process with a stick breaking prior to track the instantaneous indirect effect that are derived from a composite of nonpolynomial nonlinear functions (e.g., exponential, logarithm, and sine) in a simulation study. The results show that the semiparametric approach provides more accurate estimates as well as a higher accuracy in recovering nonpolynomial direct and indirect effect among latent factors.