Informative prior on structural equation modelling with non-homogenous error structure.

Introduction: This study investigates the impact of informative prior on Bayesian structural equation model (BSEM) with heteroscedastic error structure. A major drawback of homogeneous error structure is that, in most studies the underlying assumption of equal variance across observation is often unrealistic, hence the need to consider the non-homogenous error structure. Methods: Updating appropriate informative prior, four different forms of heteroscedastic error structures were considered at sample sizes 50, 100, 200 and 500. Results: The results show that both posterior predictive probability (PPP) and log likelihood are influenced by the sample size and the prior information, hence the model with the linear form of error structure is the best. Conclusions: The study has been able to address sufficiently the problem of heteroscedasticity of known form using four different heteroscedastic conditions, the linear form outperformed other forms of heteroscedastic error structure thus can accommodate any form of data that violates the homogenous variance assumption by updating appropriate informative prior. Thus, this approach provides an alternative approach to the existing classical method which depends solely on the sample information.