Comparison of parameter estimation in classic and Bayesian structural equation models: An application with ordered categorical data

This study compared with the parameter estimation methods of Maximum Likelihood (ML) and Bayesian approximation as Structural Equation Models (SEM) commonly used in analyzing the causual link. In the absence of classical assumptions, Bayesian Structural Equation Models (BSEM) has recently started to be used in SEM for the models including missing data, complex, multilevel, semi-parametric, non-linear or ordered categorical data. As Bayesian approach provides to obtain posterior distributions using the distributions obtained by prior knowledge, to enable working with small samples via Gibbs sampler by the Monte Carlo Markov Chain (MCMC) methods and to enable flexible modeling with different data structures, it has become an attractive method by researchers. What is more, Service Quality Scale (SERVQUAL) was used to analyse the service quality of the banks in terms of university students through classical SEM and BSEM. In practice, LISREL and OpenBUGS package program was adopted for classical SEM and BSEM respectively. As a research model, the SERVQUAL scale was employed. The threshold value approach for the use of prior knowledge in BSEM is scrutinized because of the ordered categorical structure of the scale. According to the analysis results, while "Assurance", "Physical Appearance" and "Accessibility" service dimensions were found to be statistically significant through classical approach in which "Reliability" was also found to be statistically significant in addition to the mentioned service dimensions through Bayesian approach for the model that is proposed for service quality of banking. In this study having more accurate results with BSEM rather than YEM is explained in depth, while instantiated with actual data.