A Classical and Bayesian Approach for Parameter Estimation in Structural Equation Models

Structural Equation Models (SEMs) with latent variables provide a general framework for modelling relationships in multivariate data. Although SEMs are most commonly used in studies involving intrinsically latent variables, such as happiness, quality of life, or stress, they also provide a parsimonious framework for covariance structure modelling. For this reason, they have become increasingly used outside of traditional social science applications. Frequentist inferences are based on point estimates and hypothesis tests for the measurement and latent variable parameters. Although most of the literature on SEMs is frequentist, Bayesian approaches have been proposed in the last years. This study aims to provide an easily accessible overview of a Classic and a Bayesian approach to SEMs. Due to the flexibility of the Bayesian approach, it is straightforward to apply the method in a comprehensive class of SEM-type modelling frameworks, allowing nonlinearity, interactions, missing data, mixed categorical, count, and continuous observed variables. The WinBUGS software package, which is freely available, can be used to implement Bayesian SEM analysis. Bayesian model fitting typically relies on MCMC, which involves simulating draws from the joint posterior distribution of the model unknowns (parameters and latent variables) through a computationally intensive procedure. The advantage of MCMC is that there is no need to rely on broad sample assumptions because exact posterior distributions can be estimated for any function of the model unknowns. In small to moderate samples, these exact posteriors can provide a more realistic measure of model uncertainty. Therefore, we use the MCMC method for the Bayesian approach in this study. All approaches given above are applied to the data obtained from Samsun Chamber of Commerce and Industry.