Bayesian Quantile structural equation modeling

Quantile regression is a technique frequently used in statistics and econometrics literature. Quantile regression, which gives comprehensive results compared to the mean regression model, is very limited to use in latent variable models. This thesis aims to theoretically understand and expand the quantile method and Bayesian estimation of Structural Equation Modeling (SEM), which are latent variable models. For this purpose, a simulation study and applications on subjective well-being were carried out. In both applications, Markov Chain Monte Carlo method was used to obtain the posterior distribution and the Gibbs sampling was used to sample the posterior distribution while making Bayesian estimation. In classical SEM, some assumptions must be met to perform the analysis, one of which is that the error terms fit the normal distribution. In addition, when examining the effects of exogenous variables on endogenous variables in classical SEM, only average values are interpreted. In quantile SEM (QSEM), there is no normality assumption of the distribution of error terms and the results are interpreted for different quantile values of the endogenous variable. In the simulation application, the performance of Bayesian QSEM (BQSEM) was evaluated for the cases where different sample sizes and error terms show different distributions. It has been observed that BQSEM gives better results than Bayesian SEM (BSEM) in cases where the error terms deviate from normality. For the application to be made with real data, the data set of the Life Satisfaction Survey-2020 obtained from the Turkish Statistical Institute was used. Accordingly, the variables thought to affect subjective well-being were added to the model and analyzed with BQSEM and BSEM, and the results were interpreted. R and WinBUGS programs were used in the applications. The fact that there is no study on BKYEM in the national literature constitutes the original value of the thesis.