Comparison between Maximum Likelihood and Bayesian Estimation in Structural Equation Modelling and Effects of Informative Priors

The aims of this study are to compare the maximum likelihood and Bayesian methods for estimation in structural equation modelling in real large data sets with different degrees of multivariate non-normality and to investigate the effects of non-informative and informative priors on parameter estimates in Bayesian structural equation modelling. Two data sets from the British Household Panel Survey are taken for the analyses, with total respondents of 6,522 and 7,150. In each of them, eighteen questions are drawn to be indicators for seven latent variables. In this dissertation, three separate hypothesised models are constructed in order to increase a variety of multivariate non-normality degrees; these are Models A, B and C. The research findings provided from classical structural equation modelling show that Model A and Model B are well fitted with a non-significant chi-square statistic at a bootstrap probability of more than 0.05, while Model C is also reasonably fitted with a significant chi-square statistic at a bootstrap probability of just below 0.05. The comparative fit indices in all models illustrate very high values; additionally, the root mean square error of approximation values are rather low. Furthermore, all estimated parameters are significant at a p-value of 0.001 and there are no zero values lying between their bootstrap confidence intervals. Under the multivariate non-normal condition, maximum likelihood estimators seem to lose their efficiency property, but not by much, and are robust to violation due to the large sample size. As for the findings from Bayesian structural equation modelling, all the estimated parameters of the three models are also significant. When incorporated with non-informative priors, the estimates and their standard errors are equivalent to the ones yielded by classical structural equation modelling. On the other hand, the parameters generated with informative priors vary according to the prior means but the standard errors are diminished consistently for all estimates, in comparison with the ones provided from classical structural equation modelling and Bayesian structural equation modelling with non-informative priors. The posterior distributions after being updated by the informative priors appear to be more normal owing to a decrease in skewness and kurtosis; moreover, the ones produced from Model B, which has the highest non-normality, are most affected by the informative priors according to the change in skewness and kurtosis.