A Study On Mediation Analysis Using Bayesian Structural Equation Model

Objective Mediation analysis could deeply analyze the mechanism on the path of outcome variables caused by exposure variables.In recent years,it has received extensive attention in the fields of social science,Epidemiology,Medicine and so on.Although the classical one-way path model from exposure factors,through mediation variables to response variables was simple and easy to understand,the corresponding methods has been fully developed and applied.However,researchers may encounter more complex structures,such as multiple mediation variables,measurements of multiple dimensions and including confounding variables,which required more general statistical methods for modelfitness.The mediation analysis based on structural equation model made it possible to analyze the complex structure between variables including mediation effect.Bayesian SEM can provided a more flexible and efficient framework for the estimation of complex models.Based on an example data study and simulation study,this study explored the statistical analysis strategy of mediation analysis using Bayesian structural equation model and compared its statistical performance with the classical mediation analysis method under simulated different data characteristics.Result: 1.Example data analysis results:Based on the structural equation model method and Bayesian method,the mediating effect of academic self-efficiency from statistical anxiety survey data of medical graduate students was analyzed.The results showed that the mediating effect of self-learning efficiency had statistical significant.Standard error SE(a)of regression coefficient between M and X by SEM method were 0.189,0.191 from SEM and Bayesian SEM respectively.Y and M regression coefficients of structural equation Model estimation.The standard error of b was: SE(b)= 0.387,standard error of Y and M regression coefficient b estimated by SEM and Bayesian SEM were 0.387 and 0.396 respectively.2.Simulation test results:(1)In the case of no mediation effect,the width of confidence interval became wider with the increase of b value and the coverage rate of 95% confidence interval decreased with the increase of b value.The 95% confidence interval coverage of the Bayesian method did not change with the change of the sample size and true effect value,indicating that Bayesian classical estimation method was more robust.Under the small sample size(N ? 25 and N ? 50),when there was no mediation(a=b=0),the confidence interval coverage of Bayesian method does not change with the change of sample size and true effect values.Both confidence interval from Bayesian classical confidence interval and classical regression method provide more than 95% coverage.However,when the mediation effect was medium or above(a=b=0.39,a=b=0.59),the confidence interval coverage of classical regression method and structural equation model was less than 95%.(2)In the case of large mediation effect(a=b=0.59),the calculation accuracy of the classical regression method was higher than that of SEM method,but the advantage of SEM method did not reflect the advantages of the estimation accuracy of the structural equation model method.However,the standard error of the mediation effect values estimated by SEM method are always smaller than those by Bayesian regression method,which may imply that SEM methods got more precise estimation.Conclusion 1.Conclusions on example data analysis:In the case of complex structural data,this paper discussed the mediation effect analysis strategy of combining exploratory factor,confirmational factor analysis and correlation structure analysis between variables.The standard error of coefficient estimation could be obtained by structural equation model,which could improve the accuracy of statistics to a certain extent? 2.Conclusions of simulation study:(1)In epidemiological mediation analysis,the estimation accuracy of the analysis method decreased with the increase of the correlation coefficient between the outcome variable and the independent variable in the presence of the mediation variable.It showed that the correlation between outcome variables and independent variables would affect the accuracy of statistical analysis.(2)Compared with the results of classical regression mediation analysis method and structural equation model method,it was shown that the Bayesian method has better robustness and higher confidence interval coverage than the other two methods.In the case of sample size and more complex data,it was recommended to use the combination of Bayesian method and structural equation model method for parameter estimation.