Confirmatory Factor Analysis Based On Bayesian Covariance Elastic Net

As a commonly used measurement model,confirmatory factor analysis is usually used in the development of scales.Researchers construct a confirmatory factor analysis model structure based on the existing prior information,and restrict the model through some strict assumptions.The existence of these assumptions often results in confirmatory factor analysis unable to effectively fit the data or the model structure obtained by the fit does not conform to the theoretical assumptions.Currently,the rise of Bayesian methods makes researchers more flexible when using confirmatory factor analysis.Through the choice of a prior,the regularization method is introduced.While relaxing the original assumptions,it enhances the practicality and robustness of the model when analyzing actual data.According to previous studies,the study of confirmatory factor analysis model structure under the Bayesian framework can be regarded as a Bayesian variable selection problem.Therefore,in order to further improve the model selection and parameter estimation capabilities of confirmatory factor analysis under the Bayesian framework,considered to implement the model selection of the residual covariance matrix in the confirmatory factor analysis model by introducing the Bayesian elastic net penalty.The main research of this thesis is: First,on the basis of the Bayesian elastic net model,adding block Gibbs sampling to realize the identification of the covariance matrix and the precision matrix,proposes the Bayesian covariance elastic net model,and further expands it to Bayesian adaptive Covariance elastic net model;Secondly,combine it with confirmatory factor analysis,and realize the model selection and parameter estimation of the residual covariance matrix through the Bayesian covariance elastic net model to achieve the purpose of modifying the structure of the confirmatory factor analysis model;Finally,the effectiveness and practicability of the method are evaluated through numerical simulation and empirical analysis.Through numerical simulation and case analysis,the comparison between the confirmatory factor analysis method proposed in this paper and the existing methods shows that the proposed method has good performance in identifying the model structure of confirmatory factor analysis.