Comparison Of LM-test Method And Lasso Regularization Method For Parameter Selection In Structural Equation Modeling

In order to reduce the complexity of the model identified by exploratory structural equation modeling and improve the model fit of the confirmatory factor analysis in the study of structural equation modeling(SEM),researchers have proposed that the lagrange multiplier-test(LM-test)method and lasso regularization method in SEM are used to locate additional parameters and make the analysis more reliable.In this thesis,the LM-test method and lasso regularization method are compared through a simulation study.And these two methods are further applied to the analysis of a real dataset.1.For the lasso regularization method in SEM,in order to satisfy the identifiability of the model,an existing suggestion is to fix the parameter of the factor loading with the maximum value.In this thesis,we set the variance of the exogenous latent variables to 1.Simulation results show that the bias of estimated parameter value can be reduced,and the fitted model gets closer to the population model.2.This thesis compares the performances of LM-test and lasso regularization method in parameter selection,bias of estimated parameter value and model fit through a simulation study.The results show that in terms of parameter selection,LM-test method selects correctly more non-zero factor loads,while the lasso regularization method selects incorrectly more zero factor loads.In terms of the bias of estimated parameter value,the estimated parameters obtained by LM-test method are more accurate.In terms of the model fit,when the variance of measurement error is large,the model obtained by LM-test method is better,when the variance of measurement error becomes smaller,the difference between the performances of two methods becomes small.In views of bias of estimated parameter value and model fit,the performance of LM-test method is better.As the sample size increases,the performances of two methods have improved in all aspects.When the variance of measurement error becomes smaller,the performances of two methods are improved and the difference between two methods is narrowed.3.Finally,we apply the LM-test method and lasso regularization method to the analysis of a dataset on rural transferring population.The results show that confirmatory factor model based on prior knowledge may not be adequate to fit the real data,LM-test and lasso regularization method can improve the goodness of the model.The results with real data also suggest that lasso regularization method selects more parameters,the difference between the model fit obtained by two method is small,and the results of empirical analysis are consistent with the conclusion of simulation study.