The Comparative Study Of The Performance Of The Gof In The SEM Based On Monte Carlo Simulation

Nowadays, Structural Equation Model(SEM) has become an importanttool for a multivariate data analysis.In short, compared with the traditionalregression analysis, SEM can simultaneously handle multiple dependentvariables and evaluate different theoretical models.Because of theseadvantages it has been widely studied in the past two decades. Among them,an important research issue is how to determine whether the model is set bythe investigator has been supported by the data according to the fit index.Structural equation modeling software can output multiple fit indices, onlychoosing the good performance of the index and the corresponding cutoffvalue, the investigators can get correct conclusions.In this paper, by Monte Carlo(MC) simulation, we conduct a systemiccomparative analysis of the performance of the common fit index, evaluatethe stability and reliability of the performance index and suggest theappropriate cutoff value. The model specifies selected classic Wheatonmodel in the MC simulation. Consider the impact of these three factors ofthe GOF: sample size, parameter estimation method and the model setting.Use the balanced factorial experimental design. The details are as follows:five levels of sample sizes(N=50,100,200,500,1000); two levels ofparameter estimation methods, Maximum Likelihood(ML) and GeneralizedLeast Squares(GLS);three levels model setting(true model, slightmis-setting model and heavy mis-setting model).All statistical analyzeswere performed in SAS9.1software. Based on this study, we found that comparatively speaking, GFI,AGFI,CENTRA and RMSEA are relativelysmall affected by the estimation method. Except AGFI,the rest of theindexes are sensitive to the model misspecification.Except NNFI,IFI,CEN, RMSEA, the rest of the indexes are subject to the impact of thesample size, just difference in degree. Especially RMSEA, it is moresensitive to the model misspecification and less influenced by the samplesize and estimation method.In all, it is a recommendable fit index.In the issue of selection of the cutoff value, RMSEA=0.05is better.x~2is seriously affected by the sample size, but the x~2/Df has a goodperformance. In addition, compared with other fit indices, it is suitable thatAGFI, NNFI, RFI are set to0.95.