Date of Graduation


Document Type


Degree Name

Doctor of Philosophy in Educational Statistics and Research Methods (PhD)

Degree Level



Rehabilitation, Human Resources and Communication Disorders


Wen-Juo Lo

Committee Member

Ronna Turner

Second Committee Member

George Marcoulides

Third Committee Member

Sean Mulvenon


Pure sciences, Bifactor models, Measurement invariance, Sensitivity of goodnesss-of-fit idices, Structural equation modeling


A Monte Carlo simulation study was conducted to evaluate the sensitivities of five commonly used goodness-of-fit indices to detect metric invariance properties of the bifactor model. The fit indices that performed the best in terms of power were Gamma and Mc. In addition, Gamma, Mc, CFI, and RMSEA all held Type I error to a minimum. However, only Gamma and CFI are recommended to use in the bifactor model because the other GOF indices have cutoff values that are too large. For Gamma and CFI values of -.026 to -.045 and -.004 to -.009, respectively indicate a lack of metric invariance. In the variance component analysis, the magnitude of the factor loading differences contributed the most variation to each GOF except SRMR. For SRMR the largest contribution of variance was model complexity (i.e., simple or complex). Finally, the Arkansas Benchmark Examination data was analyzed to compare the recommended cutoff criteria for Gamma and CFI of the current study to the chi-square difference (likelihood ratio) test between configural and metric level invariance. The likelihood ratio test was consistent with Gamma and CFI for rejecting the test of metric invariance in the Arkansas Benchmark data. (1923 kB)