| Summary: | A Monte Carlo simulation study was conducted to investigate Type I error rates and power of several corrections for non-normality to the normal theory chi-square difference test in the context of evaluating measurement invariance via Structural Equation Modeling (SEM). Studied statistics include: 1) the uncorrected difference test, DML, 2) Satorra’s (2000) original computationally intensive correction, DS0, 3) Satorra and Bentler’s (2001) simplified correction, DSB1, 4) Satorra and Bentler’s (2010) strictly positive correction, DSB10, and 5) a hybrid procedure, DSBH (Asparouhov & Muthén, 2010), which is equal to DSB1 when DSB1 is positive, and DSB10 when DSB1 is negative. Multiple-group data were generated from confirmatory factor analytic models invariant on some but not all parameters. A series of six nested invariance models was fit to each generated dataset. Population parameter values had little influence on the relative performance of the scaled statistics, while level of invariance being tested did. DS0 was found to over-reject in many Type I error conditions, and it is suspected that high observed rejection rates in power conditions are due to a general positive bias. DSB1 generally performed well in Type I error conditions, but severely under-rejected in power conditions. DSB10 performed reasonably well and consistently in both Type I error and power conditions. We recommend that researchers use the strictly positive corrected difference test, DSB10, to evaluate measurement invariance when data are not normally distributed. Arts, Faculty of Psychology, Department of Graduate
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