Type I Error Rates and Power of Several Versions of Scaled Chi-Square Difference Tests in Investigations of Measurement Invariance

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A Monte Carlo simulation study was conducted to investigate Type I error rates and power of several corrections for nonnormality to the normal theory chi-square difference test in the context of evaluating measurement invariance via structural equation modeling. Studied statistics include the uncorrected difference test, DML, Satorra and Bentler’s (2001) original correction, DSB1, Satorra and Bentler’s (2010) strictly positive correction, DSB10, and a hybrid procedure, DSBH (Asparouhov & Muthén, 2013). Multiple-group data were generated from confirmatory factor analytic population models invariant on all parameters, or lacking invariance on residual variances, indicator intercepts, or factor loadings. Conditions varied in terms of the number of indicators associated with each factor in the population model, the location of noninvariance (if any), sample size, sample size ratio in the 2 groups, and nature of nonnormality. Type I error rates and power of corrected statistics were evaluated for a series of 4 nested invariance models. Overall, the strictly positive correction, DSB10, is the best and most consistently performing statistic, as it was found to be much less sensitive than the original correction, DSB1, to model size and sample evenness.

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