Power of the Likelihood Ratio Test in Multiple Group Confirmatory Factor Analysis under Partial Measurement Invariance

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Abstract
The power of the likelihood ratio test in multiple group confirmatory factor analysis under partial measurement invariance is studied. A six-variable, two-factor model is considered where a specification error exists for one group. The size of the specification error as well as the size of the free parameters are varied. Power is obtained via the method of Satorra and Saris (1985). Results show that the power of the test is dependent on the size of the misspecified parameter, the size of the free loadings, as well as the correlation between the misspecified parameter and the parameter held invariant. Bias is also observed for estimates of the invariant parameters. Results are discussed in terms of strategies of multiple group modeling.