An evaluation of the Satorra‐Bentler distributional misspecification correction applied to the McDonald fit index

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Abstract
McDonald goodness‐of‐fit indices based on maximum likelihood, asymptotic distribution free, and the Satorra‐Bentler scale correction estimation methods are investigated. Sampling experiments are conducted to assess the magnitude of error for each index under variations in distributional misspecification, structural misspecification, and sample size. The Satorra‐Bentler correction‐based index is shown to have the least error under each distributional misspecification level when the model has correct structural specification. The scaled index also performs adequately when there is minor structural misspecification and distributional misspecification. However, when a model has major structural misspecification with distributional misspecification, none of the estimation methods perform adequately.