We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra-Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction factor (c), depending on the particular SEM software used. Because of how LISREL defines the SB scaled chi-square, LISREL users should compute c for each model by dividing the model's NTWLS chi-square by its SB chi-square, to recover c accurately with both tests. EQS and Mplus users, in contrast, should divide the model's ML chi-square by its SB chi-square to recover c. Because ML estimation does not minimize the NTWLS chi-square, however, it can produce a negative difference in nested NTWLS chi-square values. Thus, we recommend the standard practice of testing the scaled difference in ML chi-square values for models M 1 and M 0 (after properly recovering c for each model), to avoid an inadmissible test-numerator. We illustrate the difference in computations across software programs for the original and new scaled tests and provide LISREL, EQS, and Mplus syntax in both single-and multiple-group form for specifying the model M 10 that is involved in the new test.
Findings underscore the complexity of factors (types of informants and dimensions of psychopathology) that underlie AIDS risk in troubled youths, and they offer specific directions for designing and implementing uniquely tailored AIDS prevention programs, for example, by targeting delinquent behavior and including high-risk peers and important family members in interventions.
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