**ERIC Number:**EJ978548

**Record Type:**Journal

**Publication Date:**2012

**Pages:**27

**Abstractor:**As Provided

**Reference Count:**29

**ISBN:**N/A

**ISSN:**ISSN-1070-5511

Principles and Practice of Scaled Difference Chi-Square Testing

Bryant, Fred B.; Satorra, Albert

Structural Equation Modeling: A Multidisciplinary Journal, v19 n3 p372-398 2012

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 structural equation modeling software used. Because of how LISREL 8 defines the SB scaled chi-square, LISREL users should compute "c" for each model by dividing the model's normal theory weighted least-squares (NTWLS) chi-square by its SB chi-square, to recover "c" accurately with both tests. EQS and M"plus" users, in contrast, should divide the model's maximum likelihood (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[subscript 1] and M[subscript 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 M"plus" syntax in both single- and multiple-group form for specifying the model M[subscript 10] that is involved in the new test. (Contains 1 table.)

Descriptors: Statistical Analysis, Structural Equation Models, Goodness of Fit, Least Squares Statistics, Maximum Likelihood Statistics, Computer Software, Undergraduate Students, Personality Measures

Psychology Press. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education; Postsecondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers:**N/A