Principles and Practice of Scaled Difference Chi-Square Testing

Structural Equation Modeling

Volumn 19, Issue 3, 2012, Pages 372-398

  Bryant, Fred B ^a   Satorra, Albert ^b  

^a LOYOLA UNIVERSITY CHICAGO   (United States)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

chi square difference test statistic; goodness of fit test; moment structures; nonnormality; scaled chi square

Indexed keywords

EID: 84864675685     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705511.2012.687671     Document Type: Article

References (29)

1. Arbuckle, J. L. 2006. AMOS 7.0 user's guide. Spring House, PA: Amos Development Corporation.
2. Arbuckle, J. L. 2007. AMOS 16.0 user's guide. Chicago, IL: SPSS.
3. Asparouhov, T. and Muthén, B. 2010. Computing the strictly positive Satorra-Bentler chi-square test in Mplus. Mplus Web Notes, 12 Retrieved fromhttp://www.statmodel.com/examples/webnotes/webnote12.pdf
4. Bentler, P. M. 1995. EQS structural equations program manual. Encino, CA: Multivariate Software.
5. Bollen, K. A. 1989. Structural equations with latent variables. New York, NY: Wiley.
6. Bryant, F. B. and Cvengros, J. A. 2004. Distinguishing hope and optimism: Two sides of a coin, or two separate coins?. Journal of Social and Clinical Psychology, 23: 273-302.
7. Chang, E. C., D'Zurilla, T. J. and Maydeu-Olivares, A. 1994. Assessing the dimensionality of optimism and pessimism using a multimeasure approach. Cognitive Therapy and Research, 18: 143-160.
8. Chou, C.-E., Bentler, P. M. and Satorra, A. 1991. Scaled test statistics and robust standard errors for nonnormal data in covariance structure analysis: A Monte Carlo study. British Journal of Mathematical and Statistical Psychology, 44: 347-357.
9. Crawford, J. R. and Henry, J. D. 2004. The Positive and Negative Affect Schedule (PANAS): Construct validity, measurement properties, and normative data in a large non-clinical sample. British Journal of Clinical Psychology, 43: 245-265.
10. Curran, R. J., West, S. G. and Finch, J. E. 1996. The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1: 16-29.
11. Hayashi, K., Bentler, P. M. and Yuan, K.-H. 2007. On the likelihood ratio test for the number of factors in exploratory factor analysis. Structural Equation Modeling, 14: 505-526.
12. Hu, L., Bentler, P. M. and Kant, Y. 1992. Can test statistics in covariance structure analysis be trusted?. Psychological Bulletin, 112: 351-362.
13. Johnston, M. M. and Finney, S. J. 2010. Measuring needs satisfaction: Evaluating previous research and conducting new psychometric evaluations of the Basic Needs Satisfaction in General Scale. Contemporary Educational Psychology, 35: 280-296.
14. Jöreskog, K. and Sörbom, D. 1996a. LISREL 8: User's reference guide. Chicago, IL: Scientific Software International.
15. Jöreskog, K. and Sörbom, D. 1996b. PRELIS 2: User's reference guide. Chicago, IL: Scientific Software International.
16. Jöreskog, K., Sörbom, D., du Toit, S. and du Toit, M. 1999. LISREL 8: New statistical features. Chicago, IL: Scientific Software International.
17. Kaplan, D. 2000. Structural equation modeling: Foundations and extensions. Thousand Oaks, CA: Sage.
18. McDonald, S. D., Hartman, N. S. and Vrana, S. R. 2008. Trait anxiety, disgust sensitivity, and the hierarchic structure of fears. Journal of Anxiety Disorders, 22: 1059-1074.
19. Muthén, L. K. and Muthén, B. O. 2007. Mplus user's guide. Los Angeles, CA: Muthén & Muthén.
20. Neyman, J. and Pearson, E. S. 1928. On the use and interpretation of certain test criteria for purposes of statistical inference: Part I. Biometrika, 20A: 175-240.
21. Satorra, A. 2000. "Scaled and adjusted restricted tests in multisample analysis of moment structures.". In Innovations in multivariate statistical analysis: A festschrift for Heinz Neudecker, Edited by: Heijmails, D. D. H., Pollock, D. S. G. and Satorra, A. 233-247. Dordrecht, Netherlands: Kluwer Academic.
22. Satorra, A. and Bentler, P. M. Scaling corrections for chi-square statistics in covariance structure analysis. ASA 1988 Proceedings of the Business and Economic Statistics Section. pp.308-313. Alexandria, VA: American Statistical Association.
23. Satorra, A. and Bentler, P. M. 1994. "Corrections to test statistics and standard errors in covariance structure analysis.". In Latent variables analysis: Applications for developmental research, Edited by: von Eye, A. and Clogg, C. C. 399-419. Thousand Oaks, CA: Sage.
24. Satorra, A. and Bentler, P. M. 2001. A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66: 507-514.
25. Satorra, A. and Bentler, P. M. 2010. Ensuring positiveness of the scaled chi-square test statistic. Psychometrika, 75: 243-248.
26. Schaffer, P. A., Vogel, D. L. and Wei, M. 2006. The mediating roles of anticipated risks, anticipated benefits, and attitudes on the decision to seek professional help: An attachment perspective. Journal of Community Psychology, 53: 442-452.
27. Scheier, M. F. and Carver, C. S. 1985. Optimism, coping, and health: Assessment and implications of generalized outcome expectancies. Health Psychology, 4: 219-247.
28. Steiger, J. H., Shapiro, A. and Browne, M. W. 1985. On the multivariate asymptotic distribution of sequential chi-square statistics. Psychometrika, 50: 253-264.
29. Warren, C. S., Cepeda-Benito, A., Gleaves, D. H., Moreno, S., Rodriguez, S., Fernandez, M. C., Fingeret, M. C. and Pearson, C. A. 2007. English and Spanish versions of the Body Shape Questionnaire: Measurement equivalence across ethnicity and clinical status. International Journal of Eating Disorders, 41: 265-272.