Does any version of Amos offer the Satorra-Bentler Scaled Chi-square test statistic? Satorra, A., & Bentler, EM. (1988a). Scaling corrections for chi-square statistics in covariance structure analysis. ASA 1988 Proceedings of the Business and Eeonomic Statistics ,Section (308-313). Alexandria, VA: American Statistical Association. Satorra, A., & Bentler, EM. (1988b). Scaling corrections for statistics in covariance structure analysis (UCLA Statistics Series #2). Los Angeles, CA: University of California. Satorra, A., & Bentler, EM. (1994). Corrections to test statistics and standard enors in covariance structure analysis. In A. von Eye & C.C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399-419). Thousand Oaks, CA: Sage.
Resolving The Problem
Amos does not provide the Satorra-Bentler scaled Chi-square. Instead, Amos provides bootstrapping for situations where the assumptions underlying maximum likelihood chi-squares and standard errors may be violated. In fact, for large samples, both Amos and the Satorra-Bentler scaled Chi- square have the same p-value. Some simulation results show that bootstrapping is even better than the Satorra-Bentler scaled Chi-square.
Here are references for these simulation studies:
Fouladi, R.T. (1998) Covariance structure analysis techniques under conditions of multivariate normality and nonnormality--modified and bootstrap based test statistics. Paper presented at the annual meeting of the American Educational Research Association, San Diego, April 14, 1997.
Nevitt, J. and Hancock, G.R. (1998) Relative performance of rescaling and resampling approaches to model Chi-square and parameter standard error estimation in structural equation modeling. Paper presented at the annual meeting of the American Educational Research Association, San Diego, April 14, 1997.
A feature request to add the Satorra-Bentler Scaled Chi-Square has been filed with AMOS Development
16 June 2018