Troubleshooting
Problem
I need to determine the best means of analyzing my ordinal data (20 variables, all with three-category ordinal ratings) with Amos. I understand that Amos does not provide Weighted Least Squares (WLS) estimation. Where can I find a detailed explanation of the estimation methods available in the View->Analysis Properties->Estimation tab in AMOS: Maximum Likelihood (ML), Unweighted Least Squares (ULS), Generalized Least Squares (GLS), Browne's Asymptotically Distribution Free (ADF), and Scale-Free Least Squares (SLS). What are my best options for analyzing these ordinal variables?
Resolving The Problem
You can find some additional references and constraints on the ADF method in Technote 1476193.
AMOS has the capability to perform Bayesian estimation for ordinal data beginning with Release 7.0. You can find more information on the AMOS web site at http://amosdevelopment.com/index.html .
and in Part II: Chapter 33 of the AMOS User's Guide for versions 7.0 and above. The User's Guide, as well as videos of AMOS analyses of categorical data and other Bayesian applications, can also be found at this site. There is a technical description of the Analysis Properties->Estimation methods in Appendix B ("Discrepancy Functions") of the AMOS User's Guide for each AMOS version.
Some resources that provide more general information about estimation methods are listed below. There seems to be some support there for both ML with bootstrap and for GLS. If your ordinal variables have few categories, this data property may limit the generality of their advice to your situation, as the authors tend to discuss 4 or more categories. If you don't already belong to the SEMNET discussion group, you may want to check this resource getting the current opinions of major figures in SEM research: http://www.gsu.edu/~mkteer/semnet.html
The first edition of Barbara Byrne's guide to AMOS (2001, pp. 71-72), which was written before the Bayesian methods for ordinal data were available in AMOS, seems to favor ML in such situations, but does mention 4 or more categories as a condition for the generality of this approach: The 2010 edition of this guide adopts the Bayesian approach for analysis of categorical variables.
Barbara M. Byrne (2001). Structural Equation Modeling with AMOS: Basic Concepts, Applications, and Programming. Mahwah, NJ: Lawrence Erlbaum Associates,.
Barbara M. Byrne (2010). Structural Equation Modeling with AMOS: Basic Concepts, Applications, and Programming (2nd Ed.). New York: Routledge.
For a very thorough treatment of estimation issues, see:
Bollen, K. (1989). Structural Equations with Latent Variables. New York: Wiley.
Also consider the following paper (for which we do not have a link):
Olsson, Ulf Henning, Tron Foss, Sigurd V. Troye, and Roy D. Howell (2000). The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality. Structural Equation Modeling 7(4): 557 -- 595 .
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