Much like with regression, handling binary dependent variables in SEM requires special considerations. In particular, some of these are noted on Dave Garson's Structural Equation Modeling and include:
Polychoric correlation. LISREL/PRELIS uses polyserial, tetrachoric, and polychoric correlations to create the input correlation matrix, combined with ADF estimation (see below), for variables which cannot be assumed to have a bivariate normal distribution.
- Sample size issue. ADF [Asymptotically distribution-free] estimation in turn requires a very large sample size. Yuan and Bentler (1994) found satisfactory estimates only with a sample size of at least 2,000 and preferably 5,000. Violating this requirement may introduce problems greater than treating ordinal data as interval and using ML estimation. This is also a reason cited for preferring the Bayesian estimation approach to ordinal data taken by Amos since Bayesian estimation can handle smaller samples than ML or ADF.
- I don't know what estimation method is being used with these correlations (i.e., ADF or ML).
- My sample size is small (N = 173).
- I'm not familiar with how to interpret polychoric associations (in the case that it is appropriate for me to use them). All the other variables in my model are continuous in nature.
Any help and/or links would be greatly appreciated. I'm also considering using other software like OpenMX, but I'm still reading about how it handles binary data. Help with what other software I might want to use would also be appreciated.