Is it possible to specify an autoregressive, or banded, or similar pattern for the residuals (if indeed there are residuals)in a growth model in which the dependent variables are binary and/or ordered categorical?
Other than specifying the variables as continuous, is there any work-around for a situation like this?
Yes, this is most easily done with weighted least squares estimation using the WITH option. With maximum likelihood, each residual covariance requires one dimension of integration. See Example 6.17 in the Mplus User's Guide.
I wasn't fully clear. Example 6.17 has continuous outcomes. What I want to know is whether it is possible to specify an autoregressive-like pattern to residuals when the outcome variables are binary or ordered categorical.