Longitudinal cross-lagged SEM with categorical data I have a dataset where $X$ (binary), $Y$ (binary) and $Z$ (4-category ordinal) are repeated measurements taken at three different time points. I assume the direction of the relationship among these variables should be like the following graph ($X$, $Y$ and $Z$ have dependencies within and between their lags). There are also a few time-invariant variables ($A$, $B$, $C$, some are continuous and some are categorical) which may `affect/moderate' the relationships among $X$, $Y$, and $Z$. The design below probably requires a cross-lagged panel analysis with categorical endogenous variables ($X$, $Y$, and $Z$). Can anyone suggest me an appropriate literature and a statistical package that can get the job done?  

 A: Panel models are quite common in longitudinal SEM. It sounds like might be new to this approach to data analysis, so I would suggest Little (2013), which will give you good coverage of the basics of SEM, as well as an intro to panel models, specifically (and I'm sure many of the references throughout that chapter will be useful to you as more detail-oriented learning resources).
In terms of software, unless I'm missing something, I'd expect most SEM software would be capable of addressing your needs. The lavaan() package (Rosseel, 2012)for R is about a user-friendly as it gets (syntax is very similar to Mplus, but unlike Mplus, it's free), and it can handle categorial endogenous variables (see categorical data analysis tutorial section for the package here). If you're going to use lavaan(), Beaujean's (2014) book is also handy as an SEM primer that is lavaan()-specific. 
References
Beaujean, A. A. (2014). Latent variable modeling using R: A step-by-step guide. New York, NY: Routledge.
Little, T. D. (2013) Longitudinal structural equation modeling. New York, NY: Guilford Press. 
Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. http://www.jstatsoft.org/v48/i02/.
