Latent Change Scores can model the Latent Growth Linear Model

This is the setup of the LCS constant change model that replicates the LGM linear model, first shown by
McArdle, J. J. (2001). A latent difference score approach to longitudinal dynamic structural analyses: a festschrift in honor of Karl Jöreskog. In R. C. K. G. Jöreskog, S. H. C. D. Toit & D. Sörbom (Eds.), Structural equation modeling: Present and future (pp. 342–380). [:353]

Also, there is a simple way to replicate a 2 wave LGM model as a LCS with constant change, the setup below does not look simple because I chose to specify EVERY parameter possible:

We sketch here some practical guidelines on how to:
1. Run a paired t-test to answer the question: 'Did outcome Y change from baseline to follow-up" - in AMOS v. 5 [free software, this version only] and in Mplus.
2. Compare the paired t-test results to a flexible model where the change is allowed to depend on the initial values of Y (which the paired t-test does not allow).
3. Compute statistical power for the 2 models, and see which fares best, and why; this can be easily done with very simple syntax ran in Mplus.
For more detailed input and output files to replicate all our analyses, go to:
http://trippcenter.uchc.edu/modeling 
The changes seem dramatic when outcomes are not centered [see last image below], less impressive when wave 1 and wave 2 measures are centered on the wave 1 mean [right below], still some differences are notable, see 2nd graph of p values.