The LCS definition and setup can be seen in an applied manner [that's how one can define the parameters in fact] as in :
1. McArdle, J. J. (1991). Comments on “latent variable models for studying difference and changes” In L. Collins & J. L. Horn (Eds.), Best Methods for the Analysis of Change (pp. 164-169). Washington, D.C.: APA Press.
2. McArdle, J., J. (1991). Structural models of developmental theory in psychology. In P. V. Geert & L. Mos (Eds.), Annals of theoretical psychology (Vol. II, pp. 139-160). New York: Plenum Publishers.
3. Prindle, J. J., & McArdle, J. J. (2012). An Examination of Statistical Power in Multigroup Dynamic Structural Equation Models. Structural Equation Modeling: A Multidisciplinary Journal, 19(3), 351-371. doi: 10.1080/10705511.2012.687661
4. McArdle, J. J. (2009). Latent Variable Modeling of Differences and Changes with Longitudinal Data. Annual Review of Psychology, 60, 577-605.
5. Coman, E. N., Picho, K., McArdle, J. J., Villagra, V., Dierker, L., & Iordache, E. (2013). The paired t-test as a simple latent change score model. Frontiers in Quantitative Psychology and Measurement, 4, Article 738. doi: 10.3389/fpsyg.2013.00738 [an update 9/14/16: >4,700 reads... only 1 citation though; what would this mean...?]
6. Grimm, K. J., An, Y., McArdle, J. J., Zonderman, A. B., & Resnick, S. M. (2012). Recent Changes Leading to Subsequent Changes: Extensions of Multivariate Latent Difference Score Models. Structural Equation Modeling: A Multidisciplinary Journal, 19(2), 268-292. doi: 10.1080/10705511.2012.659627