Mediation that tests changes-leading-to-changes

Many longitudinal models with mediators do not specifically test whether a change in X leads to a change in M which then leads to a change in Y (or for experimental setups whether getting the treatment leads to changes in M which leads to changes in Y).
The only tool that specifically does this is the one using the Latent Change Scores, here are the first published such examples (parallel LGM are doing something like this, but commonly linking synchronous changes). One can also take a look at http://www.modeling.uconn.edu/archive/20131/2013/  under Testing Mediation the Way it Was Meant to be: Changes Leading to Changes then to Other Changes. Dynamic Mediation Implemented with Latent Change Scores
Here are the first 2 examples visually:

which should have then specified the green paths I added:

and 2nd:

Can you get more latents than me?

Output of a Latent Change Score model with Growth Modeling elements and measurement error

Can you beat my 10/2 ratio latent/observed variables? Here's a simple example of a model looking at changes in 1 observed outcome only, from Y1 to Y2. The Latent Change Score setup [see an excellent intro here] allows one to answer this question in a paired t-test kind of way, but can also accommodate growth modeling elements [intercept=initial level and slope=constant additive change factor]; plus, one can incorporate measurement error, i.e. strip the true measures of unreliability (assumed to be a 10% for example). This leads to the output above [this is an application using the data mentioned here under 'The paired t-test as a simple latent change score model']

*** By the way, in case you wonder about the meaning of each of those latent variables, here's a similar example of such a struggle to find the hidden side of reality, or what's behind the observed facts:

Illustrations of single- and multi-group models with some variables missing/unobserved in some groups

Fig 5.2 in
Hayduk, L. A. (1996). LISREL issues, debates, and strategies: Johns Hopkins University Press.
(Ch. 5, Stacked Models with Differing Sets of Indicator Variables_155-189).

Fig. 18.10 in
McArdle, J. J., & Nesselroade, J. R. (2003). Growth curve analysis in contemporary psychological research. In J. Schinka & W. Velicer (Eds.), Handbook of psychology (Vol. 2, pp. 447–480). New York: Pergamon.

Fig. 2 in
McArdle, J. J., & Hamagami, F. (2004). Methods for dynamic change hypotheses. In K. v. Montfort, J. Oud & A. Satorra (Eds.), Recent Developments on Structural Equation Models: Theory and Applications (Vol. 19, pp. 295-336).

Fig. 5.15 in
McArdle, J. J., & Bell, R. (2000). An introduction to latent growth models for developmental data analysis. In T. Little, K. Schnabel & J. Baumert (Eds.), Modeling longitudinal and multiple-group data: practical issues, applied approaches, and scientific examples (pp. 69-107). Mahwah, NJ: Erlbaum.

Fig. 3.2 in
McArdle, J. J., & Hamagami, F. (2003). Longitudinal tests of dynamic hypotheses on intellectual abilities measured over sixty years. In C. S. Bergeman & S. M. Boker (Eds.), Methodological Issues in Aging Research (pp. 31-98): Lawrence Erlbaum Associates, Mahwah.

Fig. 2 in
McArdle, J. J., & Woodcock, R. W. (1997). Expanding test–retest designs to include developmental time-lag components. Psychological Methods, 2(4), 403-435. doi: 10.1037/1082-989x.2.4.403

Fig 8.3 in
Hamagami, F., & McArdle, J. J. (2001). Advanced studies of individual differences linear dynamic models for longitudinal data analysis. In G. Marcoulides & R. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 203-246).

Slide 23 in
Recapturing Time in Evaluation of Causal Relations: Illustration of Latent Longitudinal and Nonrecursive SEM Models  for Simultaneous Data. Presented at the American Evaluation Association convention, Nov. 14, 2009, Orlando FL http://comm.eval.org/eval/resources/viewdocument/?DocumentKey=5f351c13-1f91-42b7-85fe-450d19f46fca