Latent growth curve with three latent variable and piecewise linear regression I already heard about piecewise linear regression but I have no experience with latent growth curves. I came across it in that paper. As far as I understood based on Figure 1 (observed sample means) they want to fit two lines to each figures data, so a piecewise linear regression is what I expect for that. But they use Latent growth curve modelling and give some figures (I think they create this using some tools, SPSS maybe?) Figure 2 and Figure 3 present growth curve models.
Do you have any idea why we use latent growth curves and not piecewise linear regression? Which one is more suitable in which cases?

Their latent growth model is piecewise linear:
it has an intercept (level at week 1), a linear slope before the midterms,
and a linear slope after the midterms. Using latent growth structural equation model, rather than simple piecewise linear regression, makes it easy to explicitly model additional parameters of interest, such as the correlation between the level at week 1 and the pre-midterm slope, or the correlation between residuals from weeks 3 and 7.

