In a growth mixture model with covariates, why is it important to regress covariates on BOTH the growth factors and the categorical latent variable used to represent class membership? I am thinking of the following basic example for a 2-class model (User's Guide, 8.1):
The way I think about this is that the most important path is from x to c. This says that class membership probability is a function of x, which in turn implies that the means of i and s are influenced by x since those means change over classes (this is like an indirect effect). The regression of i and s on x is saying that even within a given class is there influence from x. For instance, a high x value for a subject may make it more likely for the subject to be in a c class that has a high i mean (that's c on x). But within that high class, it may also be true that the higher the x value is for a subject the higher the subject's i value (that's i on x). Conceptually, you can think of i on x as a partial (residual) effect, holding c on x constant.
This also speaks for the possibility that i s on x can vary across classes because it may not be the case that x has this same extra influence in all classes.
Thanks for the reply - this makes sense, except that when I run this model, the regression coefficients and standard errors for i s ON x are identical across classes! Is this the result of a default setting that can be changed? Do I have to specify that I want i s ON x estimated differently for each class?
I've been looking through the Mplus manual and the discussion board for the syntax to relax this equality. I'm not having any luck finding this, though. How exactly do I relax this constraint? For example, here is my syntax now for a 4 class LCGA model with one covariate:
Title: latent class growth analysis on bsi hostility with covariates Data: file is id_hos_child_adult_priorvic.csv'; Variable: names are id hos1 hos2 hos3 hos4 x1 x2 x3; usevar=hos1-hos4 x3; IDVARIABLE = id; missing = all(999); CLASSES = c(4); SAVEDATA: FILE IS hos_four_priorvic_output; save=cprobabilities; Analysis: type = MIXTURE missing; STARTS = 10 2; STITERATIONS = 10; Model: %Overall% i s|hos1@0hos2@2hos3@6hos4@12; i-s@0; i s ON x3; c#1 ON x3; c#2 ON x3; c#3 ON x3; Output: sampstat standardized tech1 tech4 tech8 tech11 tech14; PLOT: SERIES = hos1-hos4 (s); TYPE=PLOT3;
You need to specify after %c#1% the statements that you want to vary like I showed above. If you can't figure this out, please send your input, data, output, and license number to firstname.lastname@example.org.