I have a data analysis problem that I have not seen covered in any examples.
I have longitudinal data over 5 assessments from both partners from gay/lesbian couples. I want to assess the extent to which two growth curves (intercepts and slopes) from partner-level continuous variables predict instability (a single couple-level dichotomous variable).
I am conceptualizing this as a parallel process multilevel growth curve problem in which partners are nested in couples for the two parallel growth curves. Basically, I want to predict stability from four predictors (the intercept and slope from each of the two continuous variables).
I haved explored this problem doing three separate analyses (two multilevel analyses in which I obtain the estimates for both sets of intercepts and slopes, and a regular logistic regression in which these four variables are used as predictors). But, I would like to do the problem in ONE analysis with the proper estimators. Is this possible with Mplus 4?
Yes, this is possible to do in a single analysis in Mplus. You are on the right track when conceptualizing this as parallel processes. Note that this is treating couples as the independent observations (the sample size is number of couples) whereas the parallel process modeling captures the within-couple non-independence. You simply have the dichotomous outcome as yet another variable in the modeling.
You can estimate this with ML, which is heavy with 4 growth factors given that you have to numerically integrate all 4 dimensions, or with WLSMV which should go quicker.