I wish to run a multilevel growth model with an intent-to-treat analysis (I have outcome data for four time-points, but some people are missing data for the latter timepoints because they finished the treatment earlier).
When I run the multilevel growth model (with an MLR estimator, time at the within level, and subject ID at the between level, hence a long data format), the number of observations is lower than the sample size (but not as low as the sample size minus the number of participants with at least one missing response). If multilevel level models are supposed to use all available data, why isnít it doing so here? When I run a single- or multi-level model with a wide-data format, the number of observations is in fact equal to the sample size. However, I assume this is estimating the missing data with FIML, and is not strictly speaking an intent-to-treat analysis.
How would I run an intent-to-treat analysis for multilevel models with wide and long data formats?
In the long format you do regression of y on time so if y is missing that observation doesn't contribute to the estimation of the regression and is deleted. In the wide format such a y borrows information from other variables observed for the individual, so FIML.
I don't know what the special considerations would be for intent to treat.
Thanks for confirming that. You raise a valid point: there is some variability in how we define 'intent to treat' analyses (see Gravel, Opatrny, & Shapiro, 2007; https://goo.gl/3C2KDE).
What I meant by intent-to-treat is that all available observations contribute to the growth model. So if there are four time-points, and a subject has observations at timepoints 1-3, then their data for TPs 1-3 will be used (they are not excluded due to a missing data point). It sounds like this is what is achieved in the long format approach you describe.
In the example above, using a wide data format, hence FIML, would not be conceptually accurate if that subject completed the treatment just at an earlier time. The 'missing' data point is justified by differences in treatment completion time.