Unbalanced growth model
Message/Author
 Harold Chui posted on Wednesday, July 10, 2013 - 2:22 pm
Hi Drs. Muthen,

I have a data set where different numbers of observations were obtained from different participants, and I want to run a multilevel/growth model examining relationships between several level 1 variables. (L1 = sessions, L2 = clients, L3 = therapists)

I learned that I should consider a two-level growth model using Mplus, instead of the traditional three-level model, but I have some questions about how to set it up.

My data have been entered such that data from each session occupies a single row. Is this the right way to do it? Or do I need to rearrange the data so that each client occupies a single row? If it were the latter, how should I take care of having different number of variables for each row?

Thanks.
Harold
 Linda K. Muthen posted on Wednesday, July 10, 2013 - 2:43 pm
Each row should represent a client. The number of variables is equal to the number of sessions. Use a missing value flag for the sessions that a client did not attend.
 Harold Chui posted on Friday, July 12, 2013 - 7:26 am
Thank you.

Just let me clarify further. The data have been collected such that there are 18 variables per session, and the number of sessions range widely from 2 to 81 for the 51 clients.

Does it mean that I have to create 81*18 = 1458 variables and fill out 1422 missing value flags for the participants with only 2 sessions (1458 - 2*18)?

Is there a limit to the number of variables allowed for each row?

Would there be problems modeling this kind of data set with so much "missing" data? (they are not really missing in the traditional sense but it is a naturalistic study where we included data from participants who had different lengths of therapy during the data collection period).
 Bengt O. Muthen posted on Friday, July 12, 2013 - 1:40 pm
Are you saying that the 18 variables per session are indicators of a construct (factor) that you want to study growth of over time?
 Harold Chui posted on Friday, July 12, 2013 - 1:47 pm
No...they are separate measures. I want to look at the relationship between these session-level variables. Should I use threelevel (session, client, therapist) instead if I am not interested in growth, even though they were repeated measures?
 Bengt O. Muthen posted on Friday, July 12, 2013 - 1:59 pm
So you have a model in mind for the relationships among your 18 variables - what is it, generally speaking? And session is just really "a nuisance" in the sense that you don't care to model it, just take it into account?
 Harold Chui posted on Friday, July 12, 2013 - 2:38 pm
The 18 variables include pre- and post-session measurement of moods, and post-session measurement of some session outcome variables, and I am interested in the relationship among these variables. Session is a nuisance when considering relationships among the mood variables (because they are states), but would be important to model when looking at the relationship between mood and session outcome, because session outcome is known to vary over time.

I have been looking at the manual examples of time-varying covariates, but also come across growth models, and so I am unsure which one to use.
 Bengt O. Muthen posted on Friday, July 12, 2013 - 3:34 pm
I may be off, but couldn't you view this as clients nested within sessions and sessions within therapists. That seems to fit with the impression that you have something like a regression model for your 18 variables with mood variables influencing session outcome variables - and that the coefficients in this regression vary across sessions (and therapists). If so, that would be 3-level modeling with random intercepts and slopes varying across sessions and therapists (assuming you have enough of each). But this is just a quick thought.