Multivariate longitudinal analysis
Message/Author
 oulhaj posted on Tuesday, April 19, 2005 - 7:04 am
Hello, I'm new to Mplus. I am wondering if Mplus can perform a Multivariate linear mixed analysis? i.e. where each statistical unit is characterized by a matrix the columns of which are the dependent variables (let us say 5) and the rows are the times of measurement. One way to proceed is to transform the problem to the univariate linear mixed models with a covariance structure of the residual terms being the kronecker product between two matrix (identity and any parametric one). Can we do that with Mplus?

Thanks alot
 bmuthen posted on Tuesday, April 19, 2005 - 12:16 pm
Mplus can do linear mixed modeling with several dependent variables. The growth processes can also be related to each other in flexible ways. See ex 6.13 as an example from the Version 3 User's Guide.
 oulhaj posted on Wednesday, April 20, 2005 - 5:57 am
Many thanks for your quick reply, I really appreciate it .

My question now is : Can we do this analysis in the non balanced case (i.e. non-equally spaced times of mesurement, individually-varying times of observations ... ). If yes, I will be grateful if you can give me the statistical reference you are using to do that.

 BMuthen posted on Wednesday, April 20, 2005 - 9:19 am
Yes. Perhaps the Raudenbush and Bryk 2002 book could be a useful reference.
 Udaya Wagle posted on Wednesday, September 07, 2011 - 8:57 am
I have some policy variables (x), their outcomes (y), and other covariates (z) measured for different units at unbalanced intervals. I am thinking of y as a function of x and z and then x purely as a function of z. I was trying to use growth modeling approach thinking time is an important factor. But I could not relate this to any specific example in the Users's Guide or other dicussions here.

Also, your examples in the User's Guide appear to be suited to wide format of the data which I do not want to go for since I have a cross-section of imbalanced but large time series with multiple x's and multiple z's.

Could you point me to the right direction for the version 6 of MPlus which I currently have?

Thanks
 Linda K. Muthen posted on Wednesday, September 07, 2011 - 5:11 pm
Example 9.16 shows how to set up a growth model for long format data. You can expand on that example by having more than one growth process of time-varying covariates.
 Udaya Wagle posted on Friday, September 09, 2011 - 8:19 am
Thank you for your suggestion. I assume my z will be equivalent to the a in the example. Even with this, however, I am not clear how I could operationalize a common factor out of the different x policy variables so that the x's would have a common effect on the final outcome y, together with the effects of the a. This is more along the line of structural equations and yet having to use the longitudinal growth framework. Your expert suggestion would be appreciated.
 Bengt O. Muthen posted on Saturday, September 10, 2011 - 9:02 am
It sounds like you have a mediation model like

y on x z;
x on z;

where all 3 of your variables z, x, y vary across time. This means that you have 2 DVs, y and x, whereas in ex 9.16 on Within there is only 1. And you have 1 IV, namely z, just like a3 in ex 9.16. So comparing to ex 9.16, you will have on Within the mediation model above and on Between you have the random intercepts for the 2 DVs, y and x. If you have person variables that do not vary across time, they will appear on Between like x1, x2 in ex 9.16. This modeling takes into account the longitudinal nature of the data, accounting for correlations across time within subjects, but without going the further step of doing growth modeling.
 Udaya Wagle posted on Saturday, September 10, 2011 - 6:24 pm
Thanks Bengt for taking the time to help me out. Actually, here is what I have (sorry about not being specific before):

Measurement equation:
eta by x1 x2 x3

Latent variable equation:
y on eta z1 z2 z3 z4
eta on z1 z2 z3 z4

All of these variables vary over time for different geographic units. I am assuming that "a" from 9.16 can be replaced with multiple z's here. But my problem has been on dealing with the different policy indicators (x1 x2 x3), which I assume have a latent factor. And since the x's and y measurements of these geographic units change over time, I was thinking growth would be an important factor.
 Bengt O. Muthen posted on Tuesday, September 13, 2011 - 9:10 am
This means that you would let both eta and y have a random intercept, that is, variation across units. These intercepts capture correlations across time within unit. But you could be more ambitious and in addition to the random intercepts specify a growth model with intercept and slope growth factors. You would have one process for eta and one for y. Just piece together parts of different UG examples.
 Udaya Wagle posted on Wednesday, September 21, 2011 - 6:53 am
Appreciate the suggestion. Will try to figure out and come back if it does not work.
 Udaya Wagle posted on Tuesday, October 11, 2011 - 8:55 am
Having tried with multilevel framework, I am not ocnvinced if I can even identify my variables as within and between. All the variables vary both within units and over time (of course except the id and year). I cannot come up with an appropriate setup of Between equation in 9.16. Also, I could not relate my situation with any example from growth modeling (Ch. 6).

Given that my eta and y would have random intercepts at the least (I am not sure if I want to go for slope growth factors since data on changes over time are not very reliable), I would appreciate your help in setting up the above measurement and latent variable equations for estimation. Thank you.
 Bep Uink posted on Thursday, January 14, 2016 - 8:23 pm
Hello, I am modelling a multivariate growth curve with 3 outcomes (depression, ability self concept & binge drinking). Ability self-concept intercept predicts binge drinking slope and the estimate is negative (as expected). In addition, ability self-concept and binge drinking slopes are significantly correlated, however, the correlation is positive. I've tried correlating residuals, adding time varying and time invariant co-variates, and model fit is acceptable. It just seems odd that the correlations are positive; the parallel process for these 2 variables also has positive slope correlations.
Could you please shed any light as to whether this is a result of a problem in my model? [or just what the data shows]
 Bengt O. Muthen posted on Friday, January 15, 2016 - 8:01 am
You may want to discuss this on SEMNET.