Equality constraints on the level-1 r... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Anonymous posted on Friday, April 22, 2005 - 11:09 am
Dear Bengt and Linda,

I am modeling a linear growth with three individually varying time points. I can run the growth modeling with either constraining the level-1 residual variances to be equal or freeing them when there are no level-2 predictors added. Since freeing the residual variance can significantly improve the model fit and the estimated residual variances indeed differ a lot, I choose to go with it. However, when I added the level-2 predictors, freeing residual variance cannot lead to convergence for some predictors, so I have to equate them for some predictors. The problem is that freeing and constraining lead to quite different estimates on both fixed and random effects. Sometimes significant effect on the growth parameters was found for one predictor by freeing the residual variance, but once I constrained them, the significant effect was gone, vice versa, which raises two questions:

1. How does freeing or constraining residual variance work when I have random time? As I understand, if we have random time, although there are only three time points for each individual, there should be more than three time points for the whole sample. So, when I free the residual variances, does it mean I free the residual variance at each random time point (should be more than 3 residual variance estimates) or just free the residual variances for y1 y2 and y3 since I only got three residual variance estimates in the output? If it is the latter, does it make sense?

2. In my case, should I stay with freeing or constraining the residual variance? I can make the analyses consistent by constraining the residual variance for all the predictors, but I am worried about whether I got the true estimates of the effects. If I constrain the residual variances for some predictors while free them for the other predictors, how can I compare their effects?

By the way, the sample size is small with n = 120. There are a few missing data, so I use type = missing h1 random.

The model part syntax is like this:

i s| y1 y2 y3 at t1 t2 t3;
i s;
i with s;
[i s];
y1 y2 y3 (1) ;
i on x1 x2;
s on x1 x2;

Any help is highly appreciated.
 bmuthen posted on Friday, April 22, 2005 - 3:32 pm
Answering 2. first, I am in favor of allowing level-1 residual variances to vary across time. You should try to figure out why you have non-convergence in some runs. I am not sure why you do one predictor at a time - if all are relevant it seems to me that you should include all of them in a single run, otherwise any one predictor's slope is misestimated.

1. You are right that with individually-varying times of observation, time represents not merely 3 different time points, but many more. But I think it is still relevant to let the residual variances vary rather than holding them equal. There are only 3 res vars estimated, however (each covering a range of times). Special modeling would have to be employed to estimate res vars for distinct time points - you would have to string out the multivariate outcome vector according to distinct time points at which you observed several individuals.
 Anonymous posted on Saturday, April 23, 2005 - 3:19 pm
Dear Bengt,

Thanks you so much for your prompt answer. I will try to figure out why the program cannot converge in some runs, which may due to the missing data in some moderators. By the way, it is just the first step to do one moderator at a time since there are too many moderators to be investigated. Once I identify some interesting moderators,i will put them together in one model as you said.
 anonymous posted on Friday, November 11, 2005 - 12:50 pm
What is the benefit of allowing the level 1 residual variances to vary over time. That is, is it specifically to improve model fit...or does freeing these variances improve the interpretation of the model?
 BMuthen posted on Saturday, November 12, 2005 - 6:28 pm
Allowing the residual variances to vary over time rather than constraining them to be equal allows the hypothesis that they do vary over time to be tested. And you may be interested in knowing that they do. If you don't free these variances, other parameter estimates may be affected.
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