Spatial power law in Multilevel model
Message/Author
 Cornelia Wrzus posted on Friday, March 27, 2009 - 1:47 am
Dear Dr. Muthen,

I am modeling longitudinal data (~54 measurements over 9 days, i.e. 5-6 measurements per day) using random coefficient multilevel modeling.

How is it possible to take into account that time between measures is unequally spaced (and thus, measurement points differently correlated)?

I read about modeling a covariance structure applying the spatial power law using SAS, but don't know whether this is possible in Mplus (so far everything in my analyses has been possible in Mplus

I browsed this very helpful discussion forum, but did not find help this time.
I would be very thankful for any ideas or references.

Best from Berlin, Germany,
Cornelia
 Bengt O. Muthen posted on Friday, March 27, 2009 - 4:18 pm
By the "spatial power law", perhaps you are referring to the version of 1st-order auto-correlated residuals where differences in timing intervals are taken into account. The Mplus UG example 6.17 shows how Model Constraint can handle the case where the timings have the same intervals. Here the "corr" parameter is the correlation between adjacent residuals. Residuals two points apart will have correlation corr**2, etc. So with non-equidistant time points, you will have to adjust those Model Constraint settings.

If there are individually-varying times of observation I think you could use the VARIABLE option CONSTRAINT = in order to read in individual timing differences and then use that constraint variable (or variables) in Model Constraint.

If you don't have individually-varying times of observation, the easiest way to handle the residual correlations for non-equisdistant time points is to let each pair of adjacent time points have their own residual covariance parameter.

In my discussion here I have assumed the use of the "wide" data approach to growth modeling, the single-level, multivariate approach.
 Cornelia Wrzus posted on Monday, March 30, 2009 - 2:06 am
Dear Dr. Muthén,

You are right that times between observation are individually-varying, but there is a variable indicating the distance which I could use in the constraint option.

Sorry for being imprecise - I assumed with about 54 repeated measures using ANALYSIS: TYPE = TWOLEVEL RANDOM would be the only applicable way.
I have used the "long" data approach, so far, because number (range 44-76, mean 54) and spacing of measurements differs between individuals.

Do you see any objections having 76 variables in the multivariate approach and many missings for some individuals?

I found that is not possible to use the CONSTRAINT command when using TYPE = TWOLEVEL, right?
I try to work it out the way you described it and might ask again.

Again, thank you very much for your help. Best, Cornelia
 Bengt O. Muthen posted on Monday, March 30, 2009 - 10:33 am
You are right that having as many as 76 variables wide with a lot of missingness is an awkward way to go. The long, two-level approach is better in this case. Model Constraint is available for Type = Twolevel in the current Mplus version. I am not sure, however, how to implement this correlated residual approach in the long approach.
 Roy Stewart posted on Friday, January 29, 2010 - 4:40 am
Dear Everybody,

I hope that in the meantime, someone has a good Mplus-example for an unbalanced longitudinal model with non-equidistant time points, where the correlated residuals were implemented in the long approach.
Is there anyone who can give me this example or references?

Roy
 Linda K. Muthen posted on Friday, January 29, 2010 - 8:46 am
In the long format, correlated residuals are not parameters in the model.
 Roy Stewart posted on Saturday, January 30, 2010 - 5:56 am
Dear Dr Muthén,

I change my question a little bite:

Is there anyone who has one or more example(s) and/or reference(s)
of an unbalanced longitudinal with ordered time points?