Between-level variance/covariance matrix
Message/Author
 William Johnston posted on Monday, June 17, 2013 - 8:33 am
Could you possibly point me to an article, webnote, or presentation that goes through the method by which the between-level variance/covariance matrix is derived?
 Bengt O. Muthen posted on Monday, June 17, 2013 - 1:08 pm
You may want to take a look at

http://www.statmodel.com/bmuthen/articles/Article_032.pdf
 John B. Nezlek posted on Wednesday, January 14, 2015 - 11:12 am
Dear Colleagues

I took a look at the article mentioned above, and my mind is still reeling from the notation. So, please forgive me if my question is stupidly simple or answered elsewhere.

I have a two level data structure with widely varying numbers of level 1 units for each level 2 group. I ran a multilevel EFA and obtained the within and between correlation/covariance matrices. Based upon some other analyses I have done, the within makes sense.

The between has me a bit puzzled however. Some of the between estimates are very different from correlations between aggregated means for the same variables -- I calculated a mean for each level 2 group and then correlated them. Some of these differences are in the sign of the correlation -- not just the magnitude.

Are the differences between these two estimates (the between from MPlus and the simple correlations) due to the fact that the level 2 units have very different numbers of observations? This is something that is not taken into account with the simple correlations, but seems to be taken into account with the MPlus estimates.

Also, is there some type of Bayes adjustment here? That is, all means are not created equal, and weighting observations as a function of this might also change things.

John
 Bengt O. Muthen posted on Wednesday, January 14, 2015 - 11:41 am
You might find this paper easier to read. It is on our website under Papers, Multilevel SEM:

Muthén, B. (1994). Multilevel covariance structure analysis. In J. Hox & I. Kreft (eds.), Multilevel Modeling, a special issue of Sociological Methods & Research, 22, 376-398.

Note in particular "Step 4" on pages 388-389. Bottom of page 388 explains that the between structure should not be expected to be captured by S_B.
 John B. Nezlek posted on Wednesday, January 14, 2015 - 12:38 pm
Bengt,

Fair enough, but on p. 389, it (you :-), states that "in practice, we might have to resort to analyzing S_B to get a notion of the Sigma_B structure". Does this not imply or suggest that the covariances/correlations among the means should be at least vaguely similar to Sigma_B?

If the correlations that I got from the analyses of aggregates simply differed from the estimates provide by MPlus (e.g., .2 vs. .4), I would not be too concerned. In some instances, they are radically (and meaningfully in terms of substance) different, e.g., -.54 from aggregates versus .27 from MPlus).

I will add that this data structure is very, very irregular (ns from 5 to 1000 for level 2 units), so much so that I realize it might not be appropriate to include all the level 2 units in the analysis.

Could such differences lead to/explain the differences in the estimates?

Thanks,
John
 John B. Nezlek posted on Wednesday, January 14, 2015 - 1:28 pm
I have also noticed that the estimates of the between level correlations in MPlus vary (sometimes considerably) as a function of exactly which variables are included in the analyses, which reduces the correspondence between these estimates and those obtained from analyses of aggregates.
 Bengt O. Muthen posted on Wednesday, January 14, 2015 - 2:54 pm
Could you send to Support the two outputs you compare. Actually, for the aggregate run please use the Mplus option Cluster_Mean to get the aggregate variables.
 John B. Nezlek posted on Wednesday, January 14, 2015 - 3:03 pm
Will do. It's midnight here in Warsaw, but I will get to it quickly tomorrow some time.

Thanks so much for the quick replies. I appreciate it very much.
 John B. Nezlek posted on Wednesday, January 14, 2015 - 3:31 pm
What the hell. Sleep is so over-rated. I will be sending some outputs to support in a few minutes.
 John B. Nezlek posted on Wednesday, January 14, 2015 - 4:36 pm
Although sleep may be over rated, attention to detail is not. I am relatively new to MPlus, and I am not as familiar as I should be with some basics -- e.g., blanks are not always treated as missing. I realized that I had not specified my missing data properly (they are all over the place). After correcting this, although there were some differences across the analyses in estimates of the same parameters, these differences were not that pronounced and well within the bounds of estimations. So, there is no drama here. My apologies. It is now 1:30, and sleep seems like a good idea.