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.
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?
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.
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.