I used Mplus 3.11 for the analysis of a dataset with about 1100 schools (as level-2 units) and 27000 stundents (as level-1 units). I also used the weight option. The average cluster size was 23.7.
I compared the intraclass correlations (ICC) that Mplus computed to those that were computed by HLM 6 (also with weighted data) and to those of SPSS 11.5 as estimated by the varcomp procedure (also with weighted data).
The results differ somewhat when the data are weighted: ICC(Mplus) = .49 ICC(HLM 6) = .57 ICC(SPSS) = .57
But I get the same results with all three programs if the data are not weighted. Is there a problem with the weight option in combination with multilevel data? Does this problem affect also the estimated model parameters?
As always, your help is highly appreciated
bmuthen posted on Friday, December 17, 2004 - 3:55 pm
There could be a couple of reasons for the difference. I don't know how the other programs do their computations - the documentation is often not sufficient. Below is what Mplus does.
First, different scaling methods might have been used. See Mplus Web Notes #7 and #8, particularly Tables 1 and 2 in note #8, to find comparisons of scaling methods A and AI. This has to do with scaling the weights to add to the sample size (within clusters). In your Mplus run you probably use method AI, while the HLM6 run might use A. By preparing weights before inputting into Mplus, you can do method A.
Second, Mplus computes icc's based on unrestricted Sigma(B) and Sigma(W) matrices, whereas perhaps HLM6 uses model-estimated matrices.
Third, Mplus uses ML-estimated Sigma(B) and Sigma(W) matrices whereas perhaps HLM6 uses unbiased estimates of those matrices.
Other differences may have to do with random slopes being present or not and conditioning on covariates or not.
You might want to try scaling method A in your Mplus run to see if your results get closer. Otherwise, you might want to send your differing results for us to look at.