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 Sarah Victor posted on Wednesday, August 01, 2018 - 7:10 am
Dear Drs. Múthen,

I am currently attending a multilevel SEM training with Dr. Kristopher Preacher, and in running several example models using multilevel SEM we have run into a new warning that we can't figure out. Specifically, when using a predictor (x) variable on both the within and between levels, a warning appears indicating that the entire observed x value is being used as a predictor on the within level, and the between portion of the x variable is being used on the between variable, rather than having the within and between portions separated, as was previously the case. The warning refers to the need to use ESTIMATOR=BAYES to get corrected latent mean centering across the within and between variables. Interestingly, the output results match exactly the results Dr. Preacher had calculated in a previous version of Mplus that did not include this warning, so it appears that the results are correct, although the warning indicates that they will not be.

Can you provide any insight into the meaning of this warning and what should be done in order to correctly latent mean center observed variables across the within and between levels? I (and the other students) would greatly appreciate your help!
 Sarah Victor posted on Wednesday, August 01, 2018 - 7:15 am
For reference, this is a model including a random effect at the within-level.
 Bengt O. Muthen posted on Wednesday, August 01, 2018 - 9:57 am
That message was added in error in Version 8.1. It should appear only when a random slope is estimated as in UG ex9.2, part 3. It should not appear for UG ex 9.1. You may want to bring this to the attention of the class. The faulty message will not appear in Version 8.2.
 Sarah Victor posted on Wednesday, August 01, 2018 - 10:15 am
Very helpful, thank you very much!
 Sarah Victor posted on Wednesday, August 01, 2018 - 10:24 am
As I reviewed the user guide, it appears that the warning should NOT appear if you have observed x on the WITHIN level and an observed mean value of x at the BETWEEN level (as in the first part of example 9.2), but that it SHOULD appear if you do not specify the level of variable x, but refer to it on both levels, as in part 3 of example 9.2. I mis-wrote earlier in the subject line; we are in fact estimating a random slope, not just a random intercept, so example 9.2 applies. Is the part 3 of example 2 a change from previous versions, where observed predictors were, by default, latent mean centered at both levels if they were not specified on either level? Oddly, the results of the syntax for an example similar to 9.2 part 3 were the same in version 8.1 as the results from an earlier version of MPlus, so it's a bit confusing as to whether the newest version is treating these variables differently in the case of random slopes models.
 Bengt O. Muthen posted on Wednesday, August 01, 2018 - 10:43 am
For UG ex9.2, part 3 on page 278 of the V8 UG, the random slope precludes the latent variable decomposition of X when using ML estimation - in version 8.1 we now print a message that warns users that the complete decomposition is not done. The same estimation takes place as before, that is (as it says on pages 278-279), the whole observed X is used on Within and the between-level latent part of X is used on Between. With ML it is difficult to do use the latent within part of X on Within. It is, however, done in Version 8.1 when using Estimator=Bayes as described in our new paper on our website:

Asparouhov, T. & Muthén, B. (2018). Latent variable centering of predictors and mediators in multilevel and time-series models. Technical Report. June 4, 2018. (Download scripts).
 Sarah Victor posted on Wednesday, August 01, 2018 - 11:54 am
Thank you so much, this is very helpful! I have shared this information with the class.
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