Save Random Slopes in a Two-Level Ana...
Message/Author
 Heidi Mauersberger posted on Saturday, November 26, 2016 - 7:06 am
Dear Linda and Bengt Muthen,

I really appreciate the easy and intuitive way of analyzing multilevel data with Mplus. Yet, in the moment I am facing a problem I don't know how to handle: I would like to know whether the association of two level-1 variables influences a level-2 variable. Thus, I somehow need to save the random slopes to use them in a following analysis. Is there a command that allows me to do that or alternatively, is there any other way to solve this problem without saving the random slopes?

Thank you very much!

Best,
Heidi
 Bengt O. Muthen posted on Saturday, November 26, 2016 - 5:08 pm
You can do that in one step using the model:

%Within%
s | y on x;

%Between%
z on s;
 Heidi Mauersberger posted on Sunday, November 27, 2016 - 6:38 am
Dear Bengt,

thank you very much for the quick response. I didn't know that this would be a valid model, as I cannot think of a reasonable underlying equation...

For
%Within%
s | y on x;

%Between%
s on z;

it should be

yij =beta0j +beta1j(xij)+rij
beta0j =gamma00 +gamma01(zj)+u0j
beta1j =gamma10 +gamma11(zj)+u1j

...but is it still possible to form a single (complex) equation when exchanging s with z on level-2?

Thanks again so much for helping me with this probably quite uncommon request.
 Bengt O. Muthen posted on Sunday, November 27, 2016 - 1:17 pm
Yes, that's the strength of Mplus. Most multilevel programs can handle a random effect such as beta1j only on the left-hand side of the equations but Mplus allows it to also be on the right-hand side. So for example

%Within%
s | y on x;

%Between%
y on z;! y is the random intercept
z on s;

translates to

yij =beta0j +beta1j(xij)+rij
beta0j =gamma00 +gamma01(zj)+u0j
zj = gamma10 + gamma11(sj)+u1j
 Jiangang Xia posted on Thursday, December 01, 2016 - 9:58 pm
Dear Bengt,
Thank you for your example. I am considering the same thing: using a random slope to predict some other outcomes. It is great to know that Mplus allows using slope as a predictor.

My question is, how about a cross-level slope? For example, the relationship (s) between principals factor (x) and teachers factor (y). Could we model the effect of s on teacher job satisfaction (J)? If so, how could I write the code and translate to equations?

Do you have any other examples or publications on this topic? Thanks.
 Bengt O. Muthen posted on Friday, December 02, 2016 - 5:31 pm
If I understand you correctly I am not convinced this makes sense. Using your example, your x (a between/principals vble) influencing your y would have to refer to the between part of y, that is, this is a between-level regression. Its slope s does not vary because it is a between-level regression. So s is not a variable and cannot therefore not influence the between part of J.
 Jiangang Xia posted on Friday, December 02, 2016 - 8:44 pm
I understand your concern. Forgot to mention that I have to add a third level so the slope could vary between third level units such as school districts. I asked the question in another post and you replied that "If you have 3-level modeling a random slope defined on level 2 can be used to predict outcomes on level 3."

This makes sense to me but is it also ok to model the slope's effect on outcomes at level 1 or level 2? Since the slope is actually a level 3 variable, I believe it could predict lower level outcomes. Do you know any publications on this kind of model? Thanks.
 Bengt O. Muthen posted on Saturday, December 03, 2016 - 11:42 am
Answered elsewhere. I am not aware of publications on this.