Three-level data: cross-level interac...
Message/Author
 Beth Livingston posted on Monday, April 21, 2014 - 1:47 pm
I am working with three-level nested data (daily observations nested in individuals nested in couples), running a multilevel path model with both within-level interactions and cross-level interactions.

I have three DVs most distal (one of which is a categorical variable, thus I am using Bayesian estimation) and other more proximal DVs. I have interactions at level 3 (couple-level)--only predictors as control variables.

So of the cross-level interactions, the three-way involves two L2 variables and one L1 variable, predicting two DVs. I have calculated cross-level interactions using the suggested method (e.g., on the within level:
s1 | guilt ON WFC;
then on the L2 between level:
s1 ON SP_ind ZGender SPXgender; where SPxgender is the calculated level 2 interaction, guilt is the DV and WFC is the L1 variable).

Question 1: This doesn't seem to give me the coefficient of the effect of WFC on guilt, just the value of the cross-level interactions with WFC on guilt? Is that possible to obtain in this way (I am used to HLM)?

Question 2: I know that defining a three-way, cross-level, interaction in the vein of "DEFINE: int1 = WFC*SP_ind*Zgender and using this approach instead is likely not correct, probably because of how it accounts for variance or calculates the SEs, but could you give me some more guidance as to why? Thanks!
 Linda K. Muthen posted on Saturday, April 26, 2014 - 4:27 pm
1. I think you want the mean of s1. You can find this in TECH4.

2. You could create such an interaction among one level 1 and two level 2 covariates and regress guilt on them on within in a fixed effect regression. But you would not have a random intercept on between, that is, the residual variance of s1 would be zero.
 Christoph Weber posted on Thursday, March 03, 2016 - 1:55 pm
Dear Mplus-team!
I'm using threelevel data (country, school, student) and want to estimate a crosslevel interaction.
the model is:
%within%
s | ACHIEV ON SES;
%between School%
s with ACHIEV;
%between Country%
s ON W;
ACHIEV ON W;
ACHIEV with S;

With this input S on W ist negativ and significant.

When I ignore the school level:
%within%
s | ACHIEV ON SES;
%between%!country
s ON W;
ACHIEV ON W;
ACHIEV with S;

S on W is significant positive (as expected).

How can I explain these results - is the input for the threelevel crosslevel interaction model correct?
Isn't it that both inputs should yield similar results, because the between country slope variance should be similar?
Thanks!
 Tihomir Asparouhov posted on Friday, March 04, 2016 - 8:58 am
It is all correct and such a result doesn't make sense. I would guess that there is some kind of outlier causing this or a near perfect singularity matrix.

You can switch to Bayes estimator and see what happens. Maybe also simulate data similar to your 3 level data and see if you can replicate this issue (although I doubt it). You can also use the factor scores at the top level and see if you can find the reason for the sign switch.

It can also be due to highly unbalanced level 3 units (the number of level 2 units vary substantially across level 3 units).

Send it to support@statmodel.com with the data if you can't figure it out.
 Tihomir Asparouhov posted on Friday, March 04, 2016 - 9:32 am
Just a little clarification for the above third paragraph. Let Nj be the number of
level 2 units in level 3 unit j. Let Nij be the number of level 1 units in level 2 unit i in level 3 unit j. If Nij and Nj are not uncorrelated with your model variables the phenomenon you have observed can easily happen.
 Christoph Weber posted on Sunday, March 06, 2016 - 2:15 pm
I can't figure it out.
I tried bayes estimation, excluded several countries with small (School) N, and also calculated factor scores for the slope in 3level and 2level models. the slopes correlate r = -0,194. It seems that there are two subgroups: countries with high (school)ICC and low ICC of the dependent variable. In both subgroups the slopes are positively correlateŽd (in the high SES Group r = 0,9). --> What does this mean?
Further I'll send the output of models.
Thanks
Christoph