Three-level data: cross-level interac... PreviousNext
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 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.
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