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I had participants in two groups respond to a series of dichotomous decisions. I investigated the interaction between group (level 2) and a level 1 predictor X on the criterion Y. I could confirm this cross-level interaction in my first study. Now, I have the hypothesis that the two groups differ in the effect X has on Y because the groups differ in the level 2 predictor M. Therefore, I am interested in analyzing whether the interaction group:X on Y is mediated by the variable M.

I have read that mediated moderation might be the term for what I am trying to do, however I did not find any examples of this for a cross-level interaction and with a binary outcome. I also read that using multilevel SEM might be a good way to do this analysis.

  1. What is the best way to test this hypothesis? I ran the multilevel logistic regression with glmer and I would prefer a solution that I can perform using glmer.
  2. Suppose I'd have to use a multilevel SEM, how would I have to setup my model in lavaan to run this analysis?
  3. What group size (level 2) and overall sample size (level 1) would I need for such an analysis?
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  • $\begingroup$ The modern approach to mediation are natural effect models, which can handle logistic regression well, see cran.r-project.org/web/packages/medflex/vignettes/medflex.pdf $\endgroup$
    – stefgehrig
    Jun 27, 2021 at 18:46
  • $\begingroup$ Interesting, I was not aware of natural effect models. However, I did not find anything on multilevel natural effect models or on mediated moderations in these models. Would that be possible too? What sample sizes do these models require? $\endgroup$
    – Max J.
    Jun 27, 2021 at 21:03

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  1. There is a paper on how to calculate and test the index of moderated mediation at https://www.tandfonline.com/doi/abs/10.1080/00273171.2014.962683. It's basically multiplying two regression coefficients together, and boostrapping to see if the confidence interval of the product includes zero or not. I'm not sure how this applies to a multilevel framework, but I'm sure someone has cited that aforementioned paper to discuss it in a multilevel context.

  2. I would use the lavaan R package. In lavaan, you can define any quantity you want. so imm := a * b would be fixing the "index of moderated mediation" or "imm" to the product of values of coefficients labeled a and b in your code. Then bootstrapping would get you a confidence interval.

  3. There's not a satisfying answer for this. People might have rules of thumb, but it's really not clear. You could simulate data from coefficients you expect to see, and see what sample size gets you 80% power.

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  • $\begingroup$ Thank you for the advice! I will look into that before further commenting or accepting the answer. $\endgroup$
    – Max J.
    Jun 28, 2021 at 15:30

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