Question

# How many Countries for Cross Level Interactions in HLM?

I have data from European Social Survey (24 countries) and want to model a cross level interaction. Can I do this with a simple random intercept (fixed slope) model? Or do I have to model a more complex random slope model? And if so, are 24 countries sufficient?
I am not explicit interested in explain the different slopes on Level 2 due to the cross level interaction. If its possible I would do that, but I think I need more countries right?
But i definetely want to show, that trust in institutions (Level 1 variable) depends on the level of corruption (level 2 variable) in a country. Can I do this with random intercept fixed slope model?

Crane Anna
Liberty University
Great question. Refer to YouTube's "Cross Level Interaction: Hierarchical Linear Modeling (HLM) in HLM 7. https://m.youtube.com>watch
As for the number of countries that you should observe, there would be a need to clarify and classify those 21 countries' forms of government. Therefore, refer to (Lune and Berg, 2017). Perhaps a Chi-Square Test with a tutorial from YouTube and more qualitative methods.

## Top contributors to discussions in this field

Christian Geiser
Christian Geiser Consulting LLC
A random intercept model is sufficient if your interest is mostly in explaining mean differences in trust across countries by level 2 predictors (so-called "means as outcomes model"). For that, a random slope is not needed.
You do need to model a random slope if you want to study potential cross-level interactions between level 1 and level 2 predictors. With a fixed slope, there would be no differences in slopes across level 2 units, and, consequently, you could not have a level 2 predictor explaining differences in the slopes.
Whether or not 24 is enough depends, among other things, on the expected effect size. You just have to try it out...
2 Recommendations
Kelvyn Jones
University of Bristol
and in terms of sample size at the higher level
you will see that when there are lots of respondents in few counties, the MCMC Bayesian approach does a good job at getting quality estimates.
and an example with a complex random part
2 Recommendations
Fatemeh Khozaei
Dhofar University
2 Recommendations
Sharif El Masry
Philipps University of Marburg
Thank you very much for the advices and sources. I think I will do a random slope model with 24 countries if theres not a big conflict. Thank for the literature also.
In the Article "How Many Countries for Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches" is written, that we better use a Bayesian Approach for the Model. Is it correct, that standard code for multilevel modeling in e.g. "R" is NOT using this approach?
Kelvyn Jones
University of Bristol
Sharif El Masry You are correct; I believe that lme4 in R does not use Bayes/MCMC estimation
there is a chapter on what it involves in
and here is one implementation in R
1 Recommendation
Sharif El Masry
Philipps University of Marburg
@Kelvy Jones Thank you very much. The code is even simple and similar as lme4.
But I think its a little bit to much for the Master Thesis. But I definetely will use it for my PhD in the near future! Thanks!
Gholamreza Latifi
Allameh Tabataba'i University
More than thirty countries.
1 Recommendation
Taghreed Idreb
Al-Mustansiriya University
simple random intercept model
20 countries
Crane Anna
Liberty University
Great question. Refer to YouTube's "Cross Level Interaction: Hierarchical Linear Modeling (HLM) in HLM 7. https://m.youtube.com>watch
As for the number of countries that you should observe, there would be a need to clarify and classify those 21 countries' forms of government. Therefore, refer to (Lune and Berg, 2017). Perhaps a Chi-Square Test with a tutorial from YouTube and more qualitative methods.

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