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I know that there are many posts concerning explanations of multi-level models, random effects, fixed effects and so on. But after having read through them, and after watching this youtube series by Prof. Mikko Rönkkö (University of Jyväskylä, Finland), I am still confused about some specific aspects.

Most importantly: When do we actually need random effect models. The youtube series, and these two articles seem to imply that if I am only interested in the average effect of the fixed part of the model, I do not need random effects model even if the data is hierarchical, as clustered standard errors suffice in such cases. Only if I am interested in the variance between clusters, do I need to employ random effect models. Is that correct?

I think it would be easiest for me to understand all of this on an example that mimics data that I am using:

  • Given there is pooled cross-sectional survey data, where individual respondents are nested in countries and the survey is held multiple times in each country over the years.

  • And the research question aims at finding out if a country-level variable (e.g. GDP) affects how respondents answer a question about life satisfaction. But I am only interested in the overall effect of GDP on life satisfaction.

  • In this example, do I need a random effects model (if the assumptions hold)? Or would clustering standard errors suffice? And what effect am I measuring here? The between effect?

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    $\begingroup$ Welcome to CV. I certainly sympathize with your confusion on these issues. They are confusing! But your questions are far too broad to be on topic here, and you have asked a whole bunch in one question (CV wants one question at a time). You might try asking a different question, asking for good references on some specific area of multilevel models. I tried searching CV for such a question, but (to my surprise) did not find one. Someone who is better at searching may find one, or, if you ask a new one, it may turn up. $\endgroup$
    – Peter Flom
    Commented Apr 24 at 11:00
  • $\begingroup$ At the risk of being downvoted, I think random effects are difficult to understand from a frequentist perspective. Consider taking a look at Bayesian Data Analysis 3rd Edition Chapter 5 which talks about hierarchical models from a Bayesian perspective - which are essentially the same thing as random effects (made freely available by the authors). The chapter goes into an example of SAT scores in high schools that really resonated with me when I first read it. $\endgroup$
    – TrynnaDoStat
    Commented Apr 24 at 17:27

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welcome to CV! And congratulations on starting to study hierarchical models. One thing that this topic helped me to understand is that there is no right answer. It all boils down to your needs and what a given method can offer you.

Multilevel models, in my mind, offer you a couple of features:

  • you can estimate the overall effect of a variable and still have a clear picture of how that effect can vary across clusters, and even be completely opposite from some particular cluster
  • you can control away variation from the cluster level
  • you can shrink the effect size per cluster towards a centroid, i.e. the main effect.
  • you can elegantly take care of clusters that have low representativeness (i.e. low sample size)
  • you want to have probability distribution (with means and sigmas) associated with cluster effects you are studying

In my opinion, with any of the reasons above, you can go for a multilevel model in your analysis. If you need a statistical test to justify the use of random effects, you can use the Hausman test.

For a more in-depth discussion see this FAQ from Ben Bolker, a researcher of mixed models. Great stuff in there.

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    $\begingroup$ This is helpful, but I think it could be improved by more explicitly stating the conditions in which (or questions for which) clustered standard errors are insufficient. $\endgroup$
    – mkt
    Commented Apr 25 at 9:08
  • $\begingroup$ To be honest, I'd love to see the counterarguments to hierarchical modeling from other perspectives, outside of common practice within a field. I know the econometricians prefer fixed effects (which is slightly different than just "dummy encoding" since it uses some clever computations in longitudinal data), or they argue on estimator consistency, which I think is valid. But idk a more systematized and intuitive way of listing them. $\endgroup$
    – Guilherme Marthe
    Commented Apr 25 at 21:26
  • $\begingroup$ Here's one perspective: psycnet.apa.org/record/2016-22467-001 $\endgroup$
    – mkt
    Commented Apr 26 at 4:42
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    $\begingroup$ awesome Ill take a look and update my answer. $\endgroup$
    – Guilherme Marthe
    Commented Apr 26 at 13:59
  • $\begingroup$ What I am still very unsure about: If FE and RE are actually used to deal with similar issues, as you hinted at in your comment and as I have read about in other threads/publications, why do we sometimes add both in a model? That is, what are circumstances when RE or FE on its own are not sufficient. $\endgroup$
    – Always_learning_new_things
    Commented Apr 29 at 14:29

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