I've skimmed through several books (Raudenbush & Bryk, Snijders & Bosker, Gelman & Hill, etc.) and several articles (Gelman, Jusko, Primo & Jacobsmeier, etc.), and I still haven't really wrapped my head around the major differences between using clustered standard errors verses multilevel modeling.
I understand the parts that have to with the research question at hand; there are certain types of answers you can only get from multilevel modeling. However, for example, for a two-level model where your coefficients of interest are only at the second level, what is the advantage of doing one method over the other? In this case, I'm not worried about making predictions or extracting individual coefficients for clusters.
The main difference I've been able to find is that clustered standard errors suffer when clusters have unequal sample sizes and that multilevel modeling is weak in that it assumes a specification of the random coefficient distribution (whereas using clustered standard errors is model-free).
And in the end, does all of this mean that for models that could ostensibly use either method, we should be getting similar results in terms of coefficients and standard errors?
Any responses or helpful resources would be greatly appreciated.
Best Answer
This post bases on personal experiences which might be specific to my data, so I'm not sure it qualifies as an answer.
I suggest to use simulations if possible to assess which method works best for your data. I did this and was surprised to find that tests (regarding parameters in the first level) based on multilevel modelling were outperforming any other method (power-wise), while retaining size even in small samples with few and unevenly sized "clusters". I am yet to find a paper that makes that point, and from how I see this is not really a niche topic and deserves more attention. I think it is fairly under-researched how different methods compare vis-a-vis finite-sample or few/uneven clusters.