I have a data on 10,000 people in total sampled from among 50 countries. I built a linear mixed effect model with a country level predictor--sex-ratio of the that country--and want to see the relationship on an individual level predictor (a response on a questionnaire). I've modeled country as a random effect, as well as world region of the country to partially control for non-independence of sex ratios; neighbouring countries might have similar sex ratios for similar reasons.

Is my statistical sample size ~50 because that's how many countries I have? or ~10,000 because that's the number of participants I have?



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This paper discusses the approach to data analysis and inference. I highly recommend it as I have read it many times with your same question in mind and learned much over the time.

They summarize three methods of analyzing the corresponding hierarchical model: the between-within degrees of freedom, the Satterthwaite approximation to the effective degrees of freedom, and the Kenward-Rogers approximation of the same form.

I have found that fitting a hierarchical model, and performing inference at the cluster level (N=50) using the between-within degree-of-freedom approach has given me the best inference. BW has: a) decent power, b) good control of alpha-level via better robustness to intracluster heteroscedasticity and c) the most interpretable analyses.

The paper, however, ultimately recommends that the Kenwood-Rogers degrees of freedom approximation to the GEE is the best approach. But I do not think that conclusion is wholly substantiated by their results.

  • $\begingroup$ This paper deals with partially clustered designs, whereas my data is fully clustered, so not sure if it applies? $\endgroup$
    – Richie
    Commented Jun 12, 2018 at 16:32
  • $\begingroup$ @Richie It still applies. The only difference is that the partly clustered designs require some careful attention to how you "roll up" the means for each cluster when they're imbalanced for within-cluster confounders like, say, ages and sexes in schools. When it's balanced, the same general approach (hierarchical model and degrees of freedom approximations) provide valid/efficient inference. $\endgroup$
    – AdamO
    Commented Jun 12, 2018 at 16:56
  • $\begingroup$ What do you mean by "best inference" ? My question is specifically about increased statistical power. $\endgroup$
    – Richie
    Commented Jun 14, 2018 at 11:22

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