I have a cross-sectional data set with about 8000 observations on child obesity (eg BMI). This data was collected in 8 countries and within schools (about 200 schools), i.e. observations are clustered within schools and countries. I am interested in how child characteristics (e.g. socio economic status) relate to child obesity. My approach was to estimate a pooled OLS and clustering at the school level and also including country dummy variables in the regressions. As I have many and reasonably large school clusters, I thought this would be a good approach. I have however been told that I should estimate a FE effect model. Is it possible to estimate a country fixed-effects model and cluster at the school level?
Solved – Clustered (multilevel) data and fixed effects
clustered-standard-errorsmultilevel-analysispanel dataregression
Related Solutions
Both approaches, using group fixed effects and/or cluster-adjusted standard error take into account different issues related to clustered (or panel) data and I would clearly view them as distinct approaches. Often you want to use both of them:
First of all, cluster-adjusted standard error account for within-cluster correlation or heteroscedasticity which the fixed-effects estimator does not take into account unless you are willing to make further assumptions, see the Imbens and Wooldridge lecture slides for an good discussion of short and long panels and various issues related to this problem. There is also a novel paper about this topic by Cameron and Miller: A Practitioner's Guide to Cluster-Robust Inference which might be interesting for you. If you do not want to model the variance-covariance matrix and you suspect that within-cluster correlation is present, I advise to use cluster robust standard error because the bias in your SE may be severe (much more problematic than for heteroscedasticity, see Angrist & Pischke Chapter III.8 for a discussion of this topic. But you need enough cluster (Angrist and Pischke say 40-50 as a role of thumb). Cluster-adjusted standard error take into account standard error but leave your point estimates unchanged (standard error will usually go up)!
Fixed-effects estimation takes into account unobserved time-invariant heterogeneity (as you mentioned). This can be good or bad: On the hand, you need less assumptions to get consistent estimations. On the other hand, you throw away a lot of variance which might be useful. Some people like Andrew Gelman prefer hierarchical modeling to fixed effects but here opinions differ. Fixed-effects estimation will change both, point and interval estimates (also here standard error will usually be higher).
So to sum up: Cluster-robust standard error are an easy way to account for possible issues related to clustered data if you do not want to bother with modeling inter- and intra-cluster correlation (and there are enough clusters available). Fixed-effects estimation will take use only certain variation, so it depends on your model whether you want to make estimates based on less variation or not. But without further assumptions fixed-effects estimation will not take care of the problems related to intra-cluster correlation for the variance matrix. Neither will cluster-robust standard error take into account problems related to the use of fixed-effects estimation.
Best Answer
I think it is doable; this would be one of the relatively rare examples where the assumptions on the sample sizes will be met sufficiently well. Most education researchers would want to fit a classic multilevel model with three levels, and then I would say that 8 countries are not enough to reliably estimate variances at level 3. Depending on the software, you might be able to mix fixed effects with clustered standard errors (Stata
xtreg ..., fe vce(cluster ...)), or you may have to include the country dummies as regressors to implement the country fixed effects.You may also want to try some country-school or country-individual interactions, as TV programs in North Korea may not be so interesting to watch as in the US, so kids would spend less time in front of TV in some countries.