# ICC in multilevel model

I would like to understand how to interpret the reported ICCs in a multilevel model. The data records interactions between an employer and an employee, and I am estimating the effect that a treatment had on effort by the employee. First, the data was collected in different sites (variable name: expnum). Then, I have repeated interactions for each individual (employer: bid, employee: sid).

Using stata, I have run the following model:

xtmixed effort i.treatment, || expnum: || bid:||  sid: , vce(cluster expnum)


From my understanding, the intercorrelation coefficient can be used to interpret whether a multilevel model is necessary (if ICC ~ 0, then clustering may not be necessary). After estimating the model I used

estat icc


to retrieve the ICC from my model. Results are shown below:

The ICC is reported for level1, then level1|level2 and finally for level1|level2|level3. The first two are close to zero, while the last one is larger. How can these be used to understand if all three levels should be used? Alternatively, should the model be ran with each level separately to understand teh amount of variation explained?

• Shouldn't the output have the result of likelihood ratio test? And why bid does not have robust standard errors and conf. intervals? Is this because you add vce(cluster expnum) option? – T.E.G. - Reinstate Monica Mar 15 '17 at 0:01
• @T.E.G. good points. Yes, the LR test doesn't automatically print with the cluster option. I'm not entirely sure why bid doesn't have standard errors, but when the model is estimated without clustering, they are still not reported. The model is converging to a solution quickly, it may just be too complicated (that is my hypothesis, that I should use only 2 levels, not 3). Here are the results without the cluster specification: imgur.com/a/zJnWa – Nox Mar 15 '17 at 15:00