Interpretation of random effect and Intraclass correlation coefficient (ICC)


I am getting a hard time to go around this and I am not sure my interpretation is correct.
I have several models that look like this:

change | trials ~ treatmentA + treatmentB + treatmentC + (1|person)

I would like to correctly interpret my group-level estimate (random effect) and its derived intraclass correlation coefficient (ICC).
The ICC can be interpreted as “the proportion of the variance explained by the grouping structure in the population”. The ICC is calculated by dividing the random effect variance, σ2i, by the total variance, i.e. the sum of the random effect variance and the residual variance, σ2ε.

Would an ICC close to 1 indicate high consistency of response across treatments within the same person, while an ICC close to zero refer to an heterogeneous intra-patient response?

How can I interpret that high ICC correlate strongly with low random effect variance, and viceversa? Could it be explained by “unexplained” variance (residual)?

Would the overall response be a better measure that I can correlate the ICC values with?

Thanks in advance!

This is more of a conceptual stats question, so you might consider posting over on

I’m far from expert in this domain myself, but yes, this follows from the definition you provided earlier.

Sorry, I don’t follow what you’re trying to ask here.