Is ICC in random-intercept models restricted to the null-model?

Question

I have seen some talks where the intraclass correlation coefficient (ICC) of the nullmodel is compared to ICC values of full models in random-intercept-models, to see how additional covariates contribute (redruce/increase) to the unexplained variance of the models.

But when I searched for papers dealing with this issue, the ICC was always computed for the nullmodel only and not reported for full models.

So my question is, is the ICC only meaningful for unconditional random-intercept-models, or can it also be meaningful for models with additional independent variables (as fixed effects)?

Answer 1

You are right about reporting ICC only for the null-model and this is also suggested by Raudenbush & Bryk (2002, p.36). However, in this book, they use the term conditional intraclass correlation when they discuss "Regression with Means-as-Outcomes" (having only level 2 predictors, p.72-75). Here is an example that is also used by Raudenbush & Bryk.

Rabe-Hesketh & Skrondal (2012) also uses the term "conditional or residual intraclass correlation" in the part they discussed random-intercept models with covariates, and noted the reduction from unconditional to conditional intraclass correlation. They argue that "the conditional intraclass correlation can also be larger than the unconditional intraclass correlation if the estimated level-1 variance decreases more than the level-2 variance does when covariates are added" (p.137). I think this implies that it is meaningful to interpret and compare (conditional and unconditional) intraclass correlations.

Rabe-Hesketh, S., & Skrondal, A. (2012). Multilevel and Longitudinal Modeling Using Stata. Vol. I: Continuous Responses. Texas: Stata Press.

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models. Thousand Oaks London New Delhi: Sage Publications.