My understanding is that intraclass correlation gives you an idea of how much variance your level two factor can explain in overall variance of the dependent variable. It is supposed to give an indication of whether a multi level analysis is justified by the variance structure of the data.
Now, I specified a null model, as a starting point for a mixed effects analysis where items of a test are nested within subjects. So I treat each subject ID as a level two unit grouping 28 items. Looks like this:
Mt01 <- lmer(APMt ~ (1|ID) + (1|content), data=mlmData, REML=FALSE) #Output: Random effects: Groups Name Variance Std.Dev. ID (Intercept) 0.102 0.319 content (Intercept) 0.300 0.548 Residual 0.213 0.462 Number of obs: 2940, groups: ID, 105; content, 28
The dependent variable is log(time) for each item. I specified two random effects, one due to subjects and one due to item content (all subjects worked on the same items).
How would I compute the ICC? Do I compute one for each random factor? Is it even necessary in this scenario? How exactly would I interpret the value?
Here are some of my approaches:
InterceptVarSubj <- VarCorr( Mt01 )$ID InterceptVarItem <- VarCorr( Mt01 )$content ResidualVar <- attr( VarCorr( Mt01 ), "sc")^2 #A icc <- InterceptVarItem / (InterceptVarItem + ResidualVar) icc  0.584 #B icc <- InterceptVarItem / (InterceptVarItem + InterceptVarSubj + ResidualVar) icc  0.488 #C icc <- InterceptVarSubj / (InterceptVarSubj + ResidualVar) icc  0.323 #D icc <- InterceptVarSubj / (InterceptVarItem + InterceptVarSubj + ResidualVar) icc  0.165