IIC are calculated for each factor only on the level the factor is defined at. The computation for between factors is the same as the one on the within level as described in the writeup.
I don't think they are additive -the two represent the information for two different factors (the within factor and the between factor)
Anna Brown posted on Monday, March 21, 2011 - 7:53 am
could you please clarify how the computation for the between factors can be the same as for within factors in the situation when the between factor is a common factor explaining variance in random intercepts, which are continuous latent variables.
If you want a simply way to compute the SE for the between level factor you can just multiply the information curve values reported by Mplus by the number of observations in the cluster - this basically is done so that you add the information contributed from all observations in the cluster.
Incidentally in Mplus there are two other methods for computing these SE. You can simply request with ML estimation the computations of these standard errors or you can use Bayes estimation and get the entire posterior distribution and a standard errors. Comparing these 3 methods is a bit of a research topic in itself.
If you are after the information curve for a single ability factor that is decomposed as a within and between factor (with all loadings held equal across the levels) then I think you should use type=complex instead of type=twolevel.