In doing some multilevel modeling, my ICC appears to be quite low (barely .01). My thought is that it would be foolish to run a multilevel model with such a low ICC. To still acccount for this very slight effect of clusters, I was thinking I should run the analysis in TYPE=Complex as conceptually and by design there are in fact clusters. Please tell me if that's logical enough.
It is not the size of the intraclass correlation alone that determines whether non-indpendence of observations needs to be accounted for. It is the design effect which is a function of the size of the intraclass correlation and average cluster size. TYPE=TWOLEVEL and TYPE=COMPLEX are two different ways to take non-independence of observations into account. With TWOLEVEL, non-independence of observations is modeled. With COMPLEX, it is taken into account. The choice depends on whether you want to know something about the cluster-level parameters or just control for non-independence of observations.
I would also calculate the Design Effect which is based on the ICC and the average cluster size, where DEFF = 1 + (Average cluster size - 1)*ICC. If you find that DEFF >= 2, then you should address the clustering.