My modeled process has binary outcomes and site and region grouping. I am modeling it with a generalized linear mixed model (using GLIMMIX) and a diagonalized covariance structure. Typically I see covariance component based formulas for ICC calculation in the literature. GLIMMIX gives me the covariance of the site indicator and the region indicator variables but not the error variance I need to fill out the formulas. I have seen a suggestion to use 3.29 (pi**2/3) as the error variance when the dispersion is near 1.0, but am not sure this is right.