Intraclass correlation (ICC) confusion

Posted by Maguin, Eugene on Jul 06, 2006; 10:03pm
URL: http://spssx-discussion.165.s1.nabble.com/post-hoc-test-on-interaction-SPSS-13-0-tp1069401p1069403.html

All,

I have some questions about understanding how ICCs are computed. The context
for my question is multilevel analyses and not ICCs between raters and
items. Peugh and Enders, in a 2005 article on how to use the spss Mixed
command for several simple types of analyses, compute the ICC as the ratio
of the intercept variance to the sum of the intercept and residual (within
subject) variances. (Every computation in this email is for an unconditional
means model.) My estimate is .000326.

I was also googling ICC and found a different definition. That one is that
ICC is [MS(between) minus MS(error)] divided by [MS(between) plus
MS(error)]. This formula was developed for unordered pairs such as would be
found in a twin study. Using the values from a oneway run This estimate is
.134. (Unianova with the 'by' variable declared as random gives the same
component values.)

I also ran Varcomp and the error variance matches the Mixed residual
variance number but the numerator printed .000, which is probably ok because
the Mixed estimate of the intercept variance is .0003.

I quite confused because, no doubt, there's something I don't understand. I
hope that someone can set me straight because I want to make some analytical
decision on the basis of the (correct) ICC value.

Thanks, Gene Maguin