Posted by
Gushta, Matthew on
Jul 06, 2006; 10:50pm
URL: http://spssx-discussion.165.s1.nabble.com/post-hoc-test-on-interaction-SPSS-13-0-tp1069401p1069404.html
gene--
a good description of ICCs can be found here:
http://www.uvm.edu/~dhowell/StatPages/More_Stuff/icc/icc.htmlspecifically, this derivation applies to your question:
http://www.uvm.edu/~dhowell/StatPages/More_Stuff/icc/icc.ht12.gifyour first equation is:
[var(intercept)]/[SUM(var(intercept)) + var(residual)] (1)
while your second equation is:
[MS(between) - MS(error)]/[MS(between) + MS(error)] (2)
we see that the relationship between these is based on:
MS(between) = k*var(between) + var(residual)
where k = number of levels of your "factor" or number of
observations (i.e., time points in a multilevel model).
...these are essentially two approaches to the same problem. typically,
ICCs are used to answer the question of "what proportion of variance is
accounted for by X?". therefore, for hand-calculation and ease of
interpretation, i use (1). the results are easily described in terms of
the original question. and it requires easily-accessed variance
components for calculation.
good luck!
--matthew
* * * * * * * * * * * * * * * * * * * *
matthew m. gushta -- research associate
computer & statistical sciences center
american institutes for research
[hidden email] -- 202.403.5079
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of
Gene Maguin
Sent: Thursday, July 06, 2006 5:04 PM
To:
[hidden email]
Subject: Intraclass correlation (ICC) confusion
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