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Re: st: intraclass correlation of slope/coeff ??


From   "Anders Alexandersson" <andersalex@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: intraclass correlation of slope/coeff ??
Date   Wed, 30 May 2007 09:49:18 -0400

On 5/29/07, Jacki Buros <jburos@gmail.com> wrote:
Correcting and to some extent summarizing myself, having run the
following two commands:

. xtmixed measurement time || patient: time || artery: time

and

. xtmixed measurement time || patient: time, cov(uns) || artery: time,
cov(uns)

Is it fair to say that the ICC of the slope (change over time) across
the arteries within patient is the following

   (1) ICC = Var(coeff_time)patient / [Var(coeff_time)artery +
Var(coeff_time)patient]

And that if estimates come from the first model the ICC is
"unadjusted" and that, using the second model, the estimates are
"adjusted for correlations between intercepts and slopes at patient-
and artery-levels"?

Earlier I had suggested that the unadjusted ICC for the slope across
arteries within a patient might be estimated from a model with
unstructured covariance matrix but upon 5 minutes' reflection I now
believe that the unadjusted ICC may be better estimated as above.

Thoughts? Sorry to post twice, thanks very much again for your time.
When calculating the ICC, the denominator usually is the total
variance (which includes the variance of the residual that is omitted
above).

Traditionally, ICCs are discussed in the more restrictive context of
1-way and 2-way ANOVA. For example, McGraw and Wong (1996) distinguish
between 10 such ICCs. Rabe-Hesketh and Skrondal (2005) give some
examples of how to calculate ICCs for multilevel models, although
without discussing the -cov(uns)- option.

Yulia Marchenko discusses a simpler example of ICC and -cov(uns)- at
http://www.stata.com/statalist/archive/2006-04/msg00142.html.

References:
McGraw, K., and Wong, S. 1996. Forming inferences about some
intraclass correlation coefficients. Psychological Methods 1(1):
30-46.
Rabe-Hesketh, S., and Skrondal, A. 2005. Multilevel and Longitudinal
Modeling Using Stata. Stata Press.
(http://www.stata.com/bookstore/mlmus.html)

Hope this helps,

Anders Alexandersson
andersalex@gmail.com
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