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


From   "Jacki Buros" <jburos@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: intraclass correlation of slope/coeff ??
Date   Tue, 29 May 2007 17:54:05 -0400

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.

Jacki


On 5/29/07, Jacki Buros <jburos@gmail.com> wrote:
Hi ..

I have what may be considered a novice question about the ICC but I'm
nonetheless stumped. Hopefully you can help.

I am working with a 3-level hierarchical linear model with the
following levels: patient, artery, and time. Observations are nested
so that each artery within each patient has several observations over
a period of time. My model has a random intercept and a random
coefficient (time) at both patient and artery levels. Time is my only
fixed effect.

My goal is to determine the intra-class correlation coefficient (ICC) for
the change over time at the patient level. In other words, to address
the question: "to what extent does the rate of change cluster within a
patient across arteries?"

I have set this up in Stata using -xtmixed- as:

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

and

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

Using the latter of the two commands to consider the possibility of
covariance, I get (as hypothesized for an earlier analysis)
significantly non-zero covariances at both the artery and patient
levels. Going forward with this model, I have the following variance
estimates with which to estimate the desired ICC:

patient: coeff_time, _cons, and cov(timeXcons)
artery: coeff_time, _cons, and cov(timeXcons)
time: residual

Question is, which calculation would best represent the ICC of the
slope within a patient across arteries?

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

   (2) ICC  = Var(coeff_time)patient / [sum of all other variance and
covariance values]

   (3) ICC  = Var(coeff_time)patient / [sum of all other variance but
not covariance values]

   (4) ICC  = Var(coeff_time)patient / [Var(coeff_time)artery +
Cov(timeXcons)artery + Var(coeff_time)patient + Cov(timeXcons)patient]

My naive sense is that (1) represents the "adjusted" ICC of the slope
-- adjusted for covariance between slope and intercept, and that (4)
represents the "unadjusted" ICC, but I'm not sure. I also have the
problem that my covariance at one of my levels is negative, so maybe I
should use its absolute value? There must be a more formal way to go
about estimating this ..

Any thoughts (and/or references) would be much appreciated ... I have
found only a few references that discuss the analysis of group-level
effects and\or group-level means, and would appreciate any insight you
might have to offer.

Thanks very much for your time.

Jacki Buros
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