Date: Thu, 3 Jul 2003 10:44:43 -0700
Reply-To: Dale McLerran <stringplayer_2@YAHOO.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Dale McLerran <stringplayer_2@YAHOO.COM>
Subject: Re: REPEATED, UN, CS intraclass correlation
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I would be troubled to see an intraclass correlation reported
when elsewhere you state (in effect) that the observations
within a class are not exchangeable. That is, once you declare
ANTE(1) to be the correct covariance structure, then you can
no longer compute an intraclass correlation. To my mind, the
intraclass correlation is only applicable when no distinction
can be made between members of the cluster within which
observations are correlated. If you can make a distinction
between members within a cluster (as implied by all covariance
structures other than CS), then there is no basis for computing
the intraclass correlation.
Note that if ANTE(1) is the appropriate covariance structure,
then some order is ascribed to the observations within a
cluster. That is, if you were to permute the labels for what
are presently specified as the first and second elements
within a cluster, then ANTE(1) would not hold. Given the
current labelling of observations within a cluster, ANTE(1)
returns the correlation structure
RCorr = | 1.00 r12 r12*r23 |
| r12 1.00 r23 |
| r12*r23 r23 1.00 |
and we have r13=r12*r23<r23. Now, if we permute labels 1 and
2 so that we have what used to be row 1/column 1 in row 2/
column 2 and what used to be row 2/column 2 in row 1/column 1,
then we would return the correlation matrix
RCorr = | 1.00 p21 p21*p13 |
| p21 1.00 p13 |
| p21*p13 p13 1.00 |
In the above correlation matrix, the subscripts refer to the
original labels. Also, I have denoted estimated correlations
with p rather than r. Note that p23=p21*p13=p12*p13<p13.
This is in direct violation of what we observe for the
ordering which reported correlations r12, r13, and r23.
There, the correlation between observations 1 and 3 was
less than the correlation between observations 2 and 3.
However, after we permute labels 1 and 2 so that we estimate
p21(=p12), p13, and p23, then the correlation between
what was originally labelled as observations 1 and 3 is
greater than the correlations between observations
originally labelled 2 and 3.
Thus, if we change the order of labels on observations within
a cluster, we cannot return the same correlation matrix.
In addition, it should be observed that unless r12 and r23
are exceedingly high, then the correlation between ordered
observation 1 and ordered observation 3 will fall off
considerably. In that case, reporting the intraclass
correlation as though it applied to all pairs of observations
within clusters would be entirely inappropriate.
Now, let me inquire whether it is reasonable to believe that
the observation labels have order? If it is reasonable to
believe that observations can be ordered, then selection of
ANTE(1) as your covariance structure may be reasonable.
However, if observations have no natural ordering, then
even though ANTE(1) turned out to have the best AIC and BIC
statistics, that could only be by chance. I would note that
you have employed the "kitchen sink" approach to choosing
the best covariance structure. That is, you have tried
every different covariance structure to see which one
maximizes AIC/BIC. You are not being guided by theory.
Selection of a covariance structure should be based, at least
in part, on reasonable theory. Given the type of data
at hand, what covariance structures are reasonable to
assume? One should examine only covariance structures which
theory would support. It is possible to find by chance
alone that some certain covariance structure fits the data
better than any other covariance structure. If you have
restricted your model fitting efforts to only those
covariance structures which theory might support, then you
reduce the chance of choosing a wrong model.
--- Akin Pala <akin@DR.COM> wrote:
> Hmm, I just read the discussion with dale, so I think my earlier
> does not mean anything. I honestly don't feel like using interclass
> correlation though. So I think I will just use CS method to calculate
> intraclass correlation and ante method to get anwers to everything
> else. I
> can report that in the paper like that. What do you think?
> Akin Pala, Ph.D.
> Tel: (286) 218 00 18 ext. 1349
> "Akin Pala" <email@example.com> wrote in message news:3f0191b7@shknews01...
> > I can calculate intraclass correlation if I type
> > proc mixed etc.;
> > repeated/type=cs subject=id;
> > by correlation=common variance/common var+residual variance which
> > something like
> > 0.74/(0.74 + 0.57) = 0.57.
> > RCORR gives me a 1.
> > Using UN with repeated/type=un subject=id;
> > gives me some other number like 1.30
> > Is there any way to calculate intraclass correlation using
> > (UN).
> > Also, is there any way to calculate that number in proc genmod
> > statement? It does not accept rcorr; not that I saw any use for it
> > So, is there any one out there who knows the answer to those? I am
> > confused about UN vs CS and I want to calculate intraclass corr
> using UN
> > because UN gives me Akaikes IC=+89.1 while CS gives me -90.1 and
> > bayesian is -90.1 for UN and -92.1 for CS.
> > Thanks and I appreciate any answer...
> > --
> > Akin Pala, Ph.D.
> > http://akin.owns.it
Fred Hutchinson Cancer Research Center
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