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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
Comments: To: Akin Pala <akin@DR.COM>
In-Reply-To:  <3f03e850@shknews01>
Content-Type: text/plain; charset=us-ascii

Akin,

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.

Dale

--- Akin Pala <akin@DR.COM> wrote: > Hmm, I just read the discussion with dale, so I think my earlier > question > 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 > the > 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. > http://akin.owns.it > Tel: (286) 218 00 18 ext. 1349 > "Akin Pala" <akin@dr.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 > is > > 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 > Unstructured > > (UN). > > Also, is there any way to calculate that number in proc genmod > repeated > > 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 > just > > 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 > Schwarz > > 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 > > > >

===== --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@fhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 ---------------------------------------

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