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st: RE: Intraclass correlation and binary hierarchical models


From   "Cohen, Elan" <cohened@upmc.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Intraclass correlation and binary hierarchical models
Date   Wed, 11 Nov 2009 15:31:03 -0500

Doug,

According to Snijders and Bosker ("Multilevel Analysis", p. 65): "Since this is a three-level model there are several kinds of intraclass correlation coefficient".  This is presumably why Stata doesn't report one.  

Check out: Raman & Hedeker, "A mixed-effect regression model for three-level ordinal response data", Statistics in Medicine, 2005.  They have a section dealing with intraclass correlation that you'll find 
helpful.

- Elan


> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Levy, Douglas E., Ph.D.
> Sent: Wednesday, November 11, 2009 3:07 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Intraclass correlation and binary hierarchical models
> 
> Hi All,
> 
> This is partly a stats question, partly a Stata question. I 
> have binary outcome
> data and I'm interested in calculating intraclass correlation for a
> multilevel/hierarchical model that is nested as follows: 
> patients within
> hospitals within regions. I want to know what proportion of 
> the variance in
> outcomes resides at each level of hierarchy to help direct 
> quality control
> efforts.
> 
> If my data were linear, I could run:
> xtmixed Y || region: || hospital:, variance
> I would add up the region, hospital, and residual variances, 
> and see what
> fraction of the total variance resided at each level.
> 
> If I had binary data and only had two levels of hierarchy, 
> say hospital and
> patient, I could run xtlogit:
> xtlogit Y, re i(hospital)
> and the rho statistic would be my estimate of intraclass 
> correlation (am I
> correct here?).
> 
> The "correct" model to run with my binary outcome data would be:
> xtmelogit Y || region: || hospital:, variance
> but this only reports the variance for region and hospital. 
> There is no residual
> variance reported to estimate the total variance (which I 
> suppose makes sense
> with binary data), and Stata does not report a level-specific 
> rho as it does
> with xtlogit.
> 
> I'd be grateful for the group's thoughts on how to tackle this issue
> statistically and/or with respect to Stata.
> 
> Best,
> Doug
> 
> [My apologies if this has appeared as a repost. I have tried 
> to post this
> message several times but I have not seen appear on the list.] 
> 
> 
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