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Re: st: Estimating the (possibly negative) intracluster correlation


From   Robert A Yaffee <bob.yaffee@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Estimating the (possibly negative) intracluster correlation
Date   Mon, 06 Sep 2010 22:09:02 -0400

analysis.  As such, it has a range of (0,1).  If one computes
this as an analog of an R^2, then a negative ICC makes little
sense.
   If, however, you compute the ICC numerator as the between
groups variance -  the within groups variance, then 
a negative ICC can emerge when the within groups variance
exceeds the between groups variance.    
   Also, if the ICC is computed with an interaction term, the inter-
action may induce such a negative effect, if it is has a negative
coefficient.
    Regards,
             Bob

  
    
   
     

Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: Bert Jung <bjung59@gmail.com>
Date: Monday, September 6, 2010 4:54 pm
Subject: Re: st: Estimating the (possibly negative) intracluster correlation
To: statalist@hsphsun2.harvard.edu


> Bob, Steve, Scott and Joseph: many thanks, your comments are very
> helpful indeed.
> 
> I have a limited set of covariates and may be unable to sufficiently
> improve the model, so now I am wondering how to address this issue
> analytically.  The standard recommendation is to simply report the
> more conservative (larger) unclustered standard errors.  For binary
> outcomes (my case) Ten Have and co-authors seem to suggest a modified
> mixed model to directly account for the correlation.  Unfortunately I
> don't have access to this paper and the Hanley piece indicates
> reservations in particular circumstances.  I would be grateful for any
> pointers to related work and how to implement these procedures in
> Stata.
> 
> Thanks again!
> Bert
> 
> PS I found the negative ICC counter-intuitive at first.  One helpful
> example is competition for resources among multiple offspring from the
> same mother (e.g. animal litter).  In this context "nature, faced with
> limited space or nutrition, in an attempt to maximize survival of
> fewer offspring, allows considerable inequality among the individual
> `competitors'" (Hanley et al page 720).
> 
> 
> Hanley et al "GEE Analysis of negatively correlated binary responses:
> a caution" Statistics in Medicine 2000; 19: 715-722,
> http://www.ncbi.nlm.nih.gov/pubmed/10700741
> 
> Ten Have et al "Accommodating negative intracluster correlation with a
> mixed effects logistic model for bivariate binary data" J Biopharm
> Stat. 1998; 8:131-49, http://www.ncbi.nlm.nih.gov/pubmed/9547432
> 
> 
> 
> 
> On Mon, Sep 6, 2010 at 1:17 PM, Joseph Coveney 
> <jcoveney@bigplanet.com> wrote:
> > Scott Baldwin wrote:
> >
> > One option is to use the residuals option with an exchangeable
> > correlation structure in xtmixed. This allows you to look at the
> > correlation among observations within a cluster rather than the
> > variance among the cluster means (as would be the case if you fit a
> > random intercept model). [remainder omitted]
> >
> > --------------------------------------------------------------------------------
> >
> > That is neat.  I'll really have to start getting familiar with what 
> -xtmixed-
> > and its new -residuals()- option can do.  The ovary dataset doesn't 
> have a
> > negative ICC, but the artificial dataset below does have a negative 
> ICC to
> > illustrate Scott's -xtmixed- approach.
> >
> > I'd known that you can do it with -xtgee- (so long as it's a linear 
> model),
> > and with the old method-of-moments technique with -anova- (for a balanced
> > dataset).
> >
> > For some reason, I'd always thought that an ML (REML) method 
> couldn't deal with
> > negative ICCs, and that you had to resort to ANOVA and method-of-moments,
> > because they admit negative variance components estimates, or to GEE.
> >
> > Joseph Coveney
> >
> > version 11.1
> > clear *
> > set more off
> > set seed `=date("2010-09-07", "YMD")'
> > matrix input C = (1 -0.7 \ -0.7 1)
> > drawnorm mu0 mu1, corr(C) n(200) clear
> > generate int pid = _n
> > quietly reshape long mu, i(pid) j(tim)
> >
> > xtmixed mu i.tim || pid:, nocons residuals(exchangeable) ///
> >        nolrtest nolog
> >
> > xtgee mu i.tim, i(pid)
> > estat wcor
> >
> > anova mu pid tim
> > scalar define sigma2_e = e(rss) / e(df_r)
> > scalar define sigma2_u = ///
> >        (e(ss_1) / e(df_1) - sigma2_e) / (e(df_2) + 1)
> > scalar define ICC = sigma2_u / (sigma2_u + sigma2_e)
> > display in smcl as text ICC
> >
> > exit
> >
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> 
> *
> *   For searches and help try:
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> *   http://www.ats.ucla.edu/stat/stata/

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