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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: > * 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: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Estimating the (possibly negative) intracluster correlation***From:*Bert Jung <bjung59@gmail.com>

**Re: st: Estimating the (possibly negative) intracluster correlation***From:*Scott Baldwin <baldwinlist@gmail.com>

**Re: st: Estimating the (possibly negative) intracluster correlation***From:*"Joseph Coveney" <jcoveney@bigplanet.com>

**Re: st: Estimating the (possibly negative) intracluster correlation***From:*Bert Jung <bjung59@gmail.com>

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