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


From   Bert Jung <bjung59@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Estimating the (possibly negative) intracluster correlation
Date   Mon, 6 Sep 2010 16:49:47 -0400

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
>
>
> *
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>

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