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

 From Scott Baldwin To statalist@hsphsun2.harvard.edu Subject Re: st: Estimating the (possibly negative) intracluster correlation Date Sun, 5 Sep 2010 22:06:34 -0600

```Hi Bert,

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). For example,

**********
webuse ovary, clear
xtmixed follicles sin1 cos1 || mare:, nocons var residuals(exchangeable)
**********
The covariance parameter in this model is the covariance among
observations within a cluster. You have to use use the "mare: ,
nocons" so that xtmixed knows what variable the cluster id variable
is.  If you exclude the var option:

******
xtmixed follicles sin1 cos1 || mare:, nocons residuals(exchangeable)
******
the correlation parameter is the intraclass correlation. Because you
have modeled the non-independence among observations within a cluster
as a correlation/covariance (as opposed to a variance), the intraclass
correlation can be negative. Both models are identical in fit to a
random intercept model. The examples above don't have a negative
intraclass correlation but will accommodate negative values. Note also
that whereas an ICC modeled using variances has a range from 0 to 1,
the negative ICC ranges from -1/(m-1) to 1, where m is the cluster
size (so as clusters get really big, ICCs can be negative but they
will be really close to zero).

Hope that helps.

Best,
Scott

On Sun, Sep 5, 2010 at 6:44 PM, Bert Jung <bjung59@gmail.com> wrote:
> Dear Statalisters,
>
> I am interested in estimating an intracluster correlation, if possible
> conditional on several covariates, that could be negative.  I wondered
> if anyone knows a command or strategy to do this?
>
> As background: I am estimating a simple OLS -regress- model and find
> that the default (unclustered, not robust) standard errors are
> *higher* than the clustered s.e.  A potential cause is model
> misspecification that can induce negative intracluster correlation, as
> discussed in http://www.stata.com/support/faqs/stat/cluster.html.  I
> hope to diagnose the problem, starting with a closer look at the
> intracluster correlation.  (I will also work on a better
> specification, of course.)
>
> -loneway- calculates the intraclass correlation as ratio of two
> variances, hence constraining the correlation to be >=0.  I am looking
> for an alternative way that also allows me to control for covariates.
>
> Thanks in advance for any pointers,
> Bert
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```