Re: st: iccvar

["Robert Fornango" <robert.fornango@f1analytics.com>]

Megan,

-iccvar- produces the intraclass correlation coefficient (ICC) for a random
intercept model after -xtmixed-. The ICC is the proportion of variation in
the outcome that is attributable to differences between clusters. In this
case, the ICC refers to the variation due to between patient differences in
your data.

However, the ICC can also be thought of as a measure of within-cluster
correlation. For example, when there is no between-cluster heterogeneity,
then there are no differences across patients, and observations do not
cluster within patients. The ICC in this case would be 0. But, as the
between-patient differences increase, so does the correlation of values
within patients, and the ICC increases as well.

The ICC is not the same as Pearson's r, as it calculates the covariance
between pairs of observations using the model estimates for the mean (B),
and standard deviations sd_(cons) and sd_(Residual). Pearson's r would be
calculated by obtaining the sample means and standard deviations for
different time points (in your case) to compute the covariance. Obviously,
if you wanted a strict Pearson's correlation, you could -reshape- your data
into wide format and obtain the correlation of observations across time
points.

I recommend pp.58-61 in: 
Rabe-Hesketh, Sophia, and Anders Skrondal. 2008. Multilevel and Longitudinal
Modeling Using Stata. 2nd Edition. College Station: Stata Press. 
The third edition of this text was released in 2012. While I'm sure the
discussion is likely to be the same on this topic, I am unsure of the page
numbers.

As a final note on -iccvar-: please be aware that the command only estimates
the ICC for random intercept models, up to 4 levels. If you have a random
intercept and random slope model, you should use -quickicc-, also by Eric C
Hedberg.

Robert J Fornango, PhD
Chief Executive Officer
F1 Analytics LLC
www.f1analytics.com



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