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st: Poisson Two Level Random Intercept ICC


From   Robert Sutter <rdsutterjr@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Poisson Two Level Random Intercept ICC
Date   Fri, 1 Mar 2013 11:20:57 -0600

How is the intraclass correlation coefficient calculated when using a
two level random intercept model?

Below is the output from a two level model for the count of excess
deaths (oediff2) as the dependent variable and the clusters are
attending physicians. sigma_u is the random intercept variance.

In Rabe-Hesketh’s book the ICC for binary data is derived by the
following formula:random intercept variance/( random intercept
variance + π2/3).  π2/3 represents the variance of the logistic
distribution.

Can the same formula be used for count data by replacing π2/3  with
the variance of oediff2?

xtpoisson oediff2, i(attending_phy_id) normal

Random-effects Poisson regression               Number of obs      =        75
Group variable: attending_ph~d                  Number of groups   =        75

Random effects u_i ~ Gaussian                   Obs per group: min =         1
                                                               avg =       1.0
                                                               max =         1

                                                Wald chi2(0)       =         .
Log likelihood  =  -213.3618                    Prob > chi2        =         .

------------------------------------------------------------------------------
     oediff2 |      Coef.            Std. Err.      z    P>|z|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   2.617512   .0323429    80.93   0.000     2.554121    2.680903
-------------+----------------------------------------------------------------
    /lnsig2u |  -5.924562   4.653182    -1.27   0.203    -15.04463    3.195508
-------------+----------------------------------------------------------------
     sigma_u |   .0517009   .1202868                      .0005409     4.94192
------------------------------------------------------------------------------


Thanks,
Bob

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