estat icc reporting of Intra-cluster correlation in three-level linear regression (mixed) different from manually calculation...

[Robert Wishart]

Hi,

I'm analyzing a three-level model I've run with mixed. It produces the following table for the variances at each level:

mixed EoYLitAC treat || School_ID: || dv_unique_class_ID:, mle variance

------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
School_ID: Identity |
var(_cons) | 31.35756 15.07998 12.21788 80.48013
-----------------------------+------------------------------------------------
dv_unique_~D: Identity |
var(_cons) | 61.52315 15.90861 37.06256 102.1272
-----------------------------+------------------------------------------------
var(Residual) | 534.9115 17.84789 501.0496 571.0619
------------------------------------------------------------------------------

I then ran the post-estimation command estat icc which produces the following:

----------------------------- ------------- -------------- ----------- ----------
Level ICC Std. Err. [95% Conf. Interval]
----------------------------- ------------- -------------- ----------- ----------
School_ID 0.049949 0.0235154 0.019517 0.1219309
dv_unique_class_ID|School_ID 0.1479482 0.0220688 0.1096902 0.1966033
----------------------------- -----

However when calculating manually I get the following:

ICC_school = 31.35756/(31.35756+61.52315+534.9115) = 0.04994894728 (i.e. the same as estat ICC)

ICC_class = 61.52315/(31.35756+61.52315+534.9115)=0.09799922493 (i.e. different to estat ICC)

Does estat icc estimate the ICCs differently?

Thanks for your help
Robert Wishart

[Andrea Discacciati]

The level-2 ICC is calculated as

. di (61.52315+31.35756)/(61.52315+31.35756+ 534.9115)
.14794817

See, for example,

https://www.stata.com/features/overview/intraclass-correlations-for-multilevel-models/

and page 2 of

https://www.stata.com/manuals/meestaticc.pdf

[Robert Wishart]

Thanks Andrea for clarifying - that's exactly what I needed to know