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st: Explained variation / variance partitioning using xtmixed


From   "Patrick P. Phillips" <ppp@ctu.mrc.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Explained variation / variance partitioning using xtmixed
Date   Fri, 16 May 2008 11:54:36 +0100

Dear StataList,

        Referring to the paper by Xu in Statistics in Medicine 2003, "Measuring explained variation in linear mixed models" (22:3527-3541), has this measure of explained variation been implemented in Stata as a postestimation command to xtmixed or anywhere else?

        From xtmixed, Stata gives the residual variance (sigma^2), that is the variance in the response variable conditional on all the fixed and random effects. How do I calculate, or convince Stata to produce, the variance in the response conditional only on the clustering (sigma_0^2)?

        Xu's formula for Omega^2 as a measure of the explained variation is the ratio of the variance of the response conditional on all fixed and random effects (sigma^2) and the variance of the response conditional on the clustering only (sigma_0^2) subtracted from 1. It is the proportion of the variance conditional on the clustering that is explained by the covariates. That is:

                Omega^2 = 1 - (sigma^2 / sigma_0^2)

This seems to be simple partitioning of the variance that I believe SAS gives you automatically, but I'm not sure how to get this from Stata.

Can anyone help me here?

Many thanks in advance,

______________________________

Patrick Phillips
Statistician
MRC Clinical Trials Unit
222 Euston Road
London NW1 2DA

Email: ppp@ctu.mrc.ac.uk
Tel: 0207 670 4637
Fax: 0207 670 4829


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