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Re: st: Explained variation / variance partitioning using xtmixed

From   Jeph Herrin <>
Subject   Re: st: Explained variation / variance partitioning using xtmixed
Date   Fri, 16 May 2008 10:18:10 -0400

Wouldn't you estimate the same model with and without
the covariates, and use the two estimates of sigma^2?

Patrick P. Phillips wrote:
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

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

Can anyone help me here?

Many thanks in advance,


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

Email: Tel: 0207 670 4637 Fax: 0207 670 4829


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