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Re: st: Explained variation / variance partitioning using xtmixed


From   Jeph Herrin <junk@spandrel.net>
To   statalist@hsphsun2.harvard.edu
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
(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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