From: <brian.cullis_at_DPI.NSW.GOV.AU>

Date: Thu, 2 Jul 2009 01:02:09 +1000

Date: Thu, 2 Jul 2009 01:02:09 +1000

Dear michelle

I am using ASReml-R to run a Gaussian model with a single response

variable and multiple fixed and random effects, and I am having problems

investigating associations between random effects.

I was under the impression that taking the square root of the diagonal

elements of the inverse average information matrix obtained from model$ai

, would give you the standard error of the variance component estimates as

outputted in summary(model)$varcomp.

However I can only get the residual variance to give the correct answer,

even when I have tried to weight by the gamma component and am unsure

about how best to proceed.

Any help you could give would be most gratefully received

****

This is in fact true. The inverse AI matrix is the variance matrix for the

vector of gammas and sigma^2, where the gammas are on the ratio scale ie

gamma_i = sigma^2_i/sigma^2 say for the ith random term. The variances

reported are for the components and their variance matrix is obtained via

the usual formulae which are given for example in Searle et al. I could

track down the actual formulae for you if you like, but this is the reason

for the apparent discrepancy. Too late at night to do the algbebra!

As a further comment, I am not that keen on using these standard errors in

general for formal inference on variance components, preferring REMLLRTs

for most applications. Others may have alternate views.

HTH

warm regards

Brian Cullis

Research Leader, Biometrics &

Senior Principal Research Scientist

NSW Department of Primary Industries

Wagga Wagga Agricultural Institute

Visiting Professorial Fellow

School of Mathematics and Applied Statistics

Faculty of Informatics

University of Wollongong

Professor,

Faculty of Agriculture, Food & Natural Resources

The University of Sydney

Adjunct Professor

School of Computing and Mathematics

Charles Sturt University

Phone: 61 2 6938 1855

Fax: 61 2 6938 1809

Mobile: 0439 448 591

Received on Fri Jul 02 2009 - 01:02:09 EST

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