Re: Calculating standard errors of variance estimates in ASRemlR

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


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

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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