Re: Estimate of mu

From: <arthur.gilmour_at_DPI.NSW.GOV.AU>
Date: Tue, 30 Oct 2007 19:46:09 +1100

Dear Peter

> I need to estimate the population mean (mu). I understand that mu can
> be estimated from the following model if there is no singularity.

> Y ~ mu c(site) c(group) c(site).c(group) !r tree

This would return the so called 'least squares' mean - i.e. the simple
mean of
the cells in the predicted table regardless od the number of
observations. Such a mean can be a long way from the mean of the
which is weighted by the frequency in each cell.

> If singularity exists, however, can I use the following PREDICT
> statement to get the correct estimate of mu?

Y ~ mu site group !r tree
predict mu !present site group !average tree

One can argue about what is 'correct'. The issue really is what is
appropriate for your purpose.
There is a difference between this predict and the former 'mu' because
is handled differently. Typically PREDICT will ignore random terms
(involving rep, tree, family)

Assuming a pedigree for 'tree' so that tree effects do not sum to zero,
the average of the tree effects
is added in, (as well as affecting the SE of the prediction - conditional
rather than marginal)

Without '!average tree', the predict statement will give the simple mean
of the cells
that are present. If the data is unbalanced, is that the mean you want?
you may want some other weights. Look at the !PRWTS qualifier if so.

May Jesus Christ be gracious to you,

Arthur Gilmour, His servant .

Mixed model regression mapping for QTL detection in experimental crosses.
Computational Statistics and Data Analysis 51:3749-3764 now available at

Personal website:,
Principal Research Scientist (Biometrics)
NSW Department of Primary Industries
Orange Agricultural Institute, Forest Rd, ORANGE, 2800, AUSTRALIA

fax: 02 6391 3899; 02 6391 3922 Australia +61
telephone work: 02 6391 3815; home: 02 6364 3288; mobile: 0438 251 426

ASREML 2 is now available from
The ASReml discussion group is at
To join it,
Archives are at

Proposed travel:
UK 28 Jan
USA 11-15 Feb
Received on Sat Oct 30 2007 - 19:46:09 EST

This webpage is part of the ASReml-l discussion list archives 2004-2010. More information on ASReml can be found at the VSN website. This discussion list is now deprecated - please use the VSN forum for discussion on ASReml. (These online archives were generated using the hypermail package.)