# 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 site.group.rep tree
site.family

This would return the so called 'least squares' mean - i.e. the simple
mean of
the cells in the predicted site.group table regardless od the number of
observations. Such a mean can be a long way from the mean of the
population
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 site.group !r site.group.rep tree site.family
predict mu !present site group !average tree

One can argue about what is 'correct'. The issue really is what is
There is a difference between this predict and the former 'mu' because
'tree'
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 site.group cells
that are present. If the data is unbalanced, is that the mean you want?
Alternatively
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
http://dx.doi.org/10.1016/j.csda.2006.12.031

Personal website: http://www.cargovale.com.au/

mailto:Arthur.Gilmour_at_dpi.nsw.gov.au, arthur_at_cargovale.com.au
Principal Research Scientist (Biometrics)
NSW Department of Primary Industries
Orange Agricultural Institute, Forest Rd, ORANGE, 2800, AUSTRALIA

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Received on Sat Oct 30 2007 - 19:46:09 EST

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