Re: Likelihood

From: Arthur Gilmour <arthur.gilmour_at_AGRIC.NSW.GOV.AU>
Date: Thu, 13 Jan 2005 16:53:52 +1100

Dear Chandra,

Shouldn't log likelihood only increase (significantly or otherwise) when
effect (fixed or random) is added to a model?
However, I have found it to decrease with the addition of an effect, in
some cases. For example, if a non-significant effect is added or if an
effect confounded with another already present in the model, is added. Is
this happening because ASReml doesn't necessarily find the highest
likelihood every time? Or maybe this is why LogL can be used for a LRT to
test significance of fixed effects using the same random model (Lynch and
Walsh- "Genetics and analysis of quantitative traits", p.860).

The LogL value reported by ASReml can change up or down if the
parameterization of the fixed model
changes, even if the model is equivalent [e.g. changing the order of
levels in a factor so that a different
level is alliased/singular, or rescaling a covariate].

This can happen subtly when singular fixed terms are in the SPARSE model
and the variance model
for some random effect is changed say from a diagonal structure to a
correlated structure.
Even though the fixed model specification has not changed, the change to
the sparcity
can result in the equations being solved in a different order and result
in the singularity being applied to
a different level of the fixed effect, changing the Loglikelihood.

However, if the only change is to random effects, then adding a random
term will either increase
or not change the LogLikelihood.

There is an exception to this and it is when ASReml fixes a
variance parameter. When a parameter is fixed, the model is fitted
conditional to it.
Occasionally, ASReml will fix a parameter early in the sequence when there
is in fact
a better model available if the fixed parameter has some other value.

Peace to you 2005 in the Name of Jesus Christ

Arthur Gilmour PhD
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;
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Received on Wed Jan 13 2005 - 16:53:52 EST

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