BLUP in lmer

To see how well the model has accomplished, would it be wrong to observe
the following:
1) response residuals to be close to zero by computing [model at y -
exp(fitted(model))] assuming the link is a log function. Can this not
help in at least identifying the outliers...those that lie far from 0?
2) Since the GLMMs are linear in their link function, can we get close
to assessing the linearity by:
	* first,  computing the means in each of the categories defined
by predictors (assuming the predictors are categorical variables)
	* second, assigning that mean to each of the observations that
fall in the category defined by the set of predictors.
	* third, wrapping the link function around the mean. Example,
log(mu)
	* lastly, computing log(mu)-fitted(model) to give link
residuals.
	* plotting link residuals against fitted(model) should give a
linear pattern with constant variance (sigma2_b + segma2_e).
Any insight on this would be very much appreciated.

Also, is there any way to assess the dispersion parameter in negative
binomial family before giving it in lmer for GLMM? Presently, I am using
the dispersion parameter estimate computed from glm.nb with random
effects of GLMM as fixed effects with treatment contrasts. However, I
suspect it to be biased due to no structural information taken in
account, which leaves lot of variation uncaptured by the model. Can you
please suggest any nicer way?

Last question, would it make any sense to use predictors with sum
contrast in GLMs when the link function is log, if I want to know how
much the effect of each of the categories of a predictor is away from
the overall average?

Thanks in advance,
Monica 

-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Douglas
Bates
Sent: Friday, March 23, 2007 10:43 AM
To: Roberts, J. Kyle
Cc: r-sig-mixed-models at r-project.org; Olivier MARTIN
Subject: Re: [R-sig-ME] BLUP in lmer

Olivier,

Do you mean something like this?
fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
with(fm1, xyplot(resid(.) ~ fitted(.)))

This gives you a plot of the residual versus the fitted.  "sleepstudy"

is included in the package.

Thanks for the reply, Kyle.  The original question was about
generalized linear mixed models and the resid function doesn't work
for them at present.  The reason is that it is not clear which
residuals should be returned.  A generalized linear model has several
different types of residuals that can be defined for it and I haven't
gotten around to determining which ones would be appropriate for
generalized linear mixed models.

The original also asked about BLUPs from a generalized linear mixed
model.

ranef(fm1)

provides what some would call the BLUPs of the random effects.  I call
them the "conditional modes" of the random effects rather than the
BLUPs or Best Linear Unbiased Predictors.  They are the modes in that
they maximize the density of the random effects conditional on the
variance-covariance parameters and the data.  For a linear mixed model
they are also the BLUPs.  For a generalized linear mixed model or a
nonlinear mixed model they aren't.  As Alan James once described the
situation, "They aren't linear (i.e. linear functions of the
observations) and they aren't unbiased and there is no clear sense in
which they are "best" but, other than than, they're exactly like the
BLUPs".

Hope this helps,
Kyle

***************************************
J. Kyle Roberts, Ph.D.
Baylor College of Medicine
Center for Educational Outreach
One Baylor Plaza, MS:  BCM411
Houston, TX   77030-3411
713-798-6672 - 713-798-8201 Fax
jkrobert at bcm.edu
***************************************

-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org

[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Olivier
MARTIN

Sent: Friday, March 23, 2007 10:30 AM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] BLUP in lmer

Hi all,

I am using 'lmer' to fit generalized linear mixed-effects models.
I would like to know if there is a function to estimate the random

effects.

And, is there a way to compare the observed values vs. fitted values

or fitted values vs. residuals ?

Thanks,
olivier

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