[R] lmer coefficient distributions and p values

[Steven McKinney]

Hi Daniel,

You might want to review further advances by Doug Bates with lme4
since the post you show in your email.

http://tolstoy.newcastle.edu.au/R/e2/help/06/10/3565.html
In this thread Doug Bates discusses fitting using maximum
likelihood for testing purposes.  There is now an anova()
method for lmer() and lmer2() fits performed using method="ML".  
You can compare different models and get p-values for 
p-value obsessed journals using this approach.

I believe I read a thread discussing the use of maximum
likelihood fitting for use in ANOVA tests, and then 
REML fits on final models for better parameter estimates - 
but I can't find that thread.  Hopefully Doug Bates
or anyone involved in that level of discussion can chime in.


See also for example this wiki 
http://wiki.r-project.org/rwiki/doku.php?id=guides:lmer-tests

and the new listserv at
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models


Also check the latest documentation for lme4 and the lmer()
and lmer2() functions at
http://cran.r-project.org/
in the 
Packages ... lme4 
pages.


Hope this helps

Steven McKinney

Statistician
Molecular Oncology and Breast Cancer Program
British Columbia Cancer Research Centre

email: smckinney +at+ bccrc +dot+ ca

tel: 604-675-8000 x7561

BCCRC
Molecular Oncology
675 West 10th Ave, Floor 4
Vancouver B.C. 
V5Z 1L3
Canada




-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch on behalf of Daniel Lakeland
Sent: Wed 8/15/2007 9:34 AM
To: r-help at stat.math.ethz.ch
Subject: [R] lmer coefficient distributions and p values
 
I am helping my wife do some statistical analysis. She is a biologist,
and she has performed some measurements on various genotypes of
mice. My background is in applied mathematics and engineering, and I
have a fairly good statistics background, but I am by no means a PhD
level expert in statistical methods.

We have used the lmer package to fit various models for the various
experiments that she has done (random effects from multiple
measurements for each animal or each trial, and fixed effects from
developmental stage, and genotype etc). The results are fairly clear
cut to me, and I suggested that she publish the results as coefficient
estimates for the relevant contrasts, and their standard error
estimates. However, she has read the statistical guidelines for the
journal and they insist on p values.

I personally think that p values, and sharp-null hypothesis tests are
misguided and should be banned from publications, but it doesn't much
matter what I think compared to what the editors want.

Based on searching the archives, and finding this message:

https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html

I am aware of the theoretical difficulties with p values from lmer
results. I am also aware of the mcmcsamp function which performs some
kind of bayesian sampling from the posterior distribution of the
coefficients based on some kind of prior (I will need to do some more
reading to more fully understand this). Is this the primary way in
which we can estimate the distribution of the model coefficients and
calculate a p value or a confidence interval?

What can I do with the t statistic provided by lmer? If as the above
message suggests, we are uncertain of the correct F and by extension t
distributions to use, what help are the t statistics? I suppose I
could test them against a very low degree of freedom t distribution
(say 3) and publish those p values?

Again, I'm content to ignore p values and stick to estimates, but the
journal isn't.

BTW: thanks to all on this list, I've benefitted greatly from R and
from the archives of help topics.

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan

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