[R] lmer coefficient distributions and p values

[Daniel Lakeland]

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