lme vs. lmer

Chris,
Thanks for that - I should probably have mentioned that I'm using
family=quasipoisson ?in glmer since my data has Poisson distribution
as well as being overdispersed. I'm unsure how one decides which term
to drop without being informed by p-values, and so don't quite
understand how the "Likelihood ratio test using anova()" , or the AIC
or BIC model comparison will work in this case (I thought one's
supposed to remove the term with the highest p-value from the model,
and compare it with the model with the term included to see if there's
a difference, not so?).

Dear Raldo:

Finally there is a question that I can help with!  It appears to me
you don't have much experience with regression modeling in R and the
other people who answer you are talking a bit "over your head".

In your case, call this fit the "full" or "unrestricted" model:

ex4o_r2<-glmer(Counts~N+G+Year+N:Year+G:Year+N:G:Year+(Year|Site),
data=ex4o, family=quasipoisson)

(I'm not commenting the specification).

Suppose you wonder "Should I leave out the multiplicative effect
between N and Year?"  THen you fit the model that excludes that one
element:

ex4o_new <-glmer(Counts~N+G+Year +G:Year+N:G:Year+(Year|Site),
data=ex4o, family=quasipoisson)

And then use the anova function to compare the 2 models

anova(ex4o_r2, ex4o_new)

This is a "pretty standard" R regression thing, similar to what people
do with all sorts of models in R.  It is what the "drop1" function
does for lm models, I believe.

You may have seen regression models where an F test is done comparing
a full model against a restricted model?  This is following the same
line of thought.

To test your question about the factor levels, here is what you should
do. SUppose the initial factor has 5 levels, and you wonder "do I
really need 5 levels, or can I drop out the separate estimations for 3
of the levels?"  Create a new factor with the simpler structure, run
it through the model in place of the original factor, and run anova to
compare the 2 models.  I wrote down some of those ideas in a paper
last spring (http://pj.freefaculty.org/Papers/MidWest09/Midwest09.pdf),
but when I was done it seemed so obvious to me (& my friends) that I
did not try to publish it.

With anova, there is a test= option where you can specify if you want
a chisq or F test.

And, for future reference, when the experts ask you for a data example
to work on, they do not mean a copy of your printout, although that
may help.  What they want is the actual data and commands that you
use.  Usually, you have to upload the data somewhere for us to see,
along with the code.

Good luck with your project.

pj

Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas