Syntax for random effect in glmmPQL

It is the same syntax as for lme.

I think you meant two *independent* variables.  I don't see the point of
treating a factor with two levels as a random effect: you don't really
expect to estimate a population from just two samples, do you?  If (as I
suspect) the sites are blocking factors they should be treated as fixed
effects (just as randomized block designs are analysed), or if you are
interested in the population of sites you should get several more.

A pedagogical hint to R-help readers:

You don't just have a data set:  you have an experiment or an
observational study you want to analyse.  If you had described the latter,
we might have been able to do better than guess at what you meant.

Dear R-listers

I wonder if someone can help me with the syntax for the random effect in
glmmPQL()? I have a data set with a response variable "y" (counts), two
dependent variables: "treat" (4 levels) and "site" (2 levels). The
latter, I want to use as a random variable. How do I specify this in the
function?

Is it like this: glmmPQL(y~treat,random=~1|site,family=poisson,
data=mydata)? What does the ~1 do?

That gives you a random intercept by site.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595