I am trying to do mixed linear model for my study in R. I would like to know if my code is correct or not.
MY design - I have 5 sites, 2 subsites within each site and 2 permanent quadrates within each site.
So I have 5 sites, 10 subsites and 20 quadrats. I have measured colony size (of corals) at all the quadrats.
My question is does the size structure vary between sites ?
In my data quadrats are nested within subsite and subsites are nested within site.
I will use site as my fixed factor and subsites and quadrats as my random effects.
I can think of two possible ways of doing this:
lmer(size ~ site + (1|subsite) + (1|quadrat)
lmer(size ~ site + (1|site:subsite) + (1|subsite:quadrant)
It depends a bit on how your subsites and quadrats are coded. Let's consider two schemes.
explicit nesting: this means that the subsites within sites and quadrats within subsites don't have unique names, e.g.
site subsite quadrat A a 1 A a 2 A b 1 A b 2 B a 1 B a 2 ... etc.
In this case, you must use interaction/nesting syntax to let R know that quadrat 1 in site A, subsite a has nothing in common with all of the other quadrats labeled "1" ...
size ~ site + (1|site:subsite) + (1|site:subsite:quadrat)
size ~ site + (1|site:(subsite/quadrat)) might work, but I haven't tested it)
implicit nesting: in this case, everything is uniquely named.
site subsite quadrat A Aa Aa1 A Aa Aa2 A Ab Ab1 A Ab Ab2 B Ba Ba1 B Ba Ba2 ... etc.
In this case, you can use either the syntax above (R automatically drops the redundant levels) or
size ~ site + (1|subsite) + (1|quadrat)
and you should get identical results. (You can always test this experimentally!)
A couple of other points:
glmer) you can greatly simplify your life by simply aggregating to the mean values per site and running a 1-way ANOVA (see Murtaugh 2007, Ecology, "Simplicity and complexity in ecological data analysis").