I am analyzing data from a field experiment, and I am interested in the effects of fauna and altitude (fixed). Altitude has two levels, and at each site I have 5 blocks for the three levels of fauna (the blocks were set up to account for the heterogeneity in the soil). I guess that the model treating block as random, in lme4, would be:
lmer(response ~ altitude + fauna + (1|block))
However, I replicated this study in 5 mountains. So can I treat mountain as another random factor and then:
lmer(response ~ altitude + fauna + (1|block) + (1|mountain))
Or should I nest my blocks within mountains?
lmer(response ~ altitude + fauna + (1|mountain:block))
I see people using nested designs when they have pseudoreplicates, but that is not my really my case as all my replicates are independent.
Here's how my data looks like:
mountain altitude treatment block response m1 high t1 b1 124.77 m1 high t2 b1 55.77 m1 high t3 b1 88.99 m1 high t1 b2 88.99 m1 high t2 b2 88.99 m1 high t3 b2 88.99 m1 low t1 b6 124.77 m1 low t2 b6 55.77 m1 low t3 b6 78.99 m1 low t1 b7 89.99 m1 low t2 b7 33.99 m1 low t3 b7 22.87 m2 . . .