I apologize in advance if this is a fairly trivial set of questions, but I'm fairly new to multi-level models...
I'm analyzing the results from a field experiment and am interested in quantifying the effects of various fertilizer treatments (2 factors, N and P, each with two levels) and environmental variables (i.e., site-level covariates [ENV1...ENVp] that were not controlled for, but measured) on plant growth [GROW] across a wide range of sites (SITE). Also, treatments were replicated within sites using a randomized complete block (BLOCK) design (the blocks are arranged parallel to hillslope contours at each site, and there is no replication within blocks). It's a fairly straightforward design, but I'm not 100% sure that I'm specifying my models correctly. My questions are:
1) If I'm interested in estimating the main effects of N and P (and their interaction) while incoporating site and block (nested within site) as random effects WITHOUT incorporating environmental variables, is the following model structure correct?
model1<- lmer(GROW ~ N + P + N*P + (1|SITE) + (1|SITE:BLOCK), options...)
The main reason I ask is that I'm obtaining a miniscule (almost zero) variance component for the SITE:BLOCK effect; though this isn't surprising, I want to make sure that I've at least specified the model correctly.
2) (partially a design question) Same basic analysis, but now I'm interested in incorporating some of the environmental variables that were measured at the site level into my model. In particular, I'm interested determining how certain factors (though I didn't control for them) may have modified the response of plants to the experimental treatments. Is the following the correct way to do so?
model2<-lmer(GROW ~ N + P + N*P + ENV1 [plus appropriate trt*cov interactions] + (1|SITE:BLOCK), options...)
I'm particularly curious if replacing the random categorical site effect with continuous covariate(s), while retaining the random nested block effect, makes sense here. And if so, whether this is the correct way to specify such a model.
Any input would be much appreciated. Thanks much!
Pete
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