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I am having troubles coming up with the proper statistical model and R code for a forestry trial we did several years ago. We looked at whether wood piles left over in clear cuts were beneficial for biodiversity. I include a schematic of the design:enter image description here

We looked at wood piles left over in forest stands 2,4,and 6 years post harvest. Within each stand we examined 8 wood piles, that we sampled using 3 traps at different locations, 1 in the center of the wood pile, 1 at the edge of the wood pile and 1 on the ground between wood piles. I understand that this is not the optimal design for an experiment, but in an operational forestry landscape it is often the best that can be done.

What I am trying to analyze is the catch of insects (y), with special attention to the Harvest age*Trap Location interaction. I want to stress that it is not a repeated measures experiment, as each of the time periods post harvest were sampled in the same year on different forest stands. I am interested in using generalized linear mixed effects modelling in R (package lme4). I am certain that the underlying distribution of the data is a negative binomial (which is very common distribution for insect data). My model summary is as follows:

Total number of samples = 144, therefore total df = 143;

Harvest Age (A) - Fixed effect - N=3 - df=2;
Trap Location (L) - Fixed effect - N=3 - df=2;
A*L - Fixed effect - (A-1)(L-1) - df=4;

I know that both Stands (S; N=2, df=1) and wood piles (P; N=8, df=7) are both Random effects. Forest stands could be thought of as blocks (replicates of Harvest Age)? I think wood piles are the experimental unit, and are nested within the ALS interaction, and would probably be the total error term in the model. I am stuck trying to figure out how to account for the variation among stands and wood piles. Any help with the model and R-code would be greatly appreciated.

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Ok, I think the design is closest to a Split-Split plot design. ANOVA table below.

enter image description here

However, I have been trying to code different models into a simple ANOVA in r to check the model degrees of freedom, but cannot get the correct error terms:

aovtest = aov(abund ~ yr + loc*yr + Error(yr*blk + loc*pil + loc*yr*pil), data=abund)  

I have also tried other variations on this theme but cannot get the right mode. Anyone out there have a suggestion?

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