I am struggling with the formulation in lme of a generalize randomized block design(GRBD's) with subsampling. The experiment consists of 2 treatments : 1.genetic diversity (g_diversity) with two levels: mix/nomix crops
2.temporal diversity (t_diversity) with two levels: 4years/2years- under crop rotation). The field divided to 4 strips: 2 strips- 4years rotation ; 2 strips- 2 year rotation. For each of those t_diversity treatments- 1 strip is crop A and the second is crop B ( I want to eliminate crop effect, so I set it (strip)as random var). Each strip consists of 3 blocks, in each block 4 experimental plots, 2 plots for each of g_diversity levels (mix/non-mix). In each plot, I took 3 samples for decomposition rate, some samples are missing (NA's). later on I want to compare between the treatments performance.
My initial model looks like this:
lme(decomposed_weight ~ g_diversity+t_diversity, random= ~1|strip/block/plot/repetition, data=Dt, na.action=na.omit)
However, I'm not sure whether this model reflect correctly the GRBD's analysis and take in consideration correctly the experimental design. Any suggestions and explanations are welcome!
Thanks
The variability within blocks must be less than the variability between blocks, which you have achieved. Then, your subjects within each block are randomly assigned to treatment conditions. So your design is good, but there is no replication. To replicate, you would have to have at least 3 identical experiments that are significantly distant from each other :)
Thank you for your answer Andrew!
Do you think that I also need to include interactions between the fixed var (g_diversity:t_diversity) in the model?
lme(decomposed_weight ~ g_diversity+t_diversity+(g_diversity:t_diversity), random= ~1|strip/block/plot/repetition, data=Dt, na.action=na.omit)
No, there is no meaningful interaction between g and t :)
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