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I am developing a research project where we are evaluating the growth of seedlings. The plots are distributed in an open greenhouse and some environmental parameters vary according to their position. To reduce this effect, we define blocks to group plots that are located under different conditions.

We will make several measurements on the different plots and therefore we must use mixed models. My question is: in an experiment without blocks, the plots are the random factor, but in this case, do I consider the blocks as the random factor?

I don't have the data yet and I haven't carried out the analysis, but my question (using R) would be how should I use the blocks in the model?:

growth ~ factor1 + factor2 + (1|block)

or

growth ~ factor1 + factor2 + block + (1|plot)
kjetil b halvorsen
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Graciliano Santos
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1 Answers1

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The smallest observational units in your experiment is the plots. There is indeed a random term associated with plots, that is the usual observational or residual variance. As that is is all models, in the R lme4 formula language that is implicit, so no need to state it.

Blocks are usually modeled with an additional random effect, one associated to each block. So the formula you should be using is your first one,

growth ~ factor1 + factor2 + (1|block)

If, as user @underflow says in a comment, there are multiple observations per plot, you could use the model

growth ~ factor1 + factor2 + (1|block/plot)

the last term her, using / to indicate nesting structure, means random intercepts for block and then for plots within blocks.

See R's lmer cheat sheet and for more detail https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf

kjetil b halvorsen
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