# Using a mixed linear model to evaluate responses in a RCBD experiment?

I am new to mixed linear models, so I have a question about them.

I have a plant study (being intentionally vague here to achieve confidentiality) evaluating plant senescence rates (leaf death) in an agricultural field. The experiment was laid out in a randomized complete block design with three replications of 20 genotypes. I then collected NDVI multispectral data from the genotypes. After getting this data, I ground-measured senescence scores for 5 plants set aside for this purpose. I visually measured each leaf for leaf senescence based on a percentage of leaf death. For instance, if the leaf was half-brown, it received a rating of 50. This was done for the first 8 leaves of the canopy for each plant. The scores for each leaf level was then averaged across the 5 plants, giving each plot an average "leaf 1" score, "leaf 2" score, .... , "leaf 8" score.

In order to test how far into the canopy a particular camera would be able to detect leaf senescence, I am interested in using a mixed linear model to see if there are any relationships between genotype, leaf canopy levels, and senescence scores to my NDVI data. This is the equation that I have found in the literature:

Y = Xβ + Zµ + ε

where the NDVI response (Y) is modeled by a set of fixed effects (β) and random effects (µ), and ε is the random error term (http://frontiersin.org/articles/10.3389/fpls.2017.01532/full)

I planned on investigating this by assigning fixed vector β as genotype (factor with 20 levels) and leaf level (factor with 8 levels), while vector µ being assigned to ground-truthed senescence scores (random effects). ε would constitute as the error term. Note: Ground-truth error scores will vary for each plot; for instance the average leaf 1 score could be 100 for any given plot, leaf 2 could be 88, and so on.

Am I building this mixed model correctly? (P.S. I'll be using the R package lme4 for this)

• Could you elaborate more on "The experiment was laid out in a randomized complete block design with three replications of 20 genotypes"? I can help specify the model, but I'm a social scientist and am not familiar with these types of designs. Maybe a table or an image of what the experiment looked like? – Mark White Apr 7 at 2:55
• @MarkWhite Sure. There were three blocks, and within each block, each plant type was planed randomly. Does that help? – ihb Apr 7 at 17:58

You are following the analysis described in paper by Potgieter et al. (2017). Based on your description, it would seem that you are doing it correctly, and lme4 should do the trick. Importantly, you should check that the assumptions of the model are true. Also it sounds like you may have smaller sample size than the one which was used in the paper. Therefore you may want to perform a power analysis to confirm that your sample size is sufficient.