# Linear mixed effect model with repeated measures using lmer

Background
I think I am close to the error structure I want for random effects but not sure about some parts of it. I am carrying an experiment on wheat plots in a field to measure the increase in aphid numbers over time.

Experimental design and coding for predictors
I put 4 populations of aphids into a wheat plot and subjected them to four different cage treatments (Cage_treatment). I measured the number of aphids before they were subjected to the treatments and after e.g. two time periods, before and after(Time). I repeated this in many wheat plots within a field. Three wheat plots are part of different three types of crop rotation (Rotation). These 3 plots x 3 crop rotations equal a block. There are four blocks in total. I am measuring aphid numbers per tiller (Total_per_tiller).

The effects I am interested in e.g. fixed effects is how the Total_per_tiller aphid numbers change over Time, how this differs for each Cage_treatment and how the Rotation effects this.

Fixed and Random effects

Fixed effects:

• Cage_treatment,
• Rotation,
• Time,

Random effects:

• Plot ID,
• Block,

This is the following code for my maximal model:

model <- lmer(Total_per_tiller~Cage_treatment*Rotation*Time + (Time|PlotID) +
(1|Block/Rotation), REML=FALSE)


Does this look right?

In your model Rotation is both a fixed effect slope and a random effect nested in Block in here: (1|Block/Rotation). If you wanted Rotation to be a random slope in Block you would have to define it as (1 + Rotation|Block). What (1|Block/Rotation) means is: (1|Block) + (1|Block:Rotation), i.e. a random intercept for Block and a random intercept for Rotation nested in Block.