Day 12 Review: hierarchical multilevel models

June 18th, 2026

In-class activity

A study was designed to determine the effect on the incidence of root rot, of variety of wheat, kinds of dust for seed treatment, method of application of the dust, and efficacy of soil inoculation with the root-rot organism. We have a data frame with 160 observations on the following 8 variables that describe a designed experiment:

row row: equivalent to “longitude” in the field coordinates
col column: equivalent to “latitude” in the field coordinates
yield yield: response variable
inoc inoculate: indicator whether soil was inoculated with root rot or not
gen genotype
dry dry/wet dust application
dust dust treatment
block block: the field was divided in 4 equally-sized subsections that showed approximately similar characteristics.

url <- "https://raw.githubusercontent.com/stat720/summer2026/refs/heads/main/data/data_inclass_06182026.csv"
df <- read.csv(url)

12.1 Exercises

12.1.1 Data structure

Draw a figure of the structure in the data. Do not consider the treatments yet.

df |> 
  ggplot(aes(col, row))+
  geom_tile(aes(fill = block))+
  coord_fixed()

df |> 
  filter(block == "B1") |> 
  ggplot(aes(col, row))+
  geom_tile(aes(fill = gen), color = "black")+
  coord_fixed()

df |> 
  filter(block == "B1", gen == "Mindum") |> 
  ggplot(aes(col, row))+
  geom_tile(aes(fill = paste(dust, dry)), color = "black")+
  geom_point(aes(fill = inoc), shape =21, size = 3)+
  coord_fixed()

12.1.2 Designed experiment

2a. Draw a figure of the different randomization steps. 2b. Indicate the experimental units for the different treatment factors. 2c. How many observations do you have for each treatment factor? 2d. What are the treatment structure and the design structure?

12.1.3 Stat model

3a. Write the statistical model that describes the data generating process. 3b. Fit the model in (3) to the data using R.

12.1.4 Bonus

How would you name this experiment design?

12.2 Acknowledgements

Data come from the agridat package.