Whereas the direction of main effects can be interpreted from the sign of the estimate, the interpretation of interaction effects often requires plots. This task is facilitated by the R package sjPlot (Lüdecke, 2022). For instance, using the plot_model function, I plotted the interaction between two continuous variables.

library(lme4)
#> Loading required package: Matrix
library(sjPlot)
#> Learn more about sjPlot with 'browseVignettes("sjPlot")'.
library(ggplot2)

theme_set(theme_sjplot())

# Create data partially based on code by Ben Bolker  
# from https://stackoverflow.com/a/38296264/7050882

set.seed(101)

spin = runif(800, 1, 24)

trait = rep(1:40, each = 20)

ID = rep(1:80, each = 10)

testdata <- data.frame(spin, trait, ID)

testdata$fatigue <- 
  testdata$spin * testdata$trait / 
  rnorm(800, mean = 6, sd = 2)

# Model
fit = lmer(fatigue ~ spin * trait + (1|ID),
           data = testdata, REML = TRUE)
#> boundary (singular) fit: see help('isSingular')

plot_model(fit, type = 'pred', terms = c('spin', 'trait'))
#> Warning: Ignoring unknown parameters: linewidth

^{Created on 2023-06-24 with reprex v2.0.2}

However, I needed an extra feature, as sjPlot by default breaks down the colour (fill) variable into few levels that do not include the minimum or the maximum values in my variable. What I would like to do is to stratify the colour variable into equally-sized levels that include the minimum and the maximum values.

Furthermore, in the legend, I would also like to display the number of levels of a grouping variable (ID) that are contained in each level of the colour variable.

Below is a solution using custom functions called deciles_interaction_plot and sextiles_interaction_plot.

library(lme4)
#> Loading required package: Matrix
library(sjPlot)
library(ggplot2)

theme_set(theme_sjplot())

# Create data partially based on code by Ben Bolker  
# from https://stackoverflow.com/a/38296264/7050882

set.seed(101)

spin = runif(800, 1, 24)

trait = rep(1:40, each = 20)

ID = rep(1:80, each = 10)

testdata <- data.frame(spin, trait, ID)

testdata$fatigue <- 
  testdata$spin * testdata$trait / 
  rnorm(800, mean = 6, sd = 2)

# Model
fit = lmer(fatigue ~ spin * trait + (1|ID),
           data = testdata, REML = TRUE)
#> boundary (singular) fit: see help('isSingular')

# plot_model(fit, type = 'pred', terms = c('spin', 'trait'))

# Binning the colour variable into ten levels (deciles)

# Read in function from GitHub
source('https://raw.githubusercontent.com/pablobernabeu/language-sensorimotor-simulation-PhD-thesis/main/R_functions/deciles_interaction_plot.R')

deciles_interaction_plot(
  model = fit, 
  x = 'spin',
  fill = 'trait',
  fill_nesting_factor = 'ID'
)
#> Loading required package: dplyr
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
#> Loading required package: RColorBrewer
#> Loading required package: ggtext
#> Loading required package: Cairo
#> Warning in RColorBrewer::brewer.pal(n, pal): n too large, allowed maximum for palette Set1 is 9
#> Returning the palette you asked for with that many colors
#> Warning: Ignoring unknown parameters: linewidth
#> Scale for 'y' is already present. Adding another scale for 'y', which will
#> replace the existing scale.
#> Scale for 'colour' is already present. Adding another scale for 'colour',
#> which will replace the existing scale.

# If you wanted or needed to make six levels (sextiles) instead 
# of ten, you could use the function sextiles_interaction_plot.

# Read in function from GitHub
source('https://raw.githubusercontent.com/pablobernabeu/language-sensorimotor-simulation-PhD-thesis/main/R_functions/sextiles_interaction_plot.R')

sextiles_interaction_plot(
  model = fit, 
  x = 'spin',
  fill = 'trait',
  fill_nesting_factor = 'ID'
)
#> Warning: Ignoring unknown parameters: linewidth
#> Scale for 'y' is already present. Adding another scale for 'y', which will
#> replace the existing scale.
#> Scale for 'colour' is already present. Adding another scale for 'colour',
#> which will replace the existing scale.

^{Created on 2023-06-24 with reprex v2.0.2}