Within- and between effects: the complex random-effects within-between model

library(tidyverse)
library(parameters)
library(lme4)
library(see)

# data generation -----------------------

set.seed(123)
n <- 5
b <- seq(1, 1.5, length.out = 5)
x <- seq(2, 2 * n, 2)

d <- do.call(rbind, lapply(1:n, function(i) {
  data.frame(x = seq(1, n, by = .2),
             y = 2 * x[i] + b[i] * seq(1, n, by = .2) + rnorm(21),
             grp = as.factor(2 * i))
}))

d <- d %>%
  group_by(grp) %>%
  mutate(x = rev(15 - (x + 1.5 * as.numeric(grp)))) %>%
  ungroup()

labs <- c("very slow", "slow", "average", "fast", "very fast")
levels(d$grp) <- rev(labs)

d <- cbind(d, demean(d, c("x", "y"), group = "grp"))




# figure 1: raw data  ------

ggplot(d, aes(x, y)) +
  geom_point(colour = "#555555", size = 2.5, alpha = .5) +
  see::theme_modern() +
  labs(x = "Typing Speed", y = "Typing Errors", colour = "Type Experience")



# figure 2: Relationship between typing errors and typing speed ------

ggplot(d, aes(x, y)) +
  geom_point(colour = "#555555", size = 2.5, alpha = .5) +
  geom_smooth(method = "lm", se = F, colour = "#555555") +
  see::scale_color_flat() +
  see::theme_modern() +
  labs(x = "Typing Speed", y = "Typing Errors", colour = "Type Experience")

m1 <- lm(y ~ x, data = d)
model_parameters(m1)



# figure 3: Relationship between typing errors and typing speed ------

ggplot(d, aes(x, y)) +
  geom_point(mapping = aes(colour = grp), size = 2.5, alpha = .5) +
  geom_smooth(method = "lm", se = F, colour = "#555555") +
  see::scale_color_flat() +
  see::theme_modern() +
  labs(x = "Typing Speed", y = "Typing Errors", colour = "Type Experience")



# figure 4: Within-effect of typing-speed ------

ggplot(d, aes(x, y)) +
  geom_smooth(mapping = aes(colour = grp), method = "lm", se = FALSE) +
  geom_point(mapping = aes(colour = grp), size = 2.2, alpha = .6) +
  see::scale_color_flat() +
  see::theme_modern() +
  labs(x = "Typing Speed", y = "Typing Errors", colour = "Type Experience")

m2 <- lm(y ~ 0 + x_within + grp, data = d)
model_parameters(m2)[1, ]



# figure 5: Between-effect of typing-speed ------

ggplot(d, aes(x, y)) +
  geom_point(mapping = aes(colour = grp), size = 2.2, alpha = .6) +
  geom_smooth(mapping = aes(x = x_between, y = y_between), method = "lm", se = F, colour = "#444444") +
  see::scale_color_flat() +
  see::theme_modern() +
  labs(x = "Typing Speed", y = "Typing Errors", colour = "Type Experience")

m3 <- lm(y ~ x_between, data = d)
model_parameters(m3)



# figure 6: Within- and between-effect of typing-speed ------

ggplot(d, aes(x, y)) +
  geom_smooth(mapping = aes(colour = grp), method = "lm", se = FALSE) +
  geom_point(mapping = aes(colour = grp), size = 2.2, alpha = .6) +
  geom_smooth(mapping = aes(x = x_between, y = y_between), method = "lm", se = F, colour = "#444444") +
  see::scale_color_flat() +
  see::theme_modern() +
  labs(x = "Typing Speed", y = "Typing Errors", colour = "Type Experience")

m4 <- lmer(y ~ x_between + x_within + (1 | grp), data = d)
model_parameters(m4)



# figure 7: Within- and between-effect of typing-speed ------

m5 <- lmer(y ~ x_between + x_within + (1 + x_within | grp), data = d)
model_parameters(m5)




model_parameters(m1)
model_parameters(m2)[1, ]
model_parameters(m3)
model_parameters(m4)
model_parameters(m5)