`degroup()` with even more complex structures

[mattansb]

Currently we have support for the following (arbitrary) structures:

• Crossed: ~ J + K + M + ...
• Nested: ~ J/K/M/...

It would be nice to have support for more complex arbitrary designs, such as ~ J + K/M

The basic algorithm would be:

For each outcome:

1. Compute the group means for each crosses structure separately (e.g., J and K/M) according to the currently implemented algorithm.
2. For each row in the input data, compute the sum of the group means
3. Finally, subtract the sum from the outcome vector to obtain the cluster mean centered (at level 1) values (issue raised in Rethinking degroup() for cross-classified data #637 still applies)
4. Return group means and cluster mean centered values.

This is already currently possible using multiple calls to dmean():

set.seed(111)
data(iris)
iris$ID <- sample(1:4, nrow(iris), replace = TRUE) # fake-ID
iris$binary <- as.factor(rbinom(150, 1, .35)) # binary variable

# (Step 1)
x1 <- datawizard::demean(
  iris,
  select = c("Sepal.Length"),
  by = "ID",
  append = FALSE
)
x2 <- datawizard::demean(
  iris,
  select = c("Sepal.Length"),
  by = "Species/binary",
  append = FALSE
)

group_means <- data.frame(Sepal.Length_ID_between = x1$Sepal.Length_between, x2[1:2])

# (Step 2)
summ <- rowMeans(group_means)

# (Step 3)
group_means$Sepal.Length_within <- iris$Sepal.Length - summ

# (Step 4)
head(group_means)
#>   Sepal.Length_ID_between Sepal.Length_Species_between Sepal.Length_binary_between Sepal.Length_within
#> 1                5.878788                        5.006                 0.009789474           1.4684742
#> 2                5.843243                        5.006                -0.006000000           1.2855856
#> 3                5.812821                        5.006                -0.006000000           1.0957265
#> 4                5.843243                        5.006                -0.006000000           0.9855856
#> 5                5.843243                        5.006                -0.006000000           1.3855856
#> 6                5.843902                        5.006                 0.009789474           1.7801027

[mattansb]

This would probably require more nuanced support for by=<formula> and possible dropping the nested= argument.

Syntax:

datawizard::demean(
  iris,
  select = "Sepal.Length",
  by = c("Species/binary", "ID"),
)

datawizard::demean(
  iris,
  select = "Sepal.Length",
  by = ~ ID + Species / binary
)

The latter being dealt with like so:

by <- ~ ID + Species / binary

if (!(length(by) == 2 && by[[1]] == as.name("~"))) {
  stop("")
}

as.character(by[[2]])[-1]
#> [1] "ID"             "Species/binary"