How can I calculate a group-level statistic omitting a given sub-group nested within the group?

Question

I have long data that is students nested within classrooms. I would like to calculate various class-level statistics for each student about the classroom that they study in, but exclude the student's own data in this calculation.

A simple example would be as below:

 df <- data.frame(
  class_id = c(rep("a", 6), rep("b", 6)),
  student_id = c(rep(1, 3), rep(2, 2), rep(3, 1), rep(4, 2), rep(5, 3), rep(6, 1)),
  value = rnorm(12)
)

As shown above, I six students in two classrooms, each of which has one or more observations of value. It's easy to get the student-level average with:

df %>% 
  group_by(class_id, student_id) %>% 
  summarize(value = mean(value))

or to add a classroom-level average with:

df %>% 
  group_by(class_id) %>% 
  mutate(class_avg = mean(value))

but I can't figure out how to tell dplyr to "leave out" a given group in the higher-level group level calculation. This is similar to the question asked here, but that calculates the mean of all groups except for the given group. I'm not sure how to modify this with dplyr to get what I want.

Thanks for your help.

Edit: After @akrun's request, the expected output is below (using a slightly modified version of @jared_mamrot's answer). As you can see, the class_mean_othstudents variable takes the value of the mean of the students in each class except for the given student. Jared's solution works but is a very manual approach and would only apply to getting a mean value. I am wondering if there is a dplyr way to do this more generally.

set.seed(123)

df <- data.frame(
  class_id = c(rep("a", 6), rep("b", 6)),
  student_id = c(rep(1, 3), rep(2, 2), rep(3, 1), rep(4, 2), rep(5, 3), rep(6, 1)),
  value = rnorm(12)
)

df %>% 
  group_by(class_id, student_id) %>%
  summarize(student_mean = mean(value)) %>% 
  mutate(class_mean_othstudents = 
           (sum(student_mean) - student_mean)/(n() - 1)
  )

`summarise()` has grouped output by 'class_id'. You can override using the `.groups` argument.
# A tibble: 6 x 4
# Groups:   class_id [2]
  class_id student_id student_mean class_mean_othstudents
  <chr>         <dbl>        <dbl>                  <dbl>
1 a                 1       0.256                  0.907 
2 a                 2       0.0999                 0.986 
3 a                 3       1.72                   0.178 
4 b                 4      -0.402                  0.195 
5 b                 5       0.0305                -0.0211
6 b                 6       0.360                 -0.186 

Answer 1

Based on the update, we may loop over the row_number(), get the 'student_mean' values that are not from the current row, get the mean

library(dplyr)
library(purrr)
df %>% 
  group_by(class_id, student_id) %>%
  summarize(student_mean = mean(value), .groups = 'drop_last') %>% 
  mutate(class_mean_othstudents = map_dbl(row_number(), ~ 
          mean(student_mean[-.x]))) %>%
  ungroup

-output

# A tibble: 6 x 4
  class_id student_id student_mean class_mean_othstudents
  <chr>         <dbl>        <dbl>                  <dbl>
1 a                 1       0.256                  0.907 
2 a                 2       0.0999                 0.986 
3 a                 3       1.72                   0.178 
4 b                 4      -0.402                  0.195 
5 b                 5       0.0305                -0.0211
6 b                 6       0.360                 -0.186 

Answer 2

Depending on the statistics you want for each classroom you could calculate them 'manually', e.g. classroom_mean = sum(x) / n; classroom_mean_excluding_the_student_in_question = sum(x) - x / n - 1

E.g.

library(tidyverse)
set.seed(123)
df <- data.frame(
  class_id = c(rep("a", 6), rep("b", 6)),
  student_id = c(rep(1, 3), rep(2, 2), rep(3, 1), rep(4, 2), rep(5, 3), rep(6, 1)),
  value = rnorm(12)
)

df %>% 
  group_by(class_id, student_id)  %>% 
  summarise(student_mean = mean(value)) %>% 
  mutate(class_mean_exc_this_student = (
    sum(student_mean) - student_mean)/(n() - 1)
    )
#> `summarise()` has grouped output by 'class_id'. You can override using the `.groups` argument.
#> # A tibble: 6 x 4
#> # Groups:   class_id [2]
#>   class_id student_id student_mean class_mean_exc_this_student
#>   <chr>         <dbl>        <dbl>                       <dbl>
#> 1 a                 1       0.256                       0.907 
#> 2 a                 2       0.0999                      0.986 
#> 3 a                 3       1.72                        0.178 
#> 4 b                 4      -0.402                       0.195 
#> 5 b                 5       0.0305                     -0.0211
#> 6 b                 6       0.360                      -0.186  

^{Created on 2021-07-13 by the reprex package (v2.0.0)}

Answer 3

Here is a solution which computes student_mean and class_mean_othstudents bottom up as overall mean. The result differs from the other answers posted so far which use the mean of means to compute class_mean_othstudents:

library(data.table)
setDT(df)[, lapply(unique(student_id), 
                   \(sid) .(student_id = sid, 
                            student_mean = mean(value[student_id == sid]),
                            class_mean_othstudents = mean(value[student_id != sid]))) |>
            rbindlist(), 
          by = .(class_id)]

   class_id student_id student_mean class_mean_othstudents
1:        a          1   0.25601839              0.6382870
2:        a          2   0.09989806              0.6207800
3:        a          3   1.71506499              0.1935703
4:        b          4  -0.40207251              0.1128452
5:        b          5   0.03052233             -0.1481104
6:        b          6   0.35981383             -0.1425156

---

For the sake of completeness and for comparison with the other answers here is the version which is using means of means:

library(data.table)
setDT(df)[, .(student_mean = mean(value)), by = .(class_id, student_id)][
  , class_student_mean := 
    .SD[, sapply(student_id, \(sid) mean(student_mean[student_id != sid])), 
        by = class_id]$V1][]

   class_id student_id student_mean class_student_mean
1:        a          1   0.25601839         0.90748153
2:        a          2   0.09989806         0.98554169
3:        a          3   1.71506499         0.17795823
4:        b          4  -0.40207251         0.19516808
5:        b          5   0.03052233        -0.02112934
6:        b          6   0.35981383        -0.18577509

This result is in line with the other two answers which are based on means of means

Data

Note that the same seed as in Jared's answer and in OP's edit ist used.

set.seed(123)
df <- data.frame(
  class_id = c(rep("a", 6), rep("b", 6)),
  student_id = c(rep(1, 3), rep(2, 2), rep(3, 1), rep(4, 2), rep(5, 3), rep(6, 1)),
  value = rnorm(12)
)