Calculating score change at two or more time point

I have a very simple question: Imagine a cognitive test with 6 items, each of which is scored separately on a 0-10 scale
now let's say 5 patients have taken this test at three (or more) different time of the day.

df <- tibble(
  id = rep(1:5, each = 3),
  time = rep(c("morning", "evening", "night"), each = 1, times = 5),
  i1 = round(runif(15, 0, 10)),
  i2 = round(runif(15, 0, 10)),
  i3 = round(runif(15, 0, 10)),
  i4 = round(runif(15, 0, 10)),
  i5 = round(runif(15, 0, 10)),
  i6 = round(runif(15, 0, 10))
)

Now, how can I calculate the changes in the score of each individual item for every patient between different times of the day?
tidyverse approaches are highly appreciated.

P.S: the output should be preferably something like this:

df <- tibble(
  id = rep(1:5, each = 3),
  time = rep(c("morning", "evening", "night"), each = 1, times = 5),
  i1 = round(runif(15, 0, 10)),
  i2 = round(runif(15, 0, 10)),
  i3 = round(runif(15, 0, 10)),
  i4 = round(runif(15, 0, 10)),
  i5 = round(runif(15, 0, 10)),
  i6 = round(runif(15, 0, 10)),
  diff_morning_evening = rep(NA, 15),
  diff_morning_night = rep(NA, 15),
  diff_evening_night = rep(NA, 15),
)

An approach calculating the changes in a compact way:

• 1st row: morning - night
• 2nd row: morning - evening
• 3rd row: evening - night

df %>% 
group_by(id) %>% 
mutate(across(i1:i6, ~ ifelse(is.na(.x - lag(.x)), 
lead(.x, 2) - .x, .x - lag(.x)), 
.names="{.col}_chg")) %>% 
ungroup()
# A tibble: 15 × 14
id time       i1    i2    i3    i4    i5    i6 i1_chg i2_chg i3_chg i4_chg
<int> <chr>   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl>
1     1 morning     1     2     4     9     5     6      7     -1      1     -8
2     1 evening     5     0     4     8     9     4      4     -2      0     -1
3     1 night       8     1     5     1     4     5      3      1      1     -7
4     2 morning     7     7     4     3     2     9     -5     -1      4      5
5     2 evening     8     9     1     2     4     5      1      2     -3     -1
6     2 night       2     6     8     8    10     2     -6     -3      7      6
7     3 morning     9     6     6     1     5     5     -8     -1      2      0
8     3 evening     3     2     8     1     3    10     -6     -4      2      0
9     3 night       1     5     8     1     3     3     -2      3      0      0
10     4 morning     7     2     9     1     5     8      1      1     -6      0
11     4 evening     3     5     9     5     6     3     -4      3      0      4
12     4 night       8     3     3     1     3     2      5     -2     -6     -4
13     5 morning     4     1     3     7     1     0      4      6      4      2
14     5 evening     7     2     7     7     5     2      3      1      4      0
15     5 night       8     7     7     9     8     4      1      5      0      2
# … with 2 more variables: i5_chg <dbl>, i6_chg <dbl>

Summing special rows approach

df %>% 
group_by(id) %>% 
summarize(across(i1:i6, ~ 
.x[which(time == "morning")] + .x[which(time == "night")]))
# A tibble: 5 × 7
id    i1    i2    i3    i4    i5    i6
<int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1     1     9     3     9    10     9    11
2     2     9    13    12    11    12    11
3     3    10    11    14     2     8     8
4     4    15     5    12     2     8    10
5     5    12     8    10    16     9     4

You can use combn to generate all combinations of 2 times, and apply diff to each combination to calculate the change by setting FUN = diff.

library(tidyverse)

df %>% 
  group_by(id) %>% 
  summarise(DIFF = combn(time, 2, paste, collapse = '_'),
            across(i1:i6, ~ combn(.x, 2, diff)), .groups = 'drop')

# # A tibble: 15 × 8
#       id DIFF                   i1        i2        i3        i4        i5        i6
#    <int> <chr[1d]>       <dbl[1d]> <dbl[1d]> <dbl[1d]> <dbl[1d]> <dbl[1d]> <dbl[1d]>
#  1     1 morning_evening         1        -2         0         5         1         3
#  2     1 morning_night          -2         5         1         3        -2        -1
#  3     1 evening_night          -3         7         1        -2        -3        -4
#  4     2 morning_evening         1         5        -2        -3         5         7
#  5     2 morning_night           2        -1         6         2        -2         1
#  6     2 evening_night           1        -6         8         5        -7        -6
# ...

If you want a wide-format output, pass the above code to tidyr::pivot_wider():

... %>%
  pivot_wider(names_from = DIFF, values_from = i1:i6, names_prefix = 'diff_')

# # A tibble: 5 × 19
#      id i1_diff_morning_evening i1_diff_morning_night i1_diff_evening_night i2_diff_morning_evening i2_diff_morning_night i2_diff_evening_night
#   <int>                   <dbl>                 <dbl>                 <dbl>                   <dbl>                 <dbl>                 <dbl>
# 1     1                       1                    -2                    -3                      -2                     5                     7
# 2     2                       1                     2                     1                       5                    -1                    -6
# 3     3                       2                    -1                    -3                       5                    -1                    -6
# 4     4                       1                     2                     1                      -2                    -4                    -2
# 5     5                       6                     7                     1                       1                     0                    -1
#
# … with 12 more variables:
# i3_diff_morning_evening <dbl>, i3_diff_morning_night <dbl>, i3_diff_evening_night <dbl>,
# i4_diff_morning_evening <dbl>, i4_diff_morning_night <dbl>, i4_diff_evening_night <dbl>,
# i5_diff_morning_evening <dbl>, i5_diff_morning_night <dbl>, i5_diff_evening_night <dbl>,
# i6_diff_morning_evening <dbl>, i6_diff_morning_night <dbl>, i6_diff_evening_night <dbl>