fill sequence of scaled numbers in r - r

Question

I'm trying to complete a data.frame with scaled scores.
First I have a set of scores that relate to a grade, and a universal score that has been calculated.
library(dplyr)
df <- tibble(grade = c("X", "E", "D", "C", "B", "A", "Max"),
score = c(0,17,25,33,41,48,60),
universal = c(0,22,44,65,87,108,108))
I expand the frame to include all integer values of score
df %>% complete(score = full_seq(score, period = 1)) %>%
fill(grade, .direction = "down")
I now want to complete the universal score that relates to each integer score based on the relative steps between the previously defined universal scores for each grade.
This is based on a conversion/scaling factor:
(universal boundary for grade above - universal boundary below)/(score boundary grade above - score boundary grade below)
For the grade U this would be (22-0)/(17-0) = 1.29. Each previous score is summed with this factor to find the corresponding next universal score.
So the first part of the result should look like this:
score grade universal
0 U 0
1 U 1.29
2 U 2.59
3 U 3.88
4 U 5.18
5 U 6.47
6 U 7.76
7 U 9.06
8 U 10.35
9 U 11.65
10 U 12.94
11 U 14.24
12 U 15.53
13 U 16.82
14 U 18.12
15 U 19.41
16 U 20.71
17 N 22.00
I'm trying to achieve this with Tidy principles and various combinations of group_by(), complete(), seq(), etc., but haven't been able to achieve it in a neat way. I think my problem is that my max value is outside the grouping variable.
Any help will be much appreciated.

Answer 1

Base R has the approx function to do this linear interpolation. You can use it in a tidyverse context like this:
df %>%
complete(score = full_seq(score, period = 1)) %>%
fill(grade, .direction = "down") %>%
mutate(universal = approx(x=score,y=universal,xout=score)$y)
# A tibble: 61 × 3
score grade universal
<dbl> <chr> <dbl>
1 0 X 0
2 1 X 1.29
3 2 X 2.59
4 3 X 3.88
5 4 X 5.18
6 5 X 6.47
7 6 X 7.76
8 7 X 9.06
9 8 X 10.4
10 9 X 11.6

Answer 2

df %>% mutate(
inc = c(diff(universal) / diff(score), NA)
) %>%
complete(score = full_seq(score, period = 1)) %>%
fill(grade, inc, .direction = "down") %>%
group_by(grade) %>%
mutate(universal = first(universal) + (row_number() - 1) * inc) %>%
ungroup() %>%
print(n = 30)
# # A tibble: 61 × 4
# score grade universal inc
# <dbl> <chr> <dbl> <dbl>
# 1 0 X 0 1.29
# 2 1 X 1.29 1.29
# 3 2 X 2.59 1.29
# 4 3 X 3.88 1.29
# 5 4 X 5.18 1.29
# 6 5 X 6.47 1.29
# 7 6 X 7.76 1.29
# 8 7 X 9.06 1.29
# 9 8 X 10.4 1.29
# 10 9 X 11.6 1.29
# 11 10 X 12.9 1.29
# 12 11 X 14.2 1.29
# 13 12 X 15.5 1.29
# 14 13 X 16.8 1.29
# 15 14 X 18.1 1.29
# 16 15 X 19.4 1.29
# 17 16 X 20.7 1.29
# 18 17 E 22 2.75
# 19 18 E 24.8 2.75
# 20 19 E 27.5 2.75
# 21 20 E 30.2 2.75
# 22 21 E 33 2.75
# 23 22 E 35.8 2.75
# 24 23 E 38.5 2.75
# 25 24 E 41.2 2.75
# 26 25 D 44 2.62
# 27 26 D 46.6 2.62
# 28 27 D 49.2 2.62
# 29 28 D 51.9 2.62
# 30 29 D 54.5 2.62
# # … with 31 more rows
# # ℹ Use `print(n = ...)` to see more rows