r average of distance by Id - r

Question

I have a dataset with two groups of subjects, Group A, Group B like this.
Id Group Age
1 A 17
2 A 14
3 A 10
4 A 17
5 A 12
6 A 6
7 A 18
8 A 7
9 B 18
9 B 13
10 B 6
10 B 12
11 B 16
11 B 17
12 B 11
12 B 18
The subjects in Group A are unique. One row per subject. The subjects in Group B are not unique. There are two or in some cases 3 rows of observations per subject in Group B, example ID 9, 10, 10 etc.
What I am trying to do is
a) estimate the average distance of subjects in GroupB to everyone in Group A. Using Age to estimate the distance.
b) estimate the distance of subjects in GroupB to the mode of subjects in Group A. Using Age to estimate the mode in Group A and Age in Group B to estimate the distance from the mode.
Expecting a dataset like this.
ID Group Age AvDistance DistanceToMedian
1 A 17 NA NA
2 A 14 NA NA
3 A 10 NA NA
4 A 17 NA NA
5 A 12 NA NA
6 A 6 NA NA
7 A 18 NA NA
8 A 7 NA NA
9 B 18 6 2.11
9 B 13 3.875 2.88
10 B 6 ... ...
10 B 12 ... ...
11 B 16 ... ...
11 B 17 ... ...
12 B 11 ... ...
12 B 18 ... ...
I can do this manually, any suggestions on how to make this more efficient is much appreciated. Thanks.
# Estimate Average Distance of Id in Group B to all subjects in Group A
(sqrt((17 - 18)^2)+ sqrt((14-18)^2)+ sqrt((10-18)^2) + sqrt((17-18)^2) + sqrt((12-18)^2) + sqrt((6-18)^2) + sqrt((18-18)^2) + sqrt((7-18)^2))/8 = 6
(sqrt((17 - 13)^2)+ sqrt((14-13)^2)+ sqrt((10 - 13)^2) + sqrt((17-13)^2) + sqrt((12-13)^2) + sqrt((6-13)^2) + sqrt((18-13)^2) + sqrt((7-13)^2))/8 = 3.875
estimate_mode <- function(x) {
d <- density(x)
d$x[which.max(d$y)]
}
# Estimate Mode for Age in Group A
x <- c(17, 14, 10, 17, 12, 6, 18, 7)
estimate_mode(x)
m1 <- estimate_mode(x)
# Estimate Mode of
sqrt((18 - m1)^2) = 2.11
sqrt((13 - m1)^2) =2.88

Answer 1

This will be easier with a unique row ID, so I'll create one:
library(dplyr)
library(tibble)
df = df %>%
mutate(rownum = paste0("row", row_number()))
ages = setNames(df$Age, df$rownum)
## make a distance matrix
dist = outer(ages[df$Group == "B"], ages[df$Group == "A"], FUN = \(x, y) abs(x - y))
## calculate average distances
av_dist = data.frame(AvDist = rowMeans(dist)) %>% rownames_to_column("rownum")
## calculate median age for A
med_a = median(ages[df$Group == "A"])
## add back to original data
df %>%
left_join(av_dist, by = "rownum") %>%
mutate(DistanceToMedian = ifelse(Group == "B", abs(Age - med_a), NA))
# Id Group Age rownum AvDist DistanceToMedian
# 1 1 A 17 row1 NA NA
# 2 2 A 14 row2 NA NA
# 3 3 A 10 row3 NA NA
# 4 4 A 17 row4 NA NA
# 5 5 A 12 row5 NA NA
# 6 6 A 6 row6 NA NA
# 7 7 A 18 row7 NA NA
# 8 8 A 7 row8 NA NA
# 9 9 B 18 row9 5.375 5
# 10 9 B 13 row10 3.875 0
# 11 10 B 6 row11 6.625 7
# 12 10 B 12 row12 3.875 1
# 13 11 B 16 row13 4.375 3
# 14 11 B 17 row14 4.625 4
# 15 12 B 11 row15 4.125 2
# 16 12 B 18 row16 5.375 5
I used median, not mode, because I was looking at your column names, but you can easily swap in your mode instead.
Using this sample data:
df = read.table(text = 'Id Group Age
1 A 17
2 A 14
3 A 10
4 A 17
5 A 12
6 A 6
7 A 18
8 A 7
9 B 18
9 B 13
10 B 6
10 B 12
11 B 16
11 B 17
12 B 11
12 B 18', header = T)