How I can calculate correlation between each variable within each group in R using dplyr package?

Question

Let's say i have data frame in R that looks like this :

var2 = c(rep("A",3),rep("B",3),rep("C",3),rep("D",3),rep("E",3),rep("F",3),
         rep("H",3),rep("I",3))

y2 = c(-1.23, -0.983, 1.28, -0.268, -0.46, -1.23,
            1.87, 0.416, -1.99, 0.289, 1.7, -0.455,
           -0.648, 0.376, -0.887,0.534,-0.679,-0.923,
           0.987,0.324,-0.783,-0.679,0.326,0.998);length(y2)
group2 = c(rep(1,6),rep(2,6),rep(3,6),rep(1,6))
data2 = tibble(var2,group2,y2)

with output :

# A tibble: 24 × 3
   var2  group2     y2
   <chr>  <dbl>  <dbl>
 1 A          1 -1.23 
 2 A          1 -0.983
 3 A          1  1.28 
 4 B          1 -0.268
 5 B          1 -0.46 
 6 B          1 -1.23 
 7 C          2  1.87 
 8 C          2  0.416
 9 C          2 -1.99 
10 D          2  0.289
11 D          2  1.7  
12 D          2 -0.455
13 E          3 -0.648
14 E          3  0.376
15 E          3 -0.887
16 F          3  0.534
17 F          3 -0.679
18 F          3 -0.923
19 H          1  0.987
20 H          1  0.324
21 H          1 -0.783
22 I          1 -0.679
23 I          1  0.326
24 I          1  0.998

i want to calculate the correlation of each distinct pair in R within each group using dplyr. Ideally i want the resulted tibble to look like this (the 4th column to contain the values of each correlation pair):

which ideally must look like this :

group	var1	var2	value
1	A	B	cor(A,B)
1	A	H	cor(A,H)
1	A	I	cor(A,I)
1	B	H	cor(B,H)
1	B	I	cor(B,I)
1	H	I	cor(H,I)
2	C	D	cor(C,D)
3	E	F	cor(E,F)

How i can do that in R ? Any help ?

Answer 1

A possible solution:

library(tidyverse)

data2 %>%
  group_by(group2) %>% 
  group_split() %>% 
  map(\(x) x %>% group_by(var2) %>% 
  group_map(~ data.frame(.x[-1]) %>% set_names(.y)) %>% 
  bind_cols() %>% cor %>% 
  {data.frame(row = rownames(.)[row(.)[upper.tri(.)]], 
              col = colnames(.)[col(.)[upper.tri(.)]], 
              corr = .[upper.tri(.)])}) %>% 
  imap_dfr(~ data.frame(group = .y, .x))

#>   group row col       corr
#> 1     1   A   B -0.9949738
#> 2     1   A   H -0.9581357
#> 3     1   B   H  0.9819901
#> 4     1   A   I  0.8533855
#> 5     1   B   I -0.9012948
#> 6     1   H   I -0.9669093
#> 7     2   C   D  0.4690460
#> 8     3   E   F -0.1864518

Answer 2

if you are okay with repeating the functions you can do:

fun <- function(x, y){
  a <- split(x, y)
  col1 <- combn(names(a), 2, paste, collapse = '_')
  col2 <- combn(unname(a), 2, do.call, what='cor')
  data.frame(vars = col1, cor = col2)
}

data2 %>%
  group_by(group2)%>%
  summarise(fun(y2, var2), .groups = 'drop')

# A tibble: 8 x 3
# Groups:   group2 [3]
  group2 vars     cor
   <dbl> <chr>  <dbl>
1      1 A_B   -0.995
2      1 A_H   -0.958
3      1 A_I    0.853
4      1 B_H    0.982
5      1 B_I   -0.901
6      1 H_I   -0.967
7      2 C_D    0.469
8      3 E_F   -0.186

If you do not want to repeat the functions as the process might be expensive, you can do:

 data2 %>%
      group_by(group2)%>%
      summarise(s=combn(split(y2, var2), 2, 
      \(x)stack(setNames(cor(x[[1]], x[[2]]), paste(names(x), collapse='_'))),
          simplify = FALSE),.groups = 'drop') %>%
      unnest(s)

# A tibble: 8 x 3
  group2 values ind  
   <dbl>  <dbl> <fct>
1      1 -0.995 A_B  
2      1 -0.958 A_H  
3      1  0.853 A_I  
4      1  0.982 B_H  
5      1 -0.901 B_I  
6      1 -0.967 H_I  
7      2  0.469 C_D  
8      3 -0.186 E_F  

Answer 3

Another option would be widyr::pairwise_cor which requires to first add an identifier for the "observation":

library(widyr)
library(dplyr)

data2 %>%
  group_by(var2, group2) %>%
  mutate(obs = row_number()) |> 
  ungroup() %>% 
  split(.$group2) %>%
  lapply(function(x) widyr::pairwise_cor(x, var2, obs, y2, upper = FALSE)) %>%
  bind_rows(.id = "group2")
#> # A tibble: 8 × 4
#>   group2 item1 item2 correlation
#>   <chr>  <chr> <chr>       <dbl>
#> 1 1      A     B          -0.995
#> 2 1      A     H          -0.958
#> 3 1      B     H           0.982
#> 4 1      A     I           0.853
#> 5 1      B     I          -0.901
#> 6 1      H     I          -0.967
#> 7 2      C     D           0.469
#> 8 3      E     F          -0.186