Create a new variable from the minimum in R - r

Question

The data contains four fields: id, x1, x2, and x3.
id <- c(1,2,3,4,5,6,7,8,9,10)
x1 <- c(2,4,5,3,6,4,3,6,7,7)
x2 <- c(0,1,2,6,7,6,0,8,2,2)
x3 <- c(5,3,4,5,8,3,4,2,5,6)
DF <- data.frame(id, x1,x2,x3)
Before I ask the question, let me create a new field (minX) which is the min of (x1,x2,x3)
DF$minX <- pmin(DF$x1, DF$x2, DF$x3)
I need to create a new field, y, that is defined as follows
if min(x1,x2,x3) = x1, then y = "x1"
if min(x1,x2,x3) = x2, then y = "x2"
if min(x1,x2,x3) = x3, then y = "x3"
Note: we assume no ties.

Answer 1

As a simply solution, do:
VARS <- colnames(DF)[-1]
y <- VARS[apply(DF[, -1], MARGIN = 1, FUN = which.min)]
DF$y <- y
The function which.min returns the index of the minimum. If the minimum is not unique it returns the first one. Since you guarantee that there is no tie, this is not an issue here.
Finally, you should be familiar with apply, right? MARGIN = 1 means applying function FUN row-wise, while MARGIN = 2 means applying FUN column-wise. This is an useful function to avoid the need for a for loop when dealing with matrix. Since your data frame only contains numerical/integer values, it is like a matrix hence we can use apply.

Answer 2

Here is another option using pmin and max.col
library(data.table)
setDT(DF)[, c("minx", "y") := list(do.call(pmin, .SD),
names(.SD)[max.col(-1*.SD)]), .SDcols= x1:x3]
DF
# id x1 x2 x3 minx y
# 1: 1 2 0 5 0 x2
# 2: 2 4 1 3 1 x2
# 3: 3 5 2 4 2 x2
# 4: 4 3 6 5 3 x1
3 5: 5 6 7 8 6 x1
# 6: 6 4 6 3 3 x3
# 7: 7 3 0 4 0 x2
# 8: 8 6 8 2 2 x3
# 9: 9 7 2 5 2 x2
#10: 10 7 2 6 2 x2

Answer 3

a data.table solution:
# create variables
id <- c(1,2,3,4,5,6,7,8,9,10)
x1 <- c(2,4,5,3,6,4,3,6,7,7)
x2 <- c(0,1,2,6,7,6,0,8,2,2)
x3 <- c(5,3,4,5,8,3,4,2,5,6)
DF <- data.frame(id, x1,x2,x3)
# load package and set data table, calculating min
library(data.table)
setDT(DF)[, minx := apply(.SD, 1, min), .SDcols=c("x1", "x2", "x3")]
# Create variable with name of minimum
DF[, y := apply(.SD, 1, function(x) names(x)[which.min(x)]), .SDcols = c("x1", "x2", "x3")]
# call result
DF
## id x1 x2 x3 minx y
1: 1 2 0 5 0 x2
2: 2 4 1 3 1 x2
3: 3 5 2 4 2 x2
4: 4 3 6 5 3 x1
5: 5 6 7 8 6 x1
6: 6 4 6 3 3 x3
7: 7 3 0 4 0 x2
8: 8 6 8 2 2 x3
9: 9 7 2 5 2 x2
10: 10 7 2 6 2 x2
The last step can be called directly, without the need to calculate minx.
Please notice that data.table is particularily fast in large data sets.
######## EDIT TO ADD: DPLYR METHOD #########
For completeness, this would be a dplyr method to produce the same (final) result. This solution is credited to #eipi10 in a question I started out of this problem (see here):
DF %>% mutate(y = apply(.[,2:4], 1, function(x) names(x)[which.min(x)]))
This solution takes about the same time as the data.table one provided in the original answer, when applyed to a 1e6 rows data frame (about 17 secs in my sony laptop).