For each row return the column name of the largest value

One option using your data (for future reference, use set.seed() to make examples using sample reproducible):

DF <- data.frame(V1=c(2,8,1),V2=c(7,3,5),V3=c(9,6,4))

colnames(DF)[apply(DF,1,which.max)]
[1] "V3" "V1" "V2"

A faster solution than using apply might be max.col:

colnames(DF)[max.col(DF,ties.method="first")]
#[1] "V3" "V1" "V2"

...where ties.method can be any of "random" "first" or "last"

This of course causes issues if you happen to have two columns which are equal to the maximum. I'm not sure what you want to do in that instance as you will have more than one result for some rows. E.g.:

DF <- data.frame(V1=c(2,8,1),V2=c(7,3,5),V3=c(7,6,4))
apply(DF,1,function(x) which(x==max(x)))

[[1]]
V2 V3 
 2  3 

[[2]]
V1 
 1 

[[3]]
V2 
 2

If you're interested in a data.table solution, here's one. It's a bit tricky since you prefer to get the id for the first maximum. It's much easier if you'd rather want the last maximum. Nevertheless, it's not that complicated and it's fast!

Here I've generated data of your dimensions (26746 * 18).

Data

set.seed(45)
DF <- data.frame(matrix(sample(10, 26746*18, TRUE), ncol=18))

data.table answer:

require(data.table)
DT <- data.table(value=unlist(DF, use.names=FALSE), 
            colid = 1:nrow(DF), rowid = rep(names(DF), each=nrow(DF)))
setkey(DT, colid, value)
t1 <- DT[J(unique(colid), DT[J(unique(colid)), value, mult="last"]), rowid, mult="first"]

Benchmarking:

# data.table solution
system.time({
DT <- data.table(value=unlist(DF, use.names=FALSE), 
            colid = 1:nrow(DF), rowid = rep(names(DF), each=nrow(DF)))
setkey(DT, colid, value)
t1 <- DT[J(unique(colid), DT[J(unique(colid)), value, mult="last"]), rowid, mult="first"]
})
#   user  system elapsed 
#  0.174   0.029   0.227 

# apply solution from @thelatemail
system.time(t2 <- colnames(DF)[apply(DF,1,which.max)])
#   user  system elapsed 
#  2.322   0.036   2.602 

identical(t1, t2)
# [1] TRUE

It's about 11 times faster on data of these dimensions, and data.table scales pretty well too.

Edit: if any of the max ids is okay, then:

DT <- data.table(value=unlist(DF, use.names=FALSE), 
            colid = 1:nrow(DF), rowid = rep(names(DF), each=nrow(DF)))
setkey(DT, colid, value)
t1 <- DT[J(unique(colid)), rowid, mult="last"]

One solution could be to reshape the date from wide to long putting all the departments in one column and counts in another, group by the employer id (in this case, the row number), and then filter to the department(s) with the max value. There are a couple of options for handling ties with this approach too.

library(tidyverse)

# sample data frame with a tie
df <- data_frame(V1=c(2,8,1),V2=c(7,3,5),V3=c(9,6,5))

# If you aren't worried about ties:  
df %>% 
  rownames_to_column('id') %>%  # creates an ID number
  gather(dept, cnt, V1:V3) %>% 
  group_by(id) %>% 
  slice(which.max(cnt)) 

# A tibble: 3 x 3
# Groups:   id [3]
  id    dept    cnt
  <chr> <chr> <dbl>
1 1     V3       9.
2 2     V1       8.
3 3     V2       5.


# If you're worried about keeping ties:
df %>% 
  rownames_to_column('id') %>%
  gather(dept, cnt, V1:V3) %>% 
  group_by(id) %>% 
  filter(cnt == max(cnt)) %>% # top_n(cnt, n = 1) also works
  arrange(id)

# A tibble: 4 x 3
# Groups:   id [3]
  id    dept    cnt
  <chr> <chr> <dbl>
1 1     V3       9.
2 2     V1       8.
3 3     V2       5.
4 3     V3       5.


# If you're worried about ties, but only want a certain department, you could use rank() and choose 'first' or 'last'
df %>% 
  rownames_to_column('id') %>%
  gather(dept, cnt, V1:V3) %>% 
  group_by(id) %>% 
  mutate(dept_rank  = rank(-cnt, ties.method = "first")) %>% # or 'last'
  filter(dept_rank == 1) %>% 
  select(-dept_rank) 

# A tibble: 3 x 3
# Groups:   id [3]
  id    dept    cnt
  <chr> <chr> <dbl>
1 2     V1       8.
2 3     V2       5.
3 1     V3       9.

# if you wanted to keep the original wide data frame
df %>% 
  rownames_to_column('id') %>%
  left_join(
    df %>% 
      rownames_to_column('id') %>%
      gather(max_dept, max_cnt, V1:V3) %>% 
      group_by(id) %>% 
      slice(which.max(max_cnt)), 
    by = 'id'
  )

# A tibble: 3 x 6
  id       V1    V2    V3 max_dept max_cnt
  <chr> <dbl> <dbl> <dbl> <chr>      <dbl>
1 1        2.    7.    9. V3            9.
2 2        8.    3.    6. V1            8.
3 3        1.    5.    5. V2            5.

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