Attribute value to new column based on values in similarly called columns

Another solution based in the tidyverse - using pivot_longer - could look as follows.

library(dplyr)
library(tidyr)
library(stringr)

sample2 %>%
  pivot_longer(-c(FID, year)) %>%
  group_by(year, FID) %>%
  slice_min(value, n = 1, with_ties = FALSE) %>%
  mutate(unit = str_sub(name, -1)) %>%
  select(-name, short_distance = value)

# Groups:   year, FID [6]
#     FID  year short_distance unit 
#   <dbl> <dbl>          <dbl> <chr>
# 1    15  1953           NA   1    
# 2    17  1957           62.9 4    
# 3    14  1983           24.3 2    
# 4    12  1990          220.  1    
# 5    12  1994           12.8 3    
# 6    18  2000           18.8 3   

My first couple of attempts at this weren't working like I imagined, either - couldn't always get the NA behavior you want - but here's one that works:

library(dplyr)
library(reshape2) # Or use tidyr if you prefer


sample2 %>%
    # Melt/unpivot to one value per row
    melt(id.vars = c("FID", "year")) %>%
    # Extract the unit number
    mutate(
        unit = sub(x = variable,
                   pattern = "^centroid_distance_",
                   replacement = "")
    ) %>%
    group_by(FID, year) %>% # Group by FID and year to get one row of output for each
    arrange(value) %>%      # Put smallest distance at the top of each group
    slice_head(n = 1)       # Take one row from the top of each group

Here is a solution using dplyr & stringr packages (but you can just import tidyverse):

library(tidyverse)

df <- sample2 %>% 
  gather('centroid', 'dist', 3:length(.)) %>%
  group_by(year) %>%
  slice(if(all(is.na(dist))) 1L else which.min(dist)) %>%
  mutate(centroid = str_replace(centroid, "centroid_distance_", ""))

df

Returns:

# A tibble: 6 x 4
# Groups:   year [6]
    FID  year centroid  dist
  <dbl> <dbl> <chr>    <dbl>
1    15  1953 1         NA  
2    17  1957 4         62.9
3    14  1983 2         24.3
4    12  1990 1        220. 
5    12  1994 3         12.8
6    18  2000 3         18.8

Base R solution

FID <- c(12, 12, 14, 15, 17, 18)
year <- c(1990, 1994, 1983, 1953, 1957, 2000)
centroid_distance_1 <- c(220.3, 220.3, 515.6, NA, 200.2, 22)
centroid_distance_2 <- c(520, 520, 24.3, NA , NA, 51.8)
centroid_distance_3 <- c(NA, 12.8, 124.2, NA, NA, 18.8)
centroid_distance_4 <- c(725.3, 725.3, 44.2, NA, 62.9, 217.9)
sample2 <- data.frame(FID, year, centroid_distance_1, centroid_distance_2, centroid_distance_3, centroid_distance_4)

Apply function min for each row and add it to the data frame as column short_distance. Ignore the warning and handle it in the next operation.

sample2$short_distance <- apply(sample2[,3:6], 1, min, na.rm = TRUE)
#> Warning in FUN(newX[, i], ...): kein nicht-fehlendes Argument für min; gebe Inf
#> zurück
sample2$short_distance[is.infinite(sample2$short_distance)] <- NA #C hange `Inf` created by the `min` function to to `NA`

Get units with which.min. ifelse is required because min.which would drop NA rows.

sample2$unit <- apply(sample2[,3:6], 1, function(x) ifelse(length(which.min(x)) == 0, NA, which.min(x)))

Keep only relevant columns

sample2 <- sample2[, c(1,2,7,8)]
sample2
#>   FID year short_distance unit
#> 1  12 1990          220.3    1
#> 2  12 1994           12.8    3
#> 3  14 1983           24.3    2
#> 4  15 1953             NA   NA
#> 5  17 1957           62.9    4
#> 6  18 2000           18.8    3

^{Created on 2021-01-18 by the reprex package (v0.3.0)}

A data.table solution

setDT(sample2)
s <- melt(sample2, id = 1:2, variable.name = "object", value.name = "distance")   ## pivot
s[, obj := as.numeric(object)    ## transform factor into numeric
  ][, .(shortest = min(distance, na.rm=TRUE), unit= which.min(distance)), by = .(FID, year)   ## calculate the shortest and which
    ][is.infinite(shortest), shortest:= NA   # transform Inf into NA  
      ][]  ## report