How to find the statistical mode?

Question

In R, mean() and median() are standard functions which do what you\'d expect. mode() tells you the internal storage mode of the objec

Answer 1

A small modification to Ken Williams' answer, adding optional params na.rm and return_multiple.

Unlike the answers relying on names(), this answer maintains the data type of x in the returned value(s).

stat_mode <- function(x, return_multiple = TRUE, na.rm = FALSE) {
  if(na.rm){
    x <- na.omit(x)
  }
  ux <- unique(x)
  freq <- tabulate(match(x, ux))
  mode_loc <- if(return_multiple) which(freq==max(freq)) else which.max(freq)
  return(ux[mode_loc])
}

To show it works with the optional params and maintains data type:

foo <- c(2L, 2L, 3L, 4L, 4L, 5L, NA, NA)
bar <- c('mouse','mouse','dog','cat','cat','bird',NA,NA)

str(stat_mode(foo)) # int [1:3] 2 4 NA
str(stat_mode(bar)) # chr [1:3] "mouse" "cat" NA
str(stat_mode(bar, na.rm=T)) # chr [1:2] "mouse" "cat"
str(stat_mode(bar, return_mult=F, na.rm=T)) # chr "mouse"

Thanks to @Frank for simplification.

Answer 2

This builds on jprockbelly's answer, by adding a speed up for very short vectors. This is useful when applying mode to a data.frame or datatable with lots of small groups:

Mode <- function(x) {
   if ( length(x) <= 2 ) return(x[1])
   if ( anyNA(x) ) x = x[!is.na(x)]
   ux <- unique(x)
   ux[which.max(tabulate(match(x, ux)))]
}

Answer 3

It seems to me that if a collection has a mode, then its elements can be mapped one-to-one with the natural numbers. So, the problem of finding the mode reduces to producing such a mapping, finding the mode of the mapped values, then mapping back to some of the items in the collection. (Dealing with NA occurs at the mapping phase).

I have a histogram function that operates on a similar principal. (The special functions and operators used in the code presented herein should be defined in Shapiro and/or the neatOveRse. The portions of Shapiro and neatOveRse duplicated herein are so duplicated with permission; the duplicated snippets may be used under the terms of this site.) R pseudocode for histogram is

.histogram <- function (i)
        if (i %|% is.empty) integer() else
        vapply2(i %|% max %|% seqN, `==` %<=% i %O% sum)

histogram <- function(i) i %|% rmna %|% .histogram

(The special binary operators accomplish piping, currying, and composition) I also have a maxloc function, which is similar to which.max, but returns all the absolute maxima of a vector. R pseudocode for maxloc is

FUNloc <- function (FUN, x, na.rm=F)
        which(x == list(identity, rmna)[[na.rm %|% index.b]](x) %|% FUN)

maxloc <- FUNloc %<=% max

minloc <- FUNloc %<=% min # I'M THROWING IN minloc TO EXPLAIN WHY I MADE FUNloc

Then

imode <- histogram %O% maxloc

and

x %|% map %|% imode %|% unmap

will compute the mode of any collection, provided appropriate map-ping and unmap-ping functions are defined.

Answer 4

Here are several ways you can do it in Theta(N) running time

from collections import defaultdict

def mode1(L):
    counts = defaultdict(int)
    for v in L:
        counts[v] += 1
    return max(counts,key=lambda x:counts[x])

def mode2(L):
    vals = set(L)
    return max(vals,key=lambda x: L.count(x))

def mode3(L):
    return max(set(L), key=lambda x: L.count(x))

Answer 5

Adding in raster::modal() as an option, although note that raster is a hefty package and may not be worth installing if you don't do geospatial work.

The source code could be pulled out of https://github.com/rspatial/raster/blob/master/src/modal.cpp and https://github.com/rspatial/raster/blob/master/R/modal.R into a personal R package, for those who are particularly keen.

Answer 6

I found Ken Williams post above to be great, I added a few lines to account for NA values and made it a function for ease.

Mode <- function(x, na.rm = FALSE) {
  if(na.rm){
    x = x[!is.na(x)]
  }

  ux <- unique(x)
  return(ux[which.max(tabulate(match(x, ux)))])
}