Grouping Functions (Tapply, By, Aggregate) and the *Apply Family

Grouping functions (tapply, by, aggregate) and the *apply family

R has many *apply functions which are ably described in the help files (e.g. ?apply). There are enough of them, though, that beginning useRs may have difficulty deciding which one is appropriate for their situation or even remembering them all. They may have a general sense that "I should be using an *apply function here", but it can be tough to keep them all straight at first.

Despite the fact (noted in other answers) that much of the functionality of the *apply family is covered by the extremely popular plyr package, the base functions remain useful and worth knowing.

This answer is intended to act as a sort of signpost for new useRs to help direct them to the correct *apply function for their particular problem. Note, this is not intended to simply regurgitate or replace the R documentation! The hope is that this answer helps you to decide which *apply function suits your situation and then it is up to you to research it further. With one exception, performance differences will not be addressed.

apply - When you want to apply a function to the rows or columns
of a matrix (and higher-dimensional analogues); not generally advisable for data frames as it will coerce to a matrix first.

 # Two dimensional matrix
 M <- matrix(seq(1,16), 4, 4)

 # apply min to rows
 apply(M, 1, min)
 [1] 1 2 3 4

 # apply max to columns
 apply(M, 2, max)
 [1]  4  8 12 16

 # 3 dimensional array
 M <- array( seq(32), dim = c(4,4,2))

 # Apply sum across each M[*, , ] - i.e Sum across 2nd and 3rd dimension
 apply(M, 1, sum)
 # Result is one-dimensional
 [1] 120 128 136 144

 # Apply sum across each M[*, *, ] - i.e Sum across 3rd dimension
 apply(M, c(1,2), sum)
 # Result is two-dimensional
      [,1] [,2] [,3] [,4]
 [1,]   18   26   34   42
 [2,]   20   28   36   44
 [3,]   22   30   38   46
 [4,]   24   32   40   48

If you want row/column means or sums for a 2D matrix, be sure to
investigate the highly optimized, lightning-quick colMeans,
rowMeans, colSums, rowSums.

lapply - When you want to apply a function to each element of a
list in turn and get a list back.
This is the workhorse of many of the other *apply functions. Peel
back their code and you will often find lapply underneath.
```
 x <- list(a = 1, b = 1:3, c = 10:100) 
 lapply(x, FUN = length) 
 $a 
 [1] 1
 $b 
 [1] 3
 $c 
 [1] 91
 lapply(x, FUN = sum) 
 $a 
 [1] 1
 $b 
 [1] 6
 $c 
 [1] 5005
```
sapply - When you want to apply a function to each element of a
list in turn, but you want a vector back, rather than a list.
If you find yourself typing unlist(lapply(...)), stop and consider
sapply.
```
 x <- list(a = 1, b = 1:3, c = 10:100)
 # Compare with above; a named vector, not a list 
 sapply(x, FUN = length)  
 a  b  c   
 1  3 91

 sapply(x, FUN = sum)   
 a    b    c    
 1    6 5005 
```
In more advanced uses of sapply it will attempt to coerce the
result to a multi-dimensional array, if appropriate. For example, if our function returns vectors of the same length, sapply will use them as columns of a matrix:
```
 sapply(1:5,function(x) rnorm(3,x))
```
If our function returns a 2 dimensional matrix, sapply will do essentially the same thing, treating each returned matrix as a single long vector:
```
 sapply(1:5,function(x) matrix(x,2,2))
```
Unless we specify simplify = "array", in which case it will use the individual matrices to build a multi-dimensional array:
```
 sapply(1:5,function(x) matrix(x,2,2), simplify = "array")
```
Each of these behaviors is of course contingent on our function returning vectors or matrices of the same length or dimension.

vapply - When you want to use sapply but perhaps need to
squeeze some more speed out of your code or want more type safety.

For vapply, you basically give R an example of what sort of thing
your function will return, which can save some time coercing returned
values to fit in a single atomic vector.

 x <- list(a = 1, b = 1:3, c = 10:100)
 #Note that since the advantage here is mainly speed, this
 # example is only for illustration. We're telling R that
 # everything returned by length() should be an integer of 
 # length 1. 
 vapply(x, FUN = length, FUN.VALUE = 0L) 
 a  b  c  
 1  3 91

mapply - For when you have several data structures (e.g.
vectors, lists) and you want to apply a function to the 1st elements
of each, and then the 2nd elements of each, etc., coercing the result
to a vector/array as in sapply.
This is multivariate in the sense that your function must accept
multiple arguments.
```
 #Sums the 1st elements, the 2nd elements, etc. 
 mapply(sum, 1:5, 1:5, 1:5) 
 [1]  3  6  9 12 15
 #To do rep(1,4), rep(2,3), etc.
 mapply(rep, 1:4, 4:1)   
 [[1]]
 [1] 1 1 1 1

 [[2]]
 [1] 2 2 2

 [[3]]
 [1] 3 3

 [[4]]
 [1] 4
```

Map - A wrapper to mapply with SIMPLIFY = FALSE, so it is guaranteed to return a list.

 Map(sum, 1:5, 1:5, 1:5)
 [[1]]
 [1] 3

 [[2]]
 [1] 6

 [[3]]
 [1] 9

 [[4]]
 [1] 12

 [[5]]
 [1] 15

rapply - For when you want to apply a function to each element of a nested list structure, recursively.

To give you some idea of how uncommon rapply is, I forgot about it when first posting this answer! Obviously, I'm sure many people use it, but YMMV. rapply is best illustrated with a user-defined function to apply:

 # Append ! to string, otherwise increment
 myFun <- function(x){
     if(is.character(x)){
       return(paste(x,"!",sep=""))
     }
     else{
       return(x + 1)
     }
 }

 #A nested list structure
 l <- list(a = list(a1 = "Boo", b1 = 2, c1 = "Eeek"), 
           b = 3, c = "Yikes", 
           d = list(a2 = 1, b2 = list(a3 = "Hey", b3 = 5)))


 # Result is named vector, coerced to character          
 rapply(l, myFun)

 # Result is a nested list like l, with values altered
 rapply(l, myFun, how="replace")

tapply - For when you want to apply a function to subsets of a
vector and the subsets are defined by some other vector, usually a
factor.
The black sheep of the *apply family, of sorts. The help file's use of
the phrase "ragged array" can be a bit confusing, but it is actually
quite simple.
A vector:
```
 x <- 1:20
```
A factor (of the same length!) defining groups:
```
 y <- factor(rep(letters[1:5], each = 4))
```
Add up the values in x within each subgroup defined by y:
```
 tapply(x, y, sum)  
  a  b  c  d  e  
 10 26 42 58 74 
```
More complex examples can be handled where the subgroups are defined
by the unique combinations of a list of several factors. tapply is
similar in spirit to the split-apply-combine functions that are
common in R (aggregate, by, ave, ddply, etc.) Hence its
black sheep status.

using of multiple functions using apply family, aggregation, with etc

each in package plyr does the trick for you too:

library(plyr)
df <- matrix(data=rnorm(50), 10, 5)
aaply(df, 2, each(min, mean, max, median, sum))

If you want another input/output format, you can play with the different functions from dplyr.

Apply multiple functions to column using tapply

You can certainly do stuff like this using ddply from the plyr package:

dat <- data.frame(x = rep(letters[1:3],3),y = 1:9)

ddply(dat,.(x),summarise,total = NROW(piece), count = sum(y))
  x total count
1 a     3    12
2 b     3    15
3 c     3    18

You can keep listing more summary functions, beyond just two, if you like. Note I'm being a little tricky here in calling NROW on an internal variable in ddply called piece. You could have just done something like length(y) instead. (And probably should; referencing the internal variable piece isn't guaranteed to work in future versions, I think. Do as I say, not as I do and just use length().)

Is there a function in R to connect tapply with round?

Is it what you are looking for? I added round(c(...), digits = 2) around the group of summary functions (mean, sd, etc.) so the function does the rounding inside tapply without creating a new object.

Edit: better version without repeating the round() function.

tapply(iris$Sepal.Length, iris$Species, 
       function(x){round(c("mean" = mean(x, na.rm = TRUE),
                     "sd" = sd(x, na.rm = TRUE), 
                     "med" = median(x, na.rm = TRUE), 
                     "min" = min(x, na.rm = TRUE), 
                     "max"= max(x, na.rm = TRUE)), digits = 2)})
#> $setosa
#> mean   sd  med  min  max 
#> 5.01 0.35 5.00 4.30 5.80 
#> 
#> $versicolor
#> mean   sd  med  min  max 
#> 5.94 0.52 5.90 4.90 7.00 
#> 
#> $virginica
#> mean   sd  med  min  max 
#> 6.59 0.64 6.50 4.90 7.90

^{Created on 2022-05-10 by the reprex package (v2.0.1)}

Use tapply(dataframe , index, function) in R giving as argument to the function 2 columns

If there are more than one column to be summarised, use aggregate instead of tapply (as tapply works for a single column)

aggregate(.~ indexes, transform(df1, indexes = indexes), FUN = yourfun)

Or another option is by

by(df1, list(indexes), FUN = yourfun)

Or it may be more flexible with tidyverse

library(dplyr)
df1 %>%
    group_by(indexes) %>%
    summarise(across(c(x, y), yourfun), .groups = 'drop')

Using a small reproducible example

indexes = rep(1:2, c(3, 2))
by(mtcars[1:5, 1:5], indexes, FUN = sum)

Data frame grouping using Group by or Aggregate in R

If you consider using a data.table instead of a data.frame (note that a data.table inherits from data.frame) this is most easily achieved

library(data.table)

ID = c(rep("A",3), rep("B",5), rep("C",4))
NRT = c(3,3,4,5,5,3,3,4,3,3,5,5)
df = as.data.frame(cbind(ID,NRT))

dt <- as.data.table(df)
dt[, list("NRT (Average)" = mean(NRT)), by = ID]

   ID NRT (Average)
1:  A    3.333333
2:  B    4.000000
3:  C    4.000000

If you want the table to be printed exactly as you posted you can do the following

library(data.table)
dt <- data.table(ID = c(rep("A",3), rep("B",5), rep("C",4)), NRT = c(3,3,4,5,5,3,3,4,3,3,5,5))
dt[, "NRT(Average)" := paste0(mean(NRT), " (average for NRT for ", ID, ")"), by = ID]
dt[, .SD[1], by = ID][, c(1, 3)]

   ID                             NRT(Average)
1:  A 3.33333333333333 (average for NRT for A)
2:  B                4 (average for NRT for B)
3:  C                4 (average for NRT for C)

Grouping Functions (Tapply, By, Aggregate) and the *Apply Family