# Say it in R with "by", "apply" and friends

R is a language, as Luis Apiolaza pointed out in his recent post. This is absolutely true, and learning a programming language is not much different from learning a foreign language. It takes time and a lot of practice to be proficient in it. I started using R when I moved to the UK and I wonder, if I have a better understanding of English or R by now.

Languages are full of surprises, in particular for non-native speakers. The other day I learned that there is courtesy and curtsey. Both words sounded very similar to me, but of course created some laughter when I mixed them up in an email.

With languages you can get into habits of using certain words and phrases, but sometimes you see or hear something, which shakes you up again. So did the following two lines in R with me:

f <- function(x) x^2sapply(1:10, f)[1]   1   4   9  16  25  36  49  64  81 100
It reminded me of the phrase that everything is a list in R. It showed me again how easily a for loop can be turned into a statement using the apply family of functions and how little I know about all the subtleties of R. I remember how happy I felt, when I finally understood the by function in R. I started to use it all the time, closing my eyes on aggregate and the apply functions family. Here is an example where I calculate the means of the various measurements by species of the famous iris data set using by.

### by

do.call(“rbind”, as.list(  by(iris, list(Species=iris\$Species), function(x){    y <- subset(x, select= -Species)    apply(y, 2, mean)  })))           Sepal.Length Sepal.Width Petal.Length Petal.Widthsetosa            5.006       3.428        1.462       0.246versicolor        5.936       2.770        4.260       1.326virginica         6.588       2.974        5.552       2.026
Now let’s find alternative ways of expressing ourselves, using other words/functions of the R language, such as aggregate, apply, sapply, tapply, data.table, ddply, sqldf, and summaryBy.

### aggregate

The aggregate function splits the data into subsets and computes summary statistics for each of them. The output of aggregate is a data.frame, including a column for species.
iris.x <- subset(iris, select= -Species)iris.s <- subset(iris, select= Species)aggregate(iris.x, iris.s, mean)     Species Sepal.Length Sepal.Width Petal.Length Petal.Width1     setosa        5.006       3.428        1.462       0.2462 versicolor        5.936       2.770        4.260       1.3263  virginica        6.588       2.974        5.552       2.026
Addition: As John Christie points out in the comments, aggregate has also a formula interface, which simplifies the call to:
aggregate( . ~ Species, iris, mean)

### apply and tapply

The combination of tapply and apply achieves a similar result, but this time the output is a matrix and hence I lose the column with species. The species are now the row names.
apply(iris.x, 2, function(x) tapply(x, iris.s, mean))           Sepal.Length Sepal.Width Petal.Length Petal.Widthsetosa            5.006       3.428        1.462       0.246versicolor        5.936       2.770        4.260       1.326virginica         6.588       2.974        5.552       2.026

### split and apply

Here I split the data first into subsets for each of the species and calculate then the mean for each column in the subset. The output is a matrix again, but transposed.
sapply(split(iris.x, iris.s), function(x) apply(x, 2, mean))             setosa versicolor virginicaSepal.Length  5.006      5.936     6.588Sepal.Width   3.428      2.770     2.974Petal.Length  1.462      4.260     5.552Petal.Width   0.246      1.326     2.026

### ddply

Hadley Wickham’s plyr package provides tools for splitting, applying and combining data. The function ddply is similar to the by function, but it returns a data.frame instead of a by list and maintains the column for the species.
library(plyr)ddply(iris, “Species”, function(x){    y <- subset(x, select= -Species)    apply(y, 2, mean)  })     Species Sepal.Length Sepal.Width Petal.Length Petal.Width1     setosa        5.006       3.428        1.462       0.2462 versicolor        5.936       2.770        4.260       1.3263  virginica        6.588       2.974        5.552       2.026
Addition: Sean mentions in the comments an alternative, using the colMeans function, while Andrew reminds us of the reshape package with its functions melt and cast.
ddply(iris, “Species”, function(x) colMeans(subset(x, select= -Species)))## orddply(iris, “Species”, colwise(mean)) ## same output as abovelibrary(reshape)cast(melt(iris, id.vars=‘Species’),formula=Species ~ variable,mean)## same output as above

### summaryBy

The summaryBy function of the doBy package by Søren Højsgaard and Ulrich Halekoh has a very intuitive interface, using formulas.
library(doBy)summaryBy(Sepal.Length + Sepal.Width + Petal.Length + Petal.Width ~ Species, data=iris, FUN=mean)     Species Sepal.Length.mean Sepal.Width.mean Petal.Length.mean Petal.Width.mean1     setosa             5.006            3.428             1.462            0.2462 versicolor             5.936            2.770             4.260            1.3263  virginica             6.588            2.974             5.552            2.026

### sqldf

If you are fluent in SQL, then the sqldf package by Gabor Grothendieck might be the one for you.
library(sqldf)sqldf(“select Species, avg(Sepal_Length), avg(Sepal_Width),     avg(Petal_Length), avg(Petal_Width) from iris     group by Species”)     Species avg(Sepal_Length) avg(Sepal_Width) avg(Petal_Length) avg(Petal_Width)1     setosa             5.006            3.428             1.462            0.2462 versicolor             5.936            2.770             4.260            1.3263  virginica             6.588            2.974             5.552            2.026

### data.table

The data.table package by M Dowle, T Short and S Lianoglou is the real rock star to me. It provides an elegant and fast way to complete the task. The statement reads in plain English from right to left: take columns 1 to 4, split them by the factor in column “Species” and calculate on the sub data (.SD) the means.
library(data.table)iris.dt <- data.table(iris)iris.dt[,lapply(.SD,mean),by=“Species”,.SDcols=1:4]        Species Sepal.Length Sepal.Width Petal.Length Petal.Width[1,]     setosa        5.006       3.428        1.462       0.246[2,] versicolor        5.936       2.770        4.260       1.326[3,]  virginica        6.588       2.974        5.552       2.026

### apply

I should mention that R provides the iris data set also in an array form. The third dimension of the iris3 array holds the species information. Therefore I can use the apply function again, I go down the third and then the second dimension to calculate the means.
apply(iris3, c(3,2), mean)           Sepal L. Sepal W. Petal L. Petal W.Setosa        5.006    3.428    1.462    0.246Versicolor    5.936    2.770    4.260    1.326Virginica     6.588    2.974    5.552    2.026

### Conclusion

Many roads lead to Rome, and there are endless ways of explaining how to get there. I only showed a few I know of, and I am curious to hear yours. As a matter of courtesy I should mention the unknownR package by Matthew Dowle. It helps you to discover what you don’t know that you don’t know in R. Thus, it can help to build your R vocabulary. Of course there is a key difference between R and English. R tells me right away when I make a mistake. Human readers are far more forgiving, but please do point out to me where I made mistakes. I am still hopeful that I can improve, but I need your help.

### R code

The R code of the examples is available on github. For more examples on the apply family see also Neil Saunders’ post.