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

January 28, 2012
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 Iris versicolor (Source: Wikipedia)

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 we calculate the means of the various measurements of the 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 ```

## apply and tapply

The combination of `tapply` and `apply` achieves a similar result, but this time the output is a `matrix` and hence we loose the column with the 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 we split the data first into subsets for each specie 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 ```

## doBy

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 library 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 underground rock star to me. It provides an elegant and fast way to complete our 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 specie information. Therefore we can use the `apply` function again, we 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 off, and I am curious to hear yours.

As a matter of courtesy I should mention the unkownR 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 forgivable, 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.

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