R : Aggregation And Restructuring Data (Transpose, aggregate, melt, cast)

Transpose

The transpose (reversing rows and columns) is perhaps the simplest method of reshaping a dataset. Use the t() function to transpose a matrix or a data frame. In the latter case, row names become variable (column) names. An example is presented in the next listing.

Listing 1 Transposing a dataset

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> cars <- mtcars[1:5,1:4] > cars mpg cyl disp hp Mazda RX4 21.0 6 160 110 Mazda RX4 Wag 21.0 6 160 110 Datsun 710 22.8 4 108 93 Hornet 4 Drive 21.4 6 258 110 Hornet Sportabout 18.7 8 360 175 > t(cars) Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive Hornet Sportabout mpg 21 21 22.8 21.4 18.7 cyl 6 6 4.0 6.0 8.0 disp 160 160 108.0 258.0 360.0 hp 110 110 93.0 110.0 175.0

Listing 1 uses a subset of the mtcars dataset in order to conserve space on the page. You’ll see a more flexible way of transposing data when we look at the reshape package later in this article.

Aggregating data

It’s relatively easy to collapse data in R using one or more by variables and a defined function. The format is

1	aggregate(x, by, FUN)

where x is the data object to be collapsed, by is a list of variables that will be crossed to form the new observations, and FUN is the scalar function used to calculate summary statistics that will make up the new observation values.

As an example, we’ll aggregate the mtcars data by number of cylinders and gears, returning means on each of the numeric variables (see the next listing).

Listing 2 Aggregating data

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> options(digits=3) > attach(mtcars) > aggdata <-aggregate(mtcars, by=list(cyl,gear), FUN=mean, na.rm=TRUE) > aggdata Group.1 Group.2 mpg cyl disp hp drat wt qsec vs am gear carb 1 4 3 21.5 4 120 97 3.70 2.46 20.0 1.0 0.00 3 1.00 2 6 3 19.8 6 242 108 2.92 3.34 19.8 1.0 0.00 3 1.00 3 8 3 15.1 8 358 194 3.12 4.10 17.1 0.0 0.00 3 3.08 4 4 4 26.9 4 103 76 4.11 2.38 19.6 1.0 0.75 4 1.50 5 6 4 19.8 6 164 116 3.91 3.09 17.7 0.5 0.50 4 4.00 6 4 5 28.2 4 108 102 4.10 1.83 16.8 0.5 1.00 5 2.00 7 6 5 19.7 6 145 175 3.62 2.77 15.5 0.0 1.00 5 6.00 8 8 5 15.4 8 326 300 3.88 3.37 14.6 0.0 1.00 5 6.00

In these results, Group.1 represents the number of cylinders (4, 6, or  and Group.2 represents the number of gears (3, 4, or 5). For example, cars with 4 cylinders and 3 gears have a mean of 21.5 miles per gallon (mpg).

When you’re using the aggregate() function , the by variables must be in a list (even if there’s only one). You can declare a custom name for the groups from within the list, for instance, using by=list(Group.cyl=cyl, Group.gears=gear).

The function specified can be any built-in or user-provided function. This gives the aggregate command a great deal of power. But when it comes to power, nothing beats the reshape package.

The reshape package

The reshape package is a tremendously versatile approach to both restructuring and aggregating datasets. Because of this versatility, it can be a bit challenging to learn.

We’ll go through the process slowly and use a small dataset so that it’s clear what’s happening. Because reshape isn’t included in the standard installation of R, you’ll need to install it one time, using install.packages(“reshape”).

Basically, you’ll “melt” data so that each row is a unique ID-variable combination. Then you’ll “cast” the melted data into any shape you desire. During the cast, you can aggregate the data with any function you wish. The dataset you’ll be working with is shown in table 1.

Table 1 The original dataset (mydata)

ID	Time	X1	X2
1	1	5	6
1	2	3	5
2	1	6	1
2	2	2	4

In this dataset, the measurements are the values in the last two columns (5, 6, 3, 5, 6, 1, 2, and 4). Each measurement is uniquely identified by a combination of ID variables (in this case ID, Time, and whether the measurement is on X1 or X2). For example, the measured value 5 in the first row is uniquely identified by knowing that it’s from observation (ID) 1, at Time 1, and on variable X1.

Melting

When you melt a dataset, you restructure it into a format where each measured variable is in its own row, along with the ID variables needed to uniquely identify it. If you melt the data from table 1, using the following code

1 2	library(reshape) md <- melt(mydata, id=(c("id", "time")))

You end up with the structure shown in table 2.

Table 2 The melted dataset

ID	Time	Variable	Value
1	1	X1	5
1	2	X1	3
2	1	X1	6
2	2	X1	2
1	1	X2	6
1	2	X2	5
2	1	X2	1
2	2	X2	4

Note that you must specify the variables needed to uniquely identify each measurement (ID and Time) and that the variable indicating the measurement variable names (X1 or X2) is created for you automatically.

Now that you have your data in a melted form, you can recast it into any shape, using the cast() function.

Casting

The cast() function starts with melted data and reshapes it using a formula that you provide and an (optional) function used to aggregate the data. The format is

1	newdata <- cast(md, formula, FUN)

Where md is the melted data, formula describes the desired end result, and FUN is the (optional) aggregating function. The formula takes the form

1	rowvar1 + rowvar2 + … ~ colvar1 + colvar2 + …

In this formula, rowvar1 + rowvar2 + … define the set of crossed variables that define the rows, and colvar1 + colvar2 + … define the set of crossed variables that define the columns. See the examples in figure 1. (click to enlarge the image)

Figure 1 Reshaping data with the melt() and cast() functions

Because the formulas on the right side (d, e, and f) don’t include a function, the data is reshaped. In contrast, the examples on the left side (a, b, and c) specify the mean as an aggregating function. Thus the data are not only reshaped but aggregated as well. For example, (a) gives the means on X1 and X2 averaged over time for each observation. Example (b) gives the mean scores of X1 and X2 at Time 1 and Time 2, averaged over observations. In (c) you have the mean score for each observation at Time 1 and Time 2, averaged over X1 and X2.

As you can see, the flexibility provided by the melt() and cast() functions is amazing. There are many times when you’ll have to reshape or aggregate your data prior to analysis. For example, you’ll typically need to place your data in what’s called long format resembling table 2 when analyzing repeated measures data (data where multiple measures are recorded for each observation).