Chapter 5 Data Management and Manipulations

In this chapter, we are going to see modify certain attributes of data (like names), how to extract a subset of data, how to clean up the data from missing values, etc. We have already seen some of these topics but here we are going to be systematic and focus on the underlying principles.

5.1 Attaching Names to the Elements of an Object

We can either provide a name for each element of a vector from the beginning when we create the vector as in this example

x <- c(Left=1, Middle=2, Right=3)
x
##   Left Middle  Right 
##      1      2      3
names(x)
## [1] "Left"   "Middle" "Right"

Or we can first create a vector and then name the elements using names function. For example, let us create a vector of integers 1 to 3. By default, there’s no name attribute attached so when we call the names function on x, names(x), it returns NULL. However, we can give a name to each element of the vector x. So for example, we can say the first element is called Left, the second element is called Middle, and the third element is called Right. So now when we print out x vector, we get a vector 1, 2, 3 but then each one has a name over it, which is the name we just specified. So when we call the names function we get also the names that are associated with each element of the vector Left, Middle, Right:

x <- c(1, 2, 3)                           # create a vector 
names(x)                                  # no names attached yet
## NULL

names(x) <- c("Left", "Middle", "Right")  # attach names
x
##   Left Middle  Right 
##      1      2      3

Naming objects is very useful for writing readable code and self-describing objects.

And matrices can also have name, these are called dimnames:

M <- matrix(1:4, nrow = 2, ncol = 2)
dimnames(M) <- list(c("Top", "Bottom"), c("Left", "Right")) 
M
##        Left Right
## Top       1     3
## Bottom    2     4

Column names and row names can be set separately using the colnames and rownames functions:

M <- matrix(1:4, nrow = 2, ncol = 2)
rownames(M) <- c("Top", "Bottom")
colnames(M) <- c("Left", "Right")
M
##        Left Right
## Top       1     3
## Bottom    2     4

Alternatively,

row_names <- c("Top", "Bottom")
col_names <- c("Left", "Right")
M <- matrix(1:4, nrow = 2, ncol = 2, dimnames = list(row_names, col_names))
M
##        Left Right
## Top       1     3
## Bottom    2     4

For data frames, there is a separate function for setting the row names, the row.names() function. Also, data frames do not have column names, they just have names (like lists). So to set the column names of a data frame just use the names() function. Here is a quick summary:

Object Function to Set Column Names
data frame names()
matrix colnames()

Finally, lists can also have names:

x <- list(x = 1, y = 2, z = 3) 
x
## $x
## [1] 1
## 
## $y
## [1] 2
## 
## $z
## [1] 3

5.2 Subsetting R Objects

There are three operators that can be used to extract subsets of R objects.

Operator Description
[ Always returns an object of the same class as the original. It can be used to select multiple elements of an object.
[[ Extracts elements of a list or a data frame. It can only be used to extract a single element and the class of the returned object will not necessarily be a list or data frame.
$ Extract elements of a list or data frame by literal name.

5.2.1 Subsetting a Vector

Vectors are basic objects in R and they can be subsetted using the [ operator.

x <- c("X", "Y", "Z", "Z", "Z", "X")  
x[1]    # Extract the first element
## [1] "X"

x[2]    # Extract the second element
## [1] "Y"

The [ operator can be used to extract multiple elements of a vector by passing the operator an integer sequence. Here we extract the first four elements of the vector.

x <- c("X", "Y", "Z", "Z", "Z", "X")
x[2:4]
## [1] "Y" "Z" "Z"

The sequence does not have to be in order; you can specify any arbitrary integer vector.

x <- c("X", "Y", "Z", "Z", "Z", "X")
x[c(1, 3, 5)]
## [1] "X" "Z" "Z"

We can also pass a logical sequence to the [ operator to extract elements of a vector that satisfy a given condition. For example, here we want the elements of x that come lexicographically after the letter Y.

x <- c("X", "Y", "Z", "T", "Z", "Z", "X", "T")
indices <- x > "T"
indices
## [1]  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE FALSE

x[indices]   # elements of x that comes after T in the alphabet
## [1] "X" "Y" "Z" "Z" "Z" "X"

Another, more compact, way to do this would be to skip the creation of a logical vector and just subset the vector directly with the logical expression.

x <- c("X", "Y", "Z", "T", "Z", "Z", "X", "T")
x[x>"T"]   # elements of x that comes after T in the alphabet
## [1] "X" "Y" "Z" "Z" "Z" "X"

5.2.2 Subsetting a Matrix

Matrices can be subsetted in the usual way with \((i,j)\) type indices. Here, we create simple 2×3 matrix with the matrix function.

M <- matrix(1:8, 2)
M
##      [,1] [,2] [,3] [,4]
## [1,]    1    3    5    7
## [2,]    2    4    6    8

M[2, 1]       # the  (2,1)  element of the matrix
## [1] 2

M[1, 3]       # the  (1,3)  element of the matrix
## [1] 5

Indices can also be missing. This behavior is used to access entire rows or columns of a matrix.

M <- matrix(1:8, 2)
M
##      [,1] [,2] [,3] [,4]
## [1,]    1    3    5    7
## [2,]    2    4    6    8

M[2, ]       # the  second row of the matrix
## [1] 2 4 6 8

M[, 3]       # the  third column of the matrix
## [1] 5 6

5.2.2.1 Dropping matrix dimensions

By default, when a single element of a matrix is retrieved, it is returned as a vector of length 1 rather than a 1×1 matrix. Often, this is exactly what we want, but this behavior can be turned off by setting drop = FALSE.

M <- matrix(1:8, 2)
M
##      [,1] [,2] [,3] [,4]
## [1,]    1    3    5    7
## [2,]    2    4    6    8

M[2, 1, drop = FALSE]       # setting drop=FALSE returns a 1×1 matrix
##      [,1]
## [1,]    2

Similarly, when we extract a single row or column of a matrix, R by default drops the dimension of length 1, so instead of getting a 1×3 matrix after extracting the first row, we get a vector of length 3. This behavior can similarly be turned off with the drop = FALSE option.

M <- matrix(1:8, 2)
M
##      [,1] [,2] [,3] [,4]
## [1,]    1    3    5    7
## [2,]    2    4    6    8

M[2, , drop = FALSE]       # setting drop=FALSE returns a 1×3 matrix
##      [,1] [,2] [,3] [,4]
## [1,]    2    4    6    8

5.2.3 Subsetting Lists

Lists in R can be subsetted using all three of the operators mentioned above, and all three are used for different purposes.

L <- list(integers = 1:4, decimal = 0.6)
L
## $integers
## [1] 1 2 3 4
## 
## $decimal
## [1] 0.6

The [[ operator can be used to extract single elements from a list. Here we extract the first element of the list:

L <- list(integers = 1:4, decimal = 0.6)
L[[1]]
## [1] 1 2 3 4

The [[ operator can also use named indices so that you don’t have to remember the exact ordering of every element of the list. You can also use the $ operator to extract elements by name.

L <- list(integers = 1:4, decimal = 0.6)
L[["decimal"]]
## [1] 0.6

L$decimal
## [1] 0.6

Notice you don’t need the quotes when you use the $ operator.

One thing that differentiates the [[ operator from the $ is that the [[ operator can be used with computed indices. The $ operator can only be used with literal names.

L <- list(integers = 1:4, decimal = 0.6, word = "hello")
name <- "integers"
# computed index for "integers"
L[[name]]  
## [1] 1 2 3 4

# element "name" doesn’t exist! (but no error here)
L$name     
## NULL

# element "integers" does exist
L$integers      
## [1] 1 2 3 4

5.2.3.1 Extracting Multiple Elements of a List

The [ operator can be used to extract multiple elements from a list. For example, if you wanted to extract the first and third elements of a list, you would do the following

L <- list(integers = 1:4, decimal = 0.6, word = "hello")
# Get the 3rd element of the 1st element
L[c(1, 3)]  
## $integers
## [1] 1 2 3 4
## 
## $word
## [1] "hello"

Remember that the [ operator always returns an object of the same class as the original. Since the original object was a list, the [ operator returns a list. In the above code, we returned a list with two elements (the first and the third).

5.2.3.2 Subsetting Nested Elements of a List

The [[ operator can take an integer sequence if you want to extract a nested element of a list.

L <- list(integers = 1:4, decimal = 0.6, word = "hello")
# Get the 3rd element of the 1st element
L[[c(1, 3)]]  
## [1] 3

# Same as above
L[[1]][[3]]   
## [1] 3

# 1st element of the 2nd element
L[[c(2, 1)]]  
## [1] 0.6

So, note that L[c(1, 3)] is not the same as L[[c(1, 3)]].

5.3 Missing Data

Missing values in R are denoted by either NA or NAN: NAN is used for undefined mathematical operations and NA is pretty much used for everything else. There is also another type of value NULL that sounds like NA but actually quite different as we will see.

5.3.1 NA and NAN

Let’s add a missing value by entering NA as an element of our vector x (NA is a legitimate logical character, so R will allow you to add it to a numeric vector) and try to compute the mean:

x <- 1:10
x <- c(x,NA)
x
##  [1]  1  2  3  4  5  6  7  8  9 10 NA

mean(x)
## [1] NA

The built-in function for the mean returns NA because of the missing data value. We need to say instead this:

mean(x, na.rm = TRUE)
## [1] 5.5

The na.rm = TRUE argument does not remove the missing value but simply omits it from the calculations. In other word, the mean is calculated when you omit the missing value, but unless you were to use another command, such as x <- x[-11] as we will see below, the vector will not change. There is a similar functionality with other functions sum, min, max, var, sd and other built-in functions.

The function is.na tests each element of a vector for missing values and returns a logical vector:

x <- c(NA, 2, NA, 1:3, NA)
is.na(x)
## [1]  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE

Remember vectors must contain data elements of the same type. To demonstrate this, let us make a vector of 10 numbers, and then add a character element to the vector. R coerces the data to a character vector because we added a character object to it. I used the index [11] to add the character element to the vector. But the vector now contains characters and you cannot do math on it:

x <- 1:10
mean(x)
## [1] 5.5
x[11] <- "A"     # appending a numeric vector with a character
x
##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "A"

mean(x)          # cannot do math on it
## Warning in mean.default(x): argument is not numeric or logical: returning
## NA
## [1] NA

We can use a negative index, [-11], to remove the character and the R function as.integer() to coerce the vector back to integers:

x <- x[-11]
x <- as.integer(x)
is.integer(x)
## [1] TRUE

mean(x)
## [1] 5.5

Let us create a numeric vector x as 1, 2, NA, 10, 3. The NA value in here is going to be a numeric missing value. So when we call is.na on x, it returns a logical vector where the logical vector indicates whether each element of the vector x is missing or not.

x <- c(1, 2, NA, 10, 3)
is.na(x)
## [1] FALSE FALSE  TRUE FALSE FALSE

is.nan(x)
## [1] FALSE FALSE FALSE FALSE FALSE

x <- c(1, 2, NaN, NA, 4)
is.na(x)
## [1] FALSE FALSE  TRUE  TRUE FALSE

is.nan(x)
## [1] FALSE FALSE  TRUE FALSE FALSE

The first two are FALSE, the third is TRUE, and the fourth and the fifth are FALSE. If we call is.nan on this vector, we see that vector that is returned is all FALSE because there aren’t any NaN values, or there aren’t any NaN values in this vector so everything is FALSE.

5.3.1.1 Removing NA Values

A common task in data analysis is removing missing values (NAs) and this can be easily done in R:

x <- c(1, 2, NA, 10, 3)
missing <- is.na(x)
print(missing)
## [1] FALSE FALSE  TRUE FALSE FALSE

x[!missing]
## [1]  1  2 10  3

What if there are multiple R objects and you want to take the subset with no missing values in any of those objects?

x <- c(1, 2, NA, 4, NA, 5)
y <- c("a", "b", NA, "d", NA, "f")
notmissing <- complete.cases(x, y)
notmissing
## [1]  TRUE  TRUE FALSE  TRUE FALSE  TRUE

x[notmissing]
## [1] 1 2 4 5

y[notmissing]
## [1] "a" "b" "d" "f"

You can use the function complete.cases on data frames too.

head(airquality)
##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 5    NA      NA 14.3   56     5   5
## 6    28      NA 14.9   66     5   6

notmissing <- complete.cases(airquality)
head(airquality[notmissing, ])
##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
## 7    23     299  8.6   65     5   7
## 8    19      99 13.8   59     5   8

5.3.2 NULL

NULL is the absence of anything. For example, functions can sometimes return NULL or their arguments can be NULL. An important difference between NA and NULL is that NULL is atomical and cannot exist within a vector. If NULL is used inside a vector, it simply disappears:

x <- c(NA, 1, NULL, 2, NA)
x
## [1] NA  1  2 NA

length(x)
## [1] 4

Thus, even though it was entered into the vector x, it did not get stored in x.

The function is.null tests for NULL values in a vector:

x <- NULL
is.null(x)
## [1] TRUE

x <- c(NA, 1, NULL, 2, NA)
is.null(x)
## [1] FALSE

5.4 An Extended Example

In this section, I will demostrate various ways of subsetting and manipulating a data set, along which I will also illustrate the use of some functions that we haven’t seen before, such as

  • which
  • recode
  • subset

Throughout the section, I will use the mpg dataset from the ggplot2 package, which should be already installed in R so we just need to load it into the current session:

library(ggplot2)

Let us first see what kind of objects are included in mpg by using summary function

summary(mpg)
##  manufacturer          model               displ            year     
##  Length:234         Length:234         Min.   :1.600   Min.   :1999  
##  Class :character   Class :character   1st Qu.:2.400   1st Qu.:1999  
##  Mode  :character   Mode  :character   Median :3.300   Median :2004  
##                                        Mean   :3.472   Mean   :2004  
##                                        3rd Qu.:4.600   3rd Qu.:2008  
##                                        Max.   :7.000   Max.   :2008  
##       cyl           trans               drv                 cty       
##  Min.   :4.000   Length:234         Length:234         Min.   : 9.00  
##  1st Qu.:4.000   Class :character   Class :character   1st Qu.:14.00  
##  Median :6.000   Mode  :character   Mode  :character   Median :17.00  
##  Mean   :5.889                                         Mean   :16.86  
##  3rd Qu.:8.000                                         3rd Qu.:19.00  
##  Max.   :8.000                                         Max.   :35.00  
##       hwy             fl               class          
##  Min.   :12.00   Length:234         Length:234        
##  1st Qu.:18.00   Class :character   Class :character  
##  Median :24.00   Mode  :character   Mode  :character  
##  Mean   :23.44                                        
##  3rd Qu.:27.00                                        
##  Max.   :44.00

and let’s see what they look like

head(mpg)
## # A tibble: 6 x 11
##   manufacturer model displ  year   cyl trans drv     cty   hwy fl    class
##   <chr>        <chr> <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <chr>
## 1 audi         a4      1.8  1999     4 auto… f        18    29 p     comp…
## 2 audi         a4      1.8  1999     4 manu… f        21    29 p     comp…
## 3 audi         a4      2    2008     4 manu… f        20    31 p     comp…
## 4 audi         a4      2    2008     4 auto… f        21    30 p     comp…
## 5 audi         a4      2.8  1999     6 auto… f        16    26 p     comp…
## 6 audi         a4      2.8  1999     6 manu… f        18    26 p     comp…
names(mpg)
##  [1] "manufacturer" "model"        "displ"        "year"        
##  [5] "cyl"          "trans"        "drv"          "cty"         
##  [9] "hwy"          "fl"           "class"

# let's save the original names
namesOriginal <- names(mpg)  

5.4.1 Rename Columns (Variables)

# rename some of the columns 
names(mpg)[c(1,8,9)] <- c("manuf", "mpg(cty)", "mpg(hwy)")   
names(mpg)
##  [1] "manuf"    "model"    "displ"    "year"     "cyl"      "trans"   
##  [7] "drv"      "mpg(cty)" "mpg(hwy)" "fl"       "class"

Rename by a variable name:

names(mpg)[names(mpg)=="year"] <- "yr"
names(mpg)
##  [1] "manuf"    "model"    "displ"    "yr"       "cyl"      "trans"   
##  [7] "drv"      "mpg(cty)" "mpg(hwy)" "fl"       "class"

# put the original names back
names(mpg) <- namesOriginal

Renaming by conditioning on an individual column name might be useful especially when we don’t know the exact column number, for instance.

5.4.2 Working with Missing Data

# let's add an odd observation to the end of the variable cty
mpg$cty[length(mpg$cty)] <- -1
# use tail function to see that -1 is indeed a bizarre observation
tail(mpg$cty)
## [1] 18 19 21 16 18 -1

# extract the indices where cty == -1
which(mpg$cty == -1)    # note that we use == not the usual =
## [1] 234

# treat these observations as missing
mpg$cty[which(mpg$cty == -1 )] <- NA

# tabulate missing values
table(is.na(mpg$cty))
## 
## FALSE  TRUE 
##   233     1

# with missing values we must use the option 'na.rm = TRUE'
mean(mpg$cty, na.rm = TRUE)
## [1] 16.85837

We can also use is.na(mpg$cty) to see if there are any NAs in the data?

5.4.3 Computing New Variables

  • Create a new variable by summing up the cty and hwy variables and append this to the mpg data frame as another column named mpg_sum
mpg$mpg_sum <- rowSums(mpg[8:9])
  • Alternative method using the apply function:
apply(mpg[, 8:9], 1, sum)
  • Compute the average mpg
mpg$mpg_avg <- mpg$mpg_sum/length(mpg$mpg_sum)
  • Drop a variable
mpg$mpg_avg <- NULL

5.4.4 Recode a Continuous Variable into a New Categorical Variable

summary(mpg$cty) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    9.00   14.00   17.00   16.86   19.00   35.00       1
mpg$cty_cat <- NA
mpg$cty_cat[mpg$cty <= 15] <-"Low"
mpg$cty_cat[mpg$cty > 15 & mpg$cty <= 30] <- "Med"
mpg$cty_cat[mpg$cty > 30] <-"High"

# let's tabulate this new variable
table(mpg$cty_cat)
## 
## High  Low  Med 
##    2   97  134

5.4.5 Recode from Continuous to Continuous using recode within the car package -

To use the recode function we need to install the car package first:

# install.packages("car")
library(car)
mpg$cyl_2 <- recode(mpg$cyl, "4=1;5=2;6=3;8=4")

5.4.6 Subsets of a Data Frame

  • Subsets by specifying the column name:
mpg[1:3, c("model", "cty", "hwy")]
## # A tibble: 3 x 3
##   model   cty   hwy
##   <chr> <dbl> <int>
## 1 a4       18    29
## 2 a4       21    29
## 3 a4       20    31
  • Subsets by specifying the row:
# Returns indices of rows where logical statement is TRUE
which(mpg$cty > 30)
## [1] 213 222

which(mpg$cty > 23 & mpg$cty < 28)
##  [1] 101 102 104 105 106 107 194 195 196 198

which(mpg$cty < 11 | mpg$cty > 32)
## [1]  55  60  66  70 127 213 222
  • Subsets by specifying conditions on some of the rows using the subset function:
# another two more ways of conditional subsetting
sub1 <- mpg[which(mpg$cty > 30), c("cty","hwy")]
sub2 <- subset(mpg, cty > 30, select = c("cty","hwy"))

# check if they are identical           
identical(sub1,sub2)
## [1] TRUE

5.4.7 Creating a Dummy Variable

The variable year has two levels: 1999, 2008. Suppose we want create a dummy variable for the year 2008:

dum2008 <- as.numeric(mpg$year == 2008)
head(dum2008)

Here, dum2008 = 1 for when years=2008 and zero otherwise.

Another example, creating a dummy for years after 1999

dum1999a <- as.numeric(mpg$year > 1999)
head(dum1999a)

More generally, we can use ifelse function to choose between two values depending on a condition. So if instead of a 0-1 dummy variable, for some reason you wanted to use, say, 4 and 7, you could use

dum99 <- ifelse(year == 1999, 1, 0)
dum08 <- ifelse(year >= 2008, 1, 0)

5.4.8 Data Frame Management: ‘attach’, ‘detach’, and ‘with’

There is an easier way of working with data frames with attach and detach functions. The attach() function adds the data frame to the R search path. When a variable name is encountered, data frames in the search path are checked for the variable in order. The detach() function removes the data frame from the search path.

These two are equivalent:

summary(mpg$cty) 
mpg$cty_cat <- NA
mpg$cty_cat[mpg$cty <= 15] <-"Low"
mpg$cty_cat[mpg$cty > 15 & mpg$cty <= 30] <- "Med"
mpg$cty_cat[mpg$cty > 30] <-"High"

# let's tabulate this new variable
table(mpg$cty_cat)

and

library(ggplot2)
attach(mpg)
print(summary(cty)) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    9.00   14.00   17.00   16.86   19.00   35.00       1
cty_cat <- NA
cty_cat[cty <= 15] <-"Low"
cty_cat[cty > 15 & cty <= 30] <- "Med"
cty_cat[cty > 30] <-"High"

# let's tabulate this new variable
table(cty_cat)
## cty_cat
## High  Low  Med 
##    2   97  134
detach(mpg)

There is an alternative way that brings the practicality

library(ggplot2)
with(mpg, {
print(summary(cty)) 
cty_cat <- NA
cty_cat[cty <= 15] <-"Low"
cty_cat[cty > 15 & cty <= 30] <- "Med"
cty_cat[cty > 30] <-"High"

# let's tabulate this new variable
table(cty_cat)
})
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    9.00   14.00   17.00   16.86   19.00   35.00       1
## cty_cat
## High  Low  Med 
##    2   97  134

If you want to save the objects created within with use <<- asignment operator. It saves the object to the global environment outside of the with() call.

library(ggplot2)
with(mpg, {
print(summary(cty)) 
cty_cat <<- NA
cty_cat[cty <= 15] <<-"Low"
cty_cat[cty > 15 & cty <= 30] <<- "Med"
cty_cat[cty > 30] <<-"High"
})
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    9.00   14.00   17.00   16.86   19.00   35.00       1
# let's tabulate this new variable
table(cty_cat)
## cty_cat
## High  Low  Med 
##    2   97  134
with(mtcars, {
   nokeepstats <- summary(mpg)
   keepstats <<- summary(mpg)
})

Now try to see which variable works outside the with().