Missing values
In some cases the components of a vector may not be completely known. When an element or value is “not available” or a “missing value” in the statistical sense, a place within a vector may be reserved for it by assigning it the special value NA. In general any operation on an NA becomes an NA. The motivation for this rule is simply that if the specification of an operation is incomplete, the result cannot be known and hence is not available. The function is.na(x) gives a logical vector of the same size as x with value TRUE if and only if the corresponding element in x is NA.
> z <- c(1:3,NA); ind <- is.na(z)
really a value but a marker for a quantity that is not available. Thus x == NA is a vector of the same length as x all of whose values are NA as the logical expression itself is incomplete and hence undecidable. Note that there is a second kind of “missing” values which are produced by numerical computation, the so-called Not a Number, NaN, values. Examples are
> 0/0
or
> Inf - Inf
which both give NaN since the result cannot be defined sensibly. In summary, is.na(xx) is TRUE both for NA and NaN values. To differentiate these, is.nan(xx) is only TRUE for NaNs. Missing values are sometimes printed as <NA>, when character vectors are printed without quotes.
Character vectors
Character quantities and character vectors are used frequently in R, for example as plot labels. Where needed they are denoted by a sequence of characters delimited by the double quote character, e.g., "x-values", "New iteration results". Character strings are entered using either double (") or single (’) quotes, but are printed using double quotes (or sometimes without quotes). They use C-style escape sequences, using \ as the escape character, so \\ is entered and printed as \\, and inside double quotes " is entered as \". Other useful escape sequences are \n, newline, \t, tab and \b, backspace.
Character vectors may be concatenated into a vector by the c() function; examples of their use will emerge frequently. The paste() function takes an arbitrary number of arguments and concatenates them one by one into character strings. Any numbers given among the arguments are coerced into character strings in the evident way, that is, in the same way they would be if they were printed. The arguments are by default separated in the result by a single blank character, but this can be changed by the named parameter, sep=string, which changes it to string, possibly empty. For example
> labs <- paste(c("X","Y"), 1:10, sep="")
makes labs into the character vector
c("X1", "Y2", "X3", "Y4", "X5", "Y6", "X7", "Y8", "X9", "Y10")
Note particularly that recycling of short lists takes place here too; thus c("X", "Y") is repeated 5 times to match the sequence 1:10.[3]
Index vectors; selecting and modifying subsets of a data set
Subsets of the elements of a vector may be selected by appending to the name of the vector an index vector in square brackets. More generally any expression that evaluates to a vector may have subsets of its elements similarly selected by appending an index vector in square brackets immediately after the expression. Such index vectors can be any of four distinct types.
1. A logical vector. In this case the index vector must be of the same length as the vector from which elements are to be selected. Values corresponding to TRUE in the index vector are selected and those corresponding to FALSE are omitted. For example
> y <- x[!is.na(x)]
creates (or re-creates) an object y which will contain the non-missing values of x, in the same order. Note that if x has missing values, y will be shorter than x. Also
> (x+1)[(!is.na(x)) & x>0] -> z
creates an object z and places in it the values of the vector x+1 for which the corresponding value in x was both non-missing and positive.
2. A vector of positive integral quantities. In this case the values in the index vector must lie in the set {1, 2, . . . , length(x)}. The corresponding elements of the vector are selected and concatenated, in that order, in the result. The index vector can be of any length and the result is of the same length as the index vector. For example x[6] is the sixth component of x and
> x[1:10]
selects the first 10 elements of x (assuming length(x) is not less than 10). Also
> c("x","y")[rep(c(1,2,2,1), times=4)]
(an admittedly unlikely thing to do) produces a character vector of length 16 consisting of "x", "y", "y", "x" repeated four times.
3. A vector of negative integral quantities. Such an index vector specifies the values to be excluded rather than included. Thus
> y <- x[-(1:5)]
gives y all but the first five elements of x.
4. A vector of character strings. This possibility only applies where an object has a names attribute to identify its components. In this case a sub-vector of the names vector may be used in the same way as the positive integral labels in item 2 further above.
> fruit <- c(5, 10, 1, 20)
> names(fruit) <- c("orange", "banana", "apple", "peach")
> lunch <- fruit[c("apple","orange")]
The advantage is that alphanumeric names are often easier to remember than numeric indices. This option is particularly useful in connection with data frames, as we shall see later. An indexed expression can also appear on the receiving end of an assignment, in which case the assignment operation is performed only on those elements of the vector. The expression must be of the form vector[index_vector] as having an arbitrary expression in place of the vector name does not make much sense here. The vector assigned must match the length of the index vector, and in the case of a logical index vector it must again be the same length as the vector it is indexing. For example
> x[is.na(x)] <- 0
replaces any missing values in x by zeros and
> y[y < 0] <- -y[y < 0]
has the same effect as
> y <- abs(y)
Other types of objects
Vectors are the most important type of object in R, but there are several others which we will meet more formally in later sections.
• matrices or more generally arrays are multi-dimensional generalizations of vectors. In fact, they are vectors that can be indexed by two or more indices and will be printed in special ways.
• factors provide compact ways to handle categorical data.
• factors provide compact ways to handle categorical data.
• lists are a general form of vector in which the various elements need not be of the same type, and are often themselves vectors or lists. Lists provide a convenient way to return the results of a statistical computation.
• data frames are matrix-like structures, in which the columns can be of different types. Think of data frames as ‘data matrices’ with one row per observational unit but with (possibly) both numerical and categorical variables. Many experiments are best described by data frames: the treatments are categorical but the response is numeric.
• functions are themselves objects in R which can be stored in the project’s workspace. This provides a simple and convenient way to extend R.
3 paste(..., collapse=ss) joins the arguments into a single character string putting ss in between. There are more tools for character manipulation, see the help for sub and substring.
Next: Objects, their modes and attributes
Summary: Index