A vector is a sequence of data elements of the same basic type. Members in a vector are officially called components. Nevertheless, they are often called elements.

Creating matrices

The function matrix creates matrices.

 matrix(data, nrow, ncol, byrow) 

The data argument is usually a list of the elements that will fill the matrix. The nrow and ncolarguments specify the dimension of the matrix. Often only one dimension argument is needed if, for example, there are 20 elements in the data list and ncol is specified to be 4 then R will automatically calculate that there should be 5 rows and 4 columns since 4*5=20. The byrowargument specifies how the matrix is to be filled. The default value for byrow is FALSE which means that by default the matrix will be filled column by column.

seq1 <- seq(1:6)

mat1 <- matrix(seq1, 2)

mat2 <- matrix(seq1, 2, byrow = T)

A list is an R structure that may contain object of any other types, including other lists. Lots of the modeling functions (like t.test() for the t test or lm() for linear models) produce lists as their return values, but you can also construct one yourself:

 mylist <- list (a = 1:5, b = "Hi There", c = function(x) x * sin(x)) 

Data Frames

A data frame is more general than a matrix, in that different columns can have different modes (numeric, character, factor, etc.). This is similar to SAS and SPSS datasets.

d <- c(1,2,3,4)<br> e <- c("red", "white", "red", NA)<br> f <- c(TRUE,TRUE,TRUE,FALSE)<br> mydata <- data.frame(d,e,f)<br> names(mydata) <- c("ID","Color","Passed") # variable names

There are a variety of ways to identify the elements of a data frame .

myframe[3:5] # columns 3,4,5 of data frame<br> myframe[c("ID","Age")] # columns ID and Age from data frame<br> myframe$X1 # variable x1 in the data frame

A data frame is a table, or two-dimensional array-like structure, in which each column contains measurements on one variable, and each row contains one case or sample (observation) with the corresponding values for each variable for that observation.

Lists

An ordered collection of objects (components). A list allows you to gather a variety of (possibly unrelated) objects under one name.

# example of a list with 4 components - <br> # a string, a numeric vector, a matrix, and a scaler <br> w <- list(name="Fred", mynumbers=a, mymatrix=y, age=5.3)<br> <br> # example of a list containing two lists <br> v <- c(list1,list2)

Identify elements of a list using the [[]] convention.

mylist[[2]] # 2nd component of the list<br> mylist[["mynumbers"]] # component named mynumbers in list

Factors

Tell R that a variable is nominal by making it a factor. The factor stores the nominal values as a vector of integers in the range [ 1... k ] (where k is the number of unique values in the nominal variable), and an internal vector of character strings (the original values) mapped to these integers.

# variable gender with 20 "male" entries and <br> # 30 "female" entries <br> gender <- c(rep("male",20), rep("female", 30)) <br> gender <- factor(gender) <br> # stores gender as 20 1s and 30 2s and associates<br> # 1=female, 2=male internally (alphabetically)<br> # R now treats gender as a nominal variable <br> summary(gender)

An ordered factor is used to represent an ordinal variable.

# variable rating coded as "large", "medium", "small'<br> rating <- ordered(rating)<br> # recodes rating to 1,2,3 and associates<br> # 1=large, 2=medium, 3=small internally<br> # R now treats rating as ordinal

R will treat factors as nominal variables and ordered factors as ordinal variables in statistical proceedures and graphical analyses. You can use options in the factor( ) and ordered( ) functions to control the mapping of integers to strings (overiding the alphabetical ordering). You can also use factors to createvalue labels.

1. Creating factor variables

Factor variables are categorical variables that can be either numeric or string variables. There are a number of advantages to converting categorical variables to factor variables. Perhaps the most important advantage is that they can be used in statistical modeling where they will be implemented correctly, i.e., they will then be assigned the correct number of degrees of freedom. Factor variables are also very useful in many different types of graphics. Furthermore, storing string variables as factor variables is a more efficient use of memory. To create a factor variable we use the factor function. The only required argument is a vector of values which can be either string or numeric. Optional arguments include the levels argument, which determines the categories of the factor variable, and the default is the sorted list of all the distinct values of the data vector. The labels argument is another optional argument which is a vector of values that will be the labels of the categories in thelevels argument.

R Programming Environment and Scope

Anonymous Functions

As remarked at several points in this book, the purpose of the R function function() is to create functions. For instance, consider this code:

 inc <- function(x) return(x+1) 

It instructs R to create a function that adds 1 to its argument and then assigns that function to inc. However, that last step—the assignment—is not always taken. We can simply use the function object created by our call tofunction() without naming that object. The functions in that context are called anonymous, since they have no name. (That is somewhat misleading, since even nonanonymous functions only have a name in the sense that a variable is pointing to them.)

Set OperationsDescription

Performs set union, intersection, (asymmetric!) difference, equality and membership on two vectors.

 union(x, y)  intersect(x, y)  setdiff(x, y)  setequal(x, y)  is.element(el, set) 

Each of union, intersect, setdiff and setequal will discard any duplicated values in the arguments, and they apply as.vector to their arguments (and so in particular coerce factors to character vectors).

is.element(x, y) is identical to x %in% y.