R Data Structures: Vectors and Data Frames

Important Data Structures in R

• Homogeneous data structures store contents of the same type, while heterogeneous can be of different types
• Atomic vectors and factors are 1-dimensional homogeneous structures
• Recursive vectors or lists are 1-dimensional heterogeneous structures
• Matrices are 2-dimensional homogeneous structures
• Data frames are 2-dimensional heterogeneous structures
• Arrays are N-dimensional homogeneous structures
• Scalars are treated as vectors with a length of one in R.
• The str() function gives a concise overview of a data structure in R

Atomic Vectors

• Atomic vectors are the simplest data structure in R
• All elements share the same type or mode, except for NA and NaN which represent missing values.
• The mode or type signifies the basic nature of an object's fundamental constituent

Types of Atomic Vectors

• Logical vectors include TRUE, FALSE, T, F
• Integer vectors such as 1L, 2L, 3L
• Numeric or double vectors for instant: 1.00, 1.25, 1.50, 1.75, 5.00
• Character Vectors include "a", "b", "c"
• c() creates vectors
• seq() creates regular sequences
• rep() creates vectors with repeated values
• sort() arranges values in a vector in ascending order

Missing Values

• NA denotes "not available" or a "missing value"
• NaN signifies "Not a Number", which is a missing value from a numerical calculation
• is.na() returns TRUE for both NA and NaN
• is.nan() returns TRUE exclusively for NaNs

Character Values

• String values should be surrounded by either single or double quotes
• The backslash \ acts as an escape character and is disregarded within a string value
• \n represents a newline, while \t indicates a tab
• \' stands for a single quote and \" for a double quote
• cat() concatenates string values
• The object letters is a character vector with "a" through "z"

Class, Types and Tests

• Every object belongs to a class
• class() verifies the class of an object
• A data structure is described by the type of its basic constituent
• typeof() determines the type or storage mode of any object.
• For atomic vectors, the class and the mode are the same
• "is" functions check if an object belongs to a specific type or class -- such as is.character(), is.double(), is.integer(), is.logical(), is.atomic(), is.numeric()

Vector Operations

• Fundamental operations are performed on an element-by-element basis
• When two vectors differ in size, elements from the smaller vector are "recycled"

Subsetting Vectors

• Bracket symbols [] index or subset data
• vec01 <- c(1.00,1.25,1.25,1.50,1.00,1.75) initiates the vector vec01 with the values listed
• vec01[2] selects the second value
• vec01[-2] removes the second value
• vec01[1:3] selects consecutive values 1 to 3
• vec01[c(1,6)] selects values in the first and sixth positions
• vec01[-c(1,6)] removes values in the first and sixth positions
• vec01[c(T,T,F,T,F,F)] selects values if TRUE
• vec01[vec01<=1.25] is conditional filtering for values less than or equal to 1.25

Modifying Parts of a Vector

• Values can be assigned on certain parts of a vector.
• vec02<-rep(NA, 5) assigns NA to 5 parts of a vector
• vec02[c(1,4)]<-"YES" Modifies parts of vec02 to "YES"

Coercion

• Every element in an atomic vector must share the same type
• Vectors of varying types will have elements converted to the most flexible type
• Hierarchy from least to most flexible data type: Logical -> Integer -> Double -> Character
• Coercion functions with the prefix "as" can convert an object into a particular class. Examples: as.integer(), as.double(), as.numeric(), as.character(), as.logical()
• Exercise caution when coercing into a more "specific" or "less flexible" class, as this may lead to the introduction of missing values (NA)
• Coercing a character vector to a numeric class can produce missing values

Attributes

• Every object possesses both a length and a type or mode
• length() and typeof() assess these characteristics.
• Objects can include custom attributes (such as variable names, category labels, dimensions) that serve to hold metadata
• The attributes() function returns a comprehensive list of all supplementary attributes assigned to an object
• A commonly utilized attribute that can be added to an object is "names"
• The function names() acts as an accessor for the names attribute
• There are several approaches to assigning names to vectors

Factors

• Factors are integer vectors with additional attributes (levels)
• A factor is a vector object created to represent categorical data
• Factors are constructed on integer vectors and include extra attributes
• Factors can be coerced to integer or numeric classes
• Factors are restricted to a specified set of values known as levels
• Levels can be either unordered (nominal) or ordered (ordinal)
• Factors are essential in specific modeling processes
• factor() modifies and creates factors
• levels() returns the predefined categories of the factor object

Factors and Character Vectors

• Factors are useful when you know the categories or "levels" linked to a variable
• Factors cannot take on values beyond those specified by their levels
• There is a slight difference in how factors are displayed compared to character vectors
• is.factor() checks the type of an object
• as.factor() coerces an object into a factor
• relevel() modifies the first level or reference level of an unordered factor

Lists

• Lists are generic containers in R
• List or recursive vectors can hold elements of any type
• A list is considered "recursive" if it can include other lists
• Created using the function list()
• The typeof() lists is list
• The storage mode is list type
• Other objects derived from lists, such as data frames, will also be categorized with list as their type
• Functions named is.list() and as.list() identify or create lists
• List may also have a name attribute, with each element in a list having a label
• The list$name notation selects a part of a list

Selecting a Part of a List

• The operators [] and $ are for subsetting
• The [[]] operator is particularly significant for working with lists
• [] returns a list, [[] accesses the actual content of the list
• The $ notation is similar to [[]] when every element of the list has a name

Review of Atomic Vectors

• Atomic vector is the simplest data structure in R.
• It is a collection of elements having the same type, and, by default, its only attributes are length and type or mode.

Arrays and Matrices

• Atomic vectors do not have a "dimension" attribute
• The dimension attribute can be accessed using the dim() function
• A matrix is an array with two dimensions
• When a dimension attribute is added to an atomic vector, the object becomes an array
• Arrays with three or more dimensions are rarely used in analyzing data
• array() and matrix() functions is a way of creating an array and matrix

Subsetting for Matrices

• The [] symbols are used for indexing or subsetting
• Since there are two dimensions, an ordered pair of vectors (numeric or logical) must be specified
• The first vector corresponds to rows, and the second vector corresponds to columns
• Subsetting a matrix may result in a matrix-type or vector-type object, depending on the dimension of the output object
• Parts of a matrix can be transformed by combining the syntax for subsetting and assignment
• Conditional processing available by subsetting in matrices
• An empty pair of brackets [] will return the whole matrix
• The order of numbers in brackets [] may change the arrangement of values

Concatenating Matrices

• The c() function is used to create vectors and/or concatenate vectors
• For matrices, the counterpart of c() function are rbind() and cbind() functions
• When rbind() is used on atomic vectors, atomic vectors are treated as row vectors
• When cbind() is used on atomic vectors, atomic vectors are treated as column vectors
• rbind() and cbind() have conformability conditions
• When working with matrices, the number of columns must be the same for rbind(), and the number of rows must be the same for cbind()

Matrix Operations

• REPETITION. Basic operations are repeated on each element
• For transpose, t() can be used
• For matrix multiplication, %*% can be used
• For the inverse of a square matrix, solve() can be used
• For the determinant of a matrix, det() can be used
• For eigenvalues and eigenvectors, eigen() can be used
• Matrix operations have conformability rules. Always check the dimensions of matrices

Attributes of a Matrix

• Matrices maintain the intrinsic properties of their vector counterpart – length and type.
• Unlike atomic vectors, matrices have a dimension attribute
• The dim() function determines the dimension of the matrix, while ncol() and nrow() determines the number of columns and rows respectively
• Homogeneous. Coercion applies when different types of atomic vectors are bounded to form a matrix.
• Matrices do not inherit names from its vector counterparts
• The counterpart of "names" among matrices are "rownames" and "colnames"
• Row and column names can be accessed using rownames() and colnames()- respectively

Data Frames

• Data Frames are a list of equal-length vectors
• Recursive Vector or List is a heterogeneous object. It can contain any type of object (vectors, lists, matrices etc.)
• List can be constructed using list() function.

More on Data Frames

• It is the most common way of storing data in R.
• Most methods for analysis would require a data frame as input.
• Data frames share properties from both the matrix and the list
• A data frame is a type of list of equal-length vectors

Data Frame Properties

• Data frames can have "names" attributes, meaning each vector can have a name
• Subsetting using [n], [[n]], or $ applies on data frames
• A data frame is a group of equal-length column vectors; has two dimensions just like a matrix
• Subsetting using two vectors [i,j] works on data frames
• Data frames has a value for dim(), and may have values for rownames(), and colnames()
• colnames() and names() are the same for data frames

Creating Data Frames

• The data.frame() function constructs data frames
• A data frame cannot be created using a list() function, even if the components are equal-length vectors
• List of equal-length vectors can be coerced to a data frame

More on Data Frames and String Values

• By default, the data.frame() function converts string-valued vectors to factors
• Use stringAsFactors = F option to change the default behavior
• View() invokes a spreadsheet-style data viewer on a matrix-like R object

Binding Data Frames and Matrices

• rbind() and cbind() are functions for matrices, but can be applied on objects with matrix-like characteristics (e.g. data frames)
• By default, these functions return matrix objects
• rbind() and cbind() return a data frame only if one or more inputs are data frames
• data.frame() ensures the output object is a data frame

Key Functions for Data Frames

• Function head() returns the first n rows of a data frame
• Function tail() returns the last n rows of a data frame
• The function order() takes a vector as input and returns an integer vector describing how the subset vector should be
• The function subset() is a specialized shorthand function for subsetting data frames

Reading Data from Files

• The function read.csv() imports CSV files into a data frame
• Columns with characters a values are saved as factors by default unless using attributes as.is or stringAsFactors
• The function setwd() sets or changes the current working directory

Review: Relationship of Data Structures

• Homogeneous elements are atomic vectors that can become factors with levels attribute, or arrays with dimension attributes and then matricies with two dimensions only
• Heterogeneous elements are lists and can relate to data frames, with two dimensions and matrix like characteristics

R Langauge Characteristics

• Review the R Language - Functional and Object Oriented
• Everything computed is an object
• Objects structure themselves to suit goals of computations
• Each object belongs to a class- wherein every member of a class shares a set of properties
• Polymorphic Functions are functions that can communicate differently