About Me

• Yijun(Sally) Chen

• Undergraduate at Fudan University

• 4th year Marketing Phd at Olin

• Data-driven research in social science

• Social network, Peer effect

• Teaching assistant for Olin courses

• Runner, Barca supporter, mom of a cat

• Welcome to Wash U!

About You

• Previous education
  • Arts & Social Science
  • Business
  • Science & Engineering
• Programming experience(Python/R/C/C++/Java…)
  • First time today
  • Have programming experience
• Experience in R
  • First time today
  • Knew something about R
  • Have experience in R

Slides

http://rpubs.com/sallychen/301448

What is R & Rstudio

• R as Statistical Programming Language
  • Pros: Data manipulating, statistical model, plots
  • Cons: Efficiency
• Free and opensource https://www.r-project.org/
  • Pros: large community, thousands of available packages
  • Cons: stability, no performance guarantee
• Rstudio https://www.rstudio.com/
  • Fabulous graphical interface
  • Supports R project as working environment
  • Flexible Markdown supports for reports,publishment and presentation
• In a word
  • R is the programming language runs inside Rstudio
  • Rstudio is the tool you use to interact with R

Course Objectives

• Contents
  • Day 1: Basics in R programming
  • Day 2: R studio,Data Processing,Statistical Analysis
  • Add-on: Write beautiful reports inside R
• Focus
  • Foundations for your future learning
  • Avoid common mistakes in a programming language
  • How to think in R and interact with R studio
• Format
  • Concepts illustrations in human languages
  • In-class demo in codes
  • In-class exercise and feedback
  • In-class Q&A
  • slides available at http://rpubs.com/sallychen/413493

Today: Contents & Agenda

• Morning
  • R Data classes & R objects
  • R Data structures: Vector,Matrix
  • Functions in R
• Afternoon
  • R Data structures:Data.frame,List,Factor

If you have not installed R & Rstudio,use Rstudio cloud verion for today’s session

https://rstudio.cloud

Data Classes and Objects

• Examples of Class & Objects
  • Human & Sally
  • Car & BMW
  • University & WashU
• Relationships between Class & Objects
  • Class is a blueprint for the object
  • A blueprint describes how object will be constructed
  • An object is an instance of a class
  • Many instances can be created from a class
• Class in R: Basic data type in R, fundamental
  • character: “hello”,“Welcome to WashU”
  • numeric: 2.3, 3.5,-1.2
  • logical: TRUE/FALSE
• Object in R
  • Everything in R is an object
  • Name & Value
  • use \(\texttt{=}\) or \(\texttt{<-}\) to assign value to an object
  • use class() to learn the class of an object
  • R object names are case sensitive
  • Name should not start with number
  • Easily overwritten
• Why is class important?
  • 2 \(\neq\) “2”
  • TRUE \(\neq\) “TRUE”
  • Numeric operators(+,-,*,/…) only work with numeric
  • Object conversions is one of the most common sources of frustration for beginners.

Demo: Class and Objects

• Let’s type the following code directly in the console and hit enter to see return

• Assign value to object

x1 = 0.02  #assign values to object with =
y1 <- "0.01"  #assign values to object with <-
z1 = TRUE

• Use class() function

class(x1)

## [1] "numeric"

class(y1)

## [1] "character"

class(z1)

## [1] "logical"

• Case sensitive

X1 = 100  #Case sensitive x1 != X1
X1

## [1] 100

x1

## [1] 0.02

• Naming an object

1x = 200  # name should not start with number

## Error: <text>:1:2: unexpected symbol
## 1: 1x
##      ^

• Overwritten

x1  # original value of x1 = 0.02

## [1] 0.02

x1 + 5

## [1] 5.02

x1  # x1 is not overwritten

## [1] 0.02

x1 = x1 + 5  # x1 is overwritten
x1  # x1 has a new value

## [1] 5.02

• Class-specific operators

class("TRUE")

## [1] "character"

"TRUE" + 1

## Error in "TRUE" + 1: non-numeric argument to binary operator

class(TRUE)

## [1] "logical"

TRUE + 1

## [1] 2

2 + "2"

## Error in 2 + "2": non-numeric argument to binary operator

Data Structures

• Use Bricks to build a wall/Use wall and windows to build a building

• Structure
  • A collection of different objects.
  • Differ in the ways objects are stored
  • Differ in what classes are accepted

Data Structures

• R Data Structure
  • vector
  • matrix
  • data.frame
  • factor
  • list

Vector

• \(1\)-dimension collection of elements with mode character, logical, integer or numeric
• Vector is designed to store a sequence of values
• Vector requires homogenous data type: can not mix two data types in one vector
• use c() to construct a vector with specific values in sequence
• use length() to see the number of elements in a vector

Demo: Vector

• Multiple ways of innitialize an empty vector

vector("numeric", length = 3)  # a empty numeric vector of length 3

## [1] 0 0 0

numeric(3)

## [1] 0 0 0

vector("character", length = 5)  # a empty character vector of length 5

## [1] "" "" "" "" ""

character(5)

## [1] "" "" "" "" ""

• use c() to construct a vector with values

x = c(1, 2, 3, 4)  #numeric vector
y = c("1", "2", "hello", "R")  #character vector

• Homogenous data type

c(1, "hello", TRUE)  # every element will be transformed to character, as there are  ' ' around 1 and TRUE

## [1] "1"     "hello" "TRUE"

• Examing vectors

x

## [1] 1 2 3 4

length(x)

## [1] 4

class(x)

## [1] "numeric"

y

## [1] "1"     "2"     "hello" "R"

length(y)

## [1] 4

class(y)

## [1] "character"

• Adding Elements to existing vector

x

## [1] 1 2 3 4

x <- c(x, 5)  # add a new element to x

Constructing numeric vectors of specific structure

• Use a:b to denote the starting point a and ending point b and create continous sequence

a = 3:7
a

## [1] 3 4 5 6 7

• use seq() to construct a sequence of vector

seq(from = 1, to = 9, by = 2)

## [1] 1 3 5 7 9

• Use rep(a,b) to replicate a for b times

a = rep(3, 4)  # replicate 3 for 4 times
a

## [1] 3 3 3 3

Some functions for numeric vectors & vector calculation

x

## [1] 1 2 3 4 5

class(x)  # x is a numeric vector

## [1] "numeric"

length(x)  # return the length of x

## [1] 5

sd(x)  # return the standard deviation of x

## [1] 1.581139

min(x)  # return the minimal of x

## [1] 1

max(x)  # return the maximal of x

## [1] 5

x + 1  # add 1 on each element

## [1] 2 3 4 5 6

exp(x)  # take expoential on each element

## [1]   2.718282   7.389056  20.085537  54.598150 148.413159

x[1] + 10  # add 1 on the first element

## [1] 11

x[1]  # x[1] is not overwritten

## [1] 1

x[1] = x[1] + 10  # x[1] is overwritten
x[1]

## [1] 11

Accesing data from numeric or character vectors

• For vector, each element has a position, which positions you want to access?
• use [n] to denote the position n you want to access
• use [1:3] to specify the starting position and ending position
• use [c(1,3)] to specify separate positions
• use [-n] to show all the elements except n

x

## [1] 11  2  3  4  5

x[1]

## [1] 11

x[1:3]

## [1] 11  2  3

x[c(1, 3)]

## [1] 11  3

x[-3]

## [1] 11  2  4  5

Data Type Coercion: Class really matters!

• mean() only works for numeric, does not work on character

z = c("1", "2", "3")  # create a character vector
class(z)

## [1] "character"

mean(z)  # calculate mean

## Warning in mean.default(z): argument is not numeric or logical: returning
## NA

## [1] NA

• use is.numeric() to check whether data is numeric

is.numeric(z)  # check whether it is numeric

## [1] FALSE

• if not, as.numeric() will coerse certain classes to numeric

z = as.numeric(z)  # transform data type
z

## [1] 1 2 3

mean(z)

## [1] 2

• as.character() will coerse certain classes to character

z = as.character(z)
z

## [1] "1" "2" "3"

Missing Values in Vector

• In R, missing values are represented by the string NA
• Any computation involving a NA will return a NA
• Use is.na() to test whether each element is NA
• Use anyNA() to test whether a vector contains a NA
• na.rm = TRUE is an argument in many stat function to remove NA values when computing

x = c(1, 4, 7, NA, 12, 19, 15, 21, 20)
mean(x)

## [1] NA

is.na(x)

## [1] FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE

anyNA(x)

## [1] TRUE

mean(x, na.rm = TRUE)  # remove NA from x, then calculate the mean()

## [1] 12.375

In class Exercise 1

• Numeric vector exercise
  • Create an empty numeric vector nv1 of length 6
  • Create a numeric vector nv2 with even numbers from 2 to 20(2,4,…20)
  • How many elements are there in nv2?
  • What is the 6th element of nv2?
  • Add a new value 22 to the end of nv2
  • Delete 2 from nv2
  • print your new nv2
  • Calucalte the mean(),min(),max(),sd() of nv2
• Class and objects exercise
  • Create a numeric vector nv3 from 1 to 10
  • Add 3 to each element of nv3
  • Coerce nv3 to character
  • Print the new nv3

nv2 = seq(2, 20, 2)
length(nv2)

## [1] 10

nv2[6]

## [1] 12

nv2 = c(nv2, 22)
nv2 = nv2[-1]
print(nv2)

##  [1]  4  6  8 10 12 14 16 18 20 22

mean(nv2)

## [1] 13

min(nv2)

## [1] 4

max(nv2)

## [1] 22

sd(nv2)

## [1] 6.055301

nv3 = 1:10
nv3 = nv3 + 3
nv3 = as.character(nv3)
print(nv3)

##  [1] "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13"

Function: Basic

• Functions: repeated usage of specific operation
• Components of a function
  • Function name
  • Arguments: Input
  • Statement: The box
  • Return: Output

• R use function() to create a function

• Structure of a R function

myfunction <- function(arg1, arg2){

statements

return(object)

}

• Call a function by parsing values to arguments

myfunction(arg1 = value1, arg2 = value2)

• Built-in functions and User-generated

Built-in Function

• seq(from,to,by): a built-in function generates an arithmetic sequence of numeric values with three arguments
  • from:starting number
  • to: ending number
  • by: increment of the sequence
• Suppose you want to generate the following sequence: 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
• Without function, you could do the following

s = c(1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2)
s

##  [1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

• With seq() function, you only specifiy the input argument from=1,to=2,by=0.1

s = seq(from = 1, to = 2, by = 0.1)
s

##  [1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

• Function is for repeated use, you could generate all arithmetic sequence with seq()

s = seq(from = 2, to = 4, by = 0.2)
s

##  [1] 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

Arguments matching: How to parse values to arguments?

• Call R function by assign values to arguments
  • func(arg1=value1,arg2=value2): argument names are given
  • func(value1,value2): no argument names, R match values with arguments by orders
• The following calls are equivalent

seq(from = 1.1, to = 3.5, by = 0.3)

## [1] 1.1 1.4 1.7 2.0 2.3 2.6 2.9 3.2 3.5

seq(1.1, 3.5, 0.3)

## [1] 1.1 1.4 1.7 2.0 2.3 2.6 2.9 3.2 3.5

seq(by = 0.3, from = 1.1, to = 3.5)

## [1] 1.1 1.4 1.7 2.0 2.3 2.6 2.9 3.2 3.5

Default argument values in functions

• Often times certain arguments of R functions are given default values at the time the function is constructed
• Default arguments are only used if no values are specified
• Not all inputs have default values
• help() function always tell you the arguments of a built-in function and the default values
• rnorm(): random normal generators
  • n: number of observations, no default, user must specify a value
  • mean: default \(0\)
  • sd: default \(1\)
• Example: use rnorm() to generate standard normal distribution

# help(rnorm)
rnorm()  # call rnorm() without specifying the length n

## Error in rnorm(): argument "n" is missing, with no default

e = rnorm(n = 1000)  # 1000 observations from Standard normal N(0,1) 
mean(e)  # check the mean

## [1] 0.03828554

sd(e)  # check the standard deviation

## [1] 0.9784108

hist(e)  # use hist() to plot the distribution

• Example: use rnorm() to generate nornal distribution with specific mean/sd

e1 = rnorm(n = 1000, mean = 3, sd = 5)  # 1000 values from N(3,5) 
mean(e1)

## [1] 2.841117

sd(e1)

## [1] 5.028204

hist(e1)

In class Exercise 2

• Call built-in functions
  • Use help() to read the R documentation of Uniform Number Generator runif()
  • Use runif() to generate a vector u1 of length 1000 with default min and max of the interval
  • Compute the min(),max(),mean() of u1
  • Plot the histogram of u1
  • Use runif() to generate a vector u2 of length 1000 with min -5 and max 5
  • Compute min(),max(),mean() and plot the histogram of u2

u1 = runif(1000)
min(u1)

## [1] 0.002355184

max(u1)

## [1] 0.9977875

mean(u1)

## [1] 0.4973576

hist(u1)

u2 = runif(1000, -5, 5)
min(u2)

## [1] -4.996475

max(u2)

## [1] 4.96678

mean(u2)

## [1] -0.01792917

hist(u2)

Short-break

Let’s take a short break of 10 minutes

Matrix

• Vector is 1 dimension, matrix takes two dimension
• Matrix dimensions: row(horizontal),column(vertical)
• use matrix(),rbind(),cbind() to construct
• matrix(data,nrow,ncol,byrow) function
  • data: a vector, no default
  • nrow: number of rows, default = \(1\)
  • ncol: number of columns, default= \(1\)
  • byrow: filled by row, default = FALSE
• Matrix only accepts homogenous data class:numeric or character
• Use dim(),nrow(),ncol() to check the dimensions of a matrix

Demo: constructing a matrix

• Filling a matrix by column

matrix(data = 1:6, nrow = 3, ncol = 2)

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

• Filling a matrix by row

matrix(data = 1:6, nrow = 3, ncol = 2, byrow = TRUE)

##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4
## [3,]    5    6

• cbind() combine vectors by column

a1 = 1:3
a2 = 4:6
cbind(a1, a2)

##      a1 a2
## [1,]  1  4
## [2,]  2  5
## [3,]  3  6

• cbind() takes vectors of same length if not, shorter vector will be recycled to achieve the length

a1 = 1:6
a2 = 4:5  # what if a1 and a2 has different length
cbind(a1, a2)

##      a1 a2
## [1,]  1  4
## [2,]  2  5
## [3,]  3  4
## [4,]  4  5
## [5,]  5  4
## [6,]  6  5

• rbind() combine vectors by rows

a1 = 1:3
a2 = 4:6
rbind(a1, a2)

##    [,1] [,2] [,3]
## a1    1    2    3
## a2    4    5    6

• Matrix only accepts values of same class, if not, R will automatically coerce

matrix(c(1, 2, 3, "4", 5, "hello"), nrow = 3, ncol = 2)  # matrix() will coerce everything to character

##      [,1] [,2]   
## [1,] "1"  "4"    
## [2,] "2"  "5"    
## [3,] "3"  "hello"

• Dimensions check

a = matrix(data = 1:6, nrow = 3, ncol = 2)
nrow(a)  #return the row dimension

## [1] 3

ncol(a)  #return the col dimension

## [1] 2

dim(a)  #return row,col

## [1] 3 2

Accesing data from matrix objects

• access or assign data to a matrix object with “[row_index,column_index]”
• [row_index,] will return the whole row
• [,column_index] will return the whole column
• use “:” to denote consecutive rows,columns

Demo: Access data from matrix objects

• First create a matrix a with 1:6

a = matrix(1:6, nrow = 3, ncol = 2)  #create a 3*2 matrix
a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

• Access one cell

a[1, 1]  # access the first cell

## [1] 1

• Access one row

a[1, ]  # access the first row

## [1] 1 4

• Access one column

a[, 2]  # access the second column

## [1] 4 5 6

• Access multiple rows/columns

a[1:2, 1:2]  # access the top 2 row and column

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5

Scalar & Matrix Calculations

• Matrix & a scalar(a number)
  • Numeric operator(+,-,*,/) applied on each cell of matrix

a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

a + 1  # add 1 to each element of the matrix

##      [,1] [,2]
## [1,]    2    5
## [2,]    3    6
## [3,]    4    7

a * 2  # multiply 2 to each element of the matrix

##      [,1] [,2]
## [1,]    2    8
## [2,]    4   10
## [3,]    6   12

Elementwise Matrix Calculations

• Matrix & Matrix Element-wise Addition/Subtraction
  • Two matrice should have the same dimension
  • Numberic operator between cells
• Same dimensions

a + a  # element-wise addition

##      [,1] [,2]
## [1,]    2    8
## [2,]    4   10
## [3,]    6   12

a - a  # element-wise addition

##      [,1] [,2]
## [1,]    0    0
## [2,]    0    0
## [3,]    0    0

• Different dimensions

b = matrix(1:6, nrow = 2, ncol = 3)
a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

b

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

a + b

## Error in a + b: non-conformable arrays

• Matrix & Matrix Element-wise Multiplication

a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

a * a

##      [,1] [,2]
## [1,]    1   16
## [2,]    4   25
## [3,]    9   36

Transpose & Matrix algebric multiplication

• Transpose a matrix with t()

a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

dim(a)  # 3*2 matrix

## [1] 3 2

t(a)

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6

dim(t(a))  #2*3 matrix

## [1] 2 3

• Matrix Algebric Multiplication with %*%

a  # 3*2 dimension

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

t(a)  # 2*3 dimension

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6

a %*% t(a)  # 3*3 dimension

##      [,1] [,2] [,3]
## [1,]   17   22   27
## [2,]   22   29   36
## [3,]   27   36   45

t(a) %*% a  # 2*2 dimension

##      [,1] [,2]
## [1,]   14   32
## [2,]   32   77

Matrix dimensions matching

• Dimensions are really important in matrix calculations
  • Element-wise operation needs two matrices of same dimension
  • Matrix mutiply needs a nm , mp matrix
• Element-wise operation of wrong dimensions

a  # 3*2

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

t(a)  # 2*3

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6

a + t(a)  # a and t(a) have different dimensions

## Error in a + t(a): non-conformable arrays

• Matrix multiplication of wrong dimensions

a %*% a

## Error in a %*% a: non-conformable arguments

Functions on Matrix

• Functions on all elements of matrix

a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

sum(a)  # sum of every elements

## [1] 21

mean(a)  # mean of all the elements

## [1] 3.5

• apply(data,MARGIN,Function) function on each row/column

a

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

apply(a, MARGIN = 1, sum)  # caculate sum of each row

## [1] 5 7 9

apply(a, MARGIN = 2, mean)  # mean of each column

## [1] 2 5

In class exercise 3

• Construct a matrix
  • Use seq() to generate a vector v3 of length 15, odd numbers from 1 to 29
  • Use matrix() to construct m1 of 3*5 from v3, fill by column
  • Use matrix() to construct m2 of 5*3 from v3, fill by column
• Matrix calculations
  • Add 1 to each element of m1
  • Multiply each element of m2 by 2
  • Compute the transpose of m2
  • Add transpose of m2 to m1
  • Multiply m1 by m2

v3 = seq(1, 29, 2)
m1 = matrix(v3, 3, 5)
m2 = matrix(v3, 5, 3)
m1 = m1 + 1
m2 = m2 * 2
t(m2)

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    2    6   10   14   18
## [2,]   22   26   30   34   38
## [3,]   42   46   50   54   58

m1 + t(m2)

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    4   14   24   34   44
## [2,]   26   36   46   56   66
## [3,]   48   58   68   78   88

m1 %*% m2

##      [,1] [,2] [,3]
## [1,]  940 2340 3740
## [2,] 1040 2640 4240
## [3,] 1140 2940 4740

Let’s Take a Rest

See you back at 1:30pm

Welcome Back!

It’s R time again… Any questions?

Recall: What we have learned

• R Classes and Object
  • Everything in R is an object
  • use = or <- to assign value to an object
  • Class is type of an object
  • Numeric class is different from character class
  • is.numeric(), as.numeric() to check or coerce
• R Data Structure: structure is how we stores values
  • vector: done!
  • matrix
  • data frame
  • factor
  • list
• R function
  • Built-in function
  • Default values and attributes matching

Data.frame

• The data.frame class is like the matrix class except that data.frame accepts heterogenous data classes, we could have one column of character and another of numeric
• Data.frame is a collection of vectors with same length
• Data.frame is the main structure for keeping real world data in R
• Data.frame has two dimension: column & row
  • Column: attributes, eg. name, gender, age
  • Row: instance, eg “Sally”,“female”,“25”
• When data is read into R from a file on disk (say through the read.csv() function) the data appears in R as a data.frame object
• Most functions in R that estimate statistical models require that the data that is needed for estimation is passed in as a data.frame object

Example: a Built-in Data Frame

• See the description of a built-in data.frame mtcars

help(mtcars)

• Use head() to print the first several cars

head(mtcars, 2)  # see the first 2 rows

##               mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4      21   6  160 110  3.9 2.620 16.46  0  1    4    4
## Mazda RX4 Wag  21   6  160 110  3.9 2.875 17.02  0  1    4    4

• Use tail() to print the last several cars

tail(mtcars, 2)

##                mpg cyl disp  hp drat   wt qsec vs am gear carb
## Maserati Bora 15.0   8  301 335 3.54 3.57 14.6  0  1    5    8
## Volvo 142E    21.4   4  121 109 4.11 2.78 18.6  1  1    4    2

• colnames(),rownames(),nrow(),ncol() to check a data.frame

colnames(mtcars)  # names of columns

##  [1] "mpg"  "cyl"  "disp" "hp"   "drat" "wt"   "qsec" "vs"   "am"   "gear"
## [11] "carb"

rownames(mtcars)  # name of rows

##  [1] "Mazda RX4"           "Mazda RX4 Wag"       "Datsun 710"         
##  [4] "Hornet 4 Drive"      "Hornet Sportabout"   "Valiant"            
##  [7] "Duster 360"          "Merc 240D"           "Merc 230"           
## [10] "Merc 280"            "Merc 280C"           "Merc 450SE"         
## [13] "Merc 450SL"          "Merc 450SLC"         "Cadillac Fleetwood" 
## [16] "Lincoln Continental" "Chrysler Imperial"   "Fiat 128"           
## [19] "Honda Civic"         "Toyota Corolla"      "Toyota Corona"      
## [22] "Dodge Challenger"    "AMC Javelin"         "Camaro Z28"         
## [25] "Pontiac Firebird"    "Fiat X1-9"           "Porsche 914-2"      
## [28] "Lotus Europa"        "Ford Pantera L"      "Ferrari Dino"       
## [31] "Maserati Bora"       "Volvo 142E"

ncol(mtcars)  # number of columns

## [1] 11

nrow(mtcars)  # number of rows

## [1] 32

Creating a data.frame object

• Use the data.frame() constructor to create a dataframe object with a collection of vectors
• Each vector is one attribute of the data, takes one column
• Each column should have same length
• Use as.data.frame() to tranform other data types to data.frame

name = c("Messi", "Ronaldo", "Neymar")  # a character vector
age = c(31, 33, 26)  # a numeric vector
golden_ball = c(TRUE, TRUE, FALSE)
players = data.frame(name, age, golden_ball)
head(players)

##      name age golden_ball
## 1   Messi  31        TRUE
## 2 Ronaldo  33        TRUE
## 3  Neymar  26       FALSE

• Columns of different length is not taken by data.frame

golden_ball = c(TRUE, TRUE)  # golden ball has one missing value
length(name)

## [1] 3

length(golden_ball)

## [1] 2

data.frame(name, golden_ball)  # data frame do not accept columns of different lengths

## Error in data.frame(name, golden_ball): arguments imply differing number of rows: 3, 2

• Use NA to place missing value

golden_ball = c(TRUE, TRUE, NA)  # use NA to indicate missing value 
data.frame(name, age, golden_ball)

##      name age golden_ball
## 1   Messi  31        TRUE
## 2 Ronaldo  33        TRUE
## 3  Neymar  26          NA

• as.data.frame() coerce to data.frame

m = matrix(1:6, nrow = 2, ncol = 3)
class(m)

## [1] "matrix"

m

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

m = as.data.frame(m)
class(m)

## [1] "data.frame"

m

##   V1 V2 V3
## 1  1  3  5
## 2  2  4  6

Accesing data from a data.frame

• This can be done using the same access operators for matrix objects [row,column]

• The 1st row

players[1, ]

##    name age golden_ball
## 1 Messi  31        TRUE

• The 2nd column

players[, 2]

## [1] 31 33 26

• The first 2 rows

players[1:2, ]

##      name age golden_ball
## 1   Messi  31        TRUE
## 2 Ronaldo  33        TRUE

• The first 2 columns

players[, 1:2]

##      name age
## 1   Messi  31
## 2 Ronaldo  33
## 3  Neymar  26

• Particular columns of the data.frame object can be accessed with the $ access operator followed by the column name

• The name column of the data.frame players

players$name

## [1] Messi   Ronaldo Neymar 
## Levels: Messi Neymar Ronaldo

• The second element of the name column

players$name[2]

## [1] Ronaldo
## Levels: Messi Neymar Ronaldo

Operations on data.frame

• Change the value

players$age + 2  # add 2 to all the element of the age column

## [1] 33 35 28

players$age[1] + 3  # add 1 to the first element of the age column

## [1] 34

• Add a new column with cbind()

assists = c(9, 8, 3)
players <- cbind(players, assists)  # add one column with cbind()
players

##      name age golden_ball assists
## 1   Messi  31        TRUE       9
## 2 Ronaldo  33        TRUE       8
## 3  Neymar  26       FALSE       3

• Add a new column with $

players$goals = c(20, 30, 10)  # add one column with $
players

##      name age golden_ball assists goals
## 1   Messi  31        TRUE       9    20
## 2 Ronaldo  33        TRUE       8    30
## 3  Neymar  26       FALSE       3    10

• Add new row with rbind()

new_player = data.frame(name = "Suarez", age = 31, golden_ball = FALSE, goals = 40, 
    assists = 4)  # add a new row to existing data.frame
rbind(players, new_player)

##      name age golden_ball assists goals
## 1   Messi  31        TRUE       9    20
## 2 Ronaldo  33        TRUE       8    30
## 3  Neymar  26       FALSE       3    10
## 4  Suarez  31       FALSE       4    40

players <- rbind(players, new_player)

Functions on data.frame

• mean(),max(),hist()…functions work on all numeric columns, since each column is a vector

mean(mtcars$mpg)

## [1] 20.09062

max(mtcars$carb)

## [1] 8

hist(mtcars$mpg)

• summary() returns summary statistics of each column

summary(mtcars)

##       mpg             cyl             disp             hp       
##  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
##  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
##  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
##  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
##  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
##  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
##       drat             wt             qsec             vs        
##  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
##  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
##  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
##  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
##  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
##        am              gear            carb      
##  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
##  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
##  Median :0.0000   Median :4.000   Median :2.000  
##  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
##  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
##  Max.   :1.0000   Max.   :5.000   Max.   :8.000

summary(mtcars$mpg)  # summary of a specific column

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   10.40   15.42   19.20   20.09   22.80   33.90

In class exercise 4

• Create your a data.frame called running with the following data

• Add the following column to running

• Add the following row to running

Name = c("Sally", "Mike", "Carol")
Gender = c("F", "M", "F")
TenK = c(55, 46, 62)
PR = c(52, 44, 58)
Qualified = c(FALSE, TRUE, FALSE)
running = data.frame(Name, Gender, TenK, PR, Qualified)
running

##    Name Gender TenK PR Qualified
## 1 Sally      F   55 52     FALSE
## 2  Mike      M   46 44      TRUE
## 3 Carol      F   62 58     FALSE

running$HalfMarathon = c(120, 100, 140)
running

##    Name Gender TenK PR Qualified HalfMarathon
## 1 Sally      F   55 52     FALSE          120
## 2  Mike      M   46 44      TRUE          100
## 3 Carol      F   62 58     FALSE          140

newrunner = data.frame(Name = "Sage", Gender = "M", TenK = 40, PR = 42, Qualified = TRUE, 
    HalfMarathon = 81)
running = rbind(running, newrunner)
running

##    Name Gender TenK PR Qualified HalfMarathon
## 1 Sally      F   55 52     FALSE          120
## 2  Mike      M   46 44      TRUE          100
## 3 Carol      F   62 58     FALSE          140
## 4  Sage      M   40 42      TRUE           81

List

• A list is a generic vector containing any other objects.
• We can create a list containning one dataframe, one vector, and one matrix

• R uses list for complex, hierarchical objects

• Use list() to construct

my_list = list(players, c(1, 2, 3), matrix(1:6, 2, 3))
my_list

## [[1]]
##      name age golden_ball assists goals
## 1   Messi  31        TRUE       9    20
## 2 Ronaldo  33        TRUE       8    30
## 3  Neymar  26       FALSE       3    10
## 4  Suarez  31       FALSE       4    40
## 
## [[2]]
## [1] 1 2 3
## 
## [[3]]
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

List: Reference & Sublist

• Use [[n]] to refer each slice of a list

my_list[[1]]  # returns the object of the 2nd member of my_list 

##      name age golden_ball assists goals
## 1   Messi  31        TRUE       9    20
## 2 Ronaldo  33        TRUE       8    30
## 3  Neymar  26       FALSE       3    10
## 4  Suarez  31       FALSE       4    40

class(my_list[[1]])  # it is a data.frame

## [1] "data.frame"

summary(my_list[[1]])

##       name        age        golden_ball        assists         goals     
##  Messi  :1   Min.   :26.00   Mode :logical   Min.   :3.00   Min.   :10.0  
##  Neymar :1   1st Qu.:29.75   FALSE:2         1st Qu.:3.75   1st Qu.:17.5  
##  Ronaldo:1   Median :31.00   TRUE :2         Median :6.00   Median :25.0  
##  Suarez :1   Mean   :30.25   NA's :0         Mean   :6.00   Mean   :25.0  
##              3rd Qu.:31.50                   3rd Qu.:8.25   3rd Qu.:32.5  
##              Max.   :33.00                   Max.   :9.00   Max.   :40.0

• Use [n] to retrieve a sublist from a list

my_list[1]  # return a sublist 

## [[1]]
##      name age golden_ball assists goals
## 1   Messi  31        TRUE       9    20
## 2 Ronaldo  33        TRUE       8    30
## 3  Neymar  26       FALSE       3    10
## 4  Suarez  31       FALSE       4    40

class(my_list[1])  # it is a list

## [1] "list"

mean(my_list[1])  # my_list[1] is a list, mean() does not work on list

## Warning in mean.default(my_list[1]): argument is not numeric or logical:
## returning NA

## [1] NA

• use [n1:n2],[c()] to get a sublist of multiple members

my_list[2:3]

## [[1]]
## [1] 1 2 3
## 
## [[2]]
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

my_list[c(1, 3)]

## [[1]]
##      name age golden_ball assists goals
## 1   Messi  31        TRUE       9    20
## 2 Ronaldo  33        TRUE       8    30
## 3  Neymar  26       FALSE       3    10
## 4  Suarez  31       FALSE       4    40
## 
## [[2]]
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

• Class is really important in R

my_list[[2]]  # a vector

## [1] 1 2 3

my_list[2]  # a list 

## [[1]]
## [1] 1 2 3

mean(my_list[[2]])  # mean() works on vector

## [1] 2

mean(my_list[2])  # mean() does not work on list

## Warning in mean.default(my_list[2]): argument is not numeric or logical:
## returning NA

## [1] NA

• Change a value of a member

my_list[[3]]

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

my_list[[3]] = matrix(1:6, 3, 2)
my_list[[3]]

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

• Add new member to a list

my_list[[4]] = runif(5)
my_list[[4]]

## [1] 0.5553994 0.5335197 0.6975176 0.2739090 0.2006292

• Delete a member from a list

my_list[[4]] <- NULL
my_list[[4]]  # the 4th member is already deleted

## Error in my_list[[4]]: subscript out of bounds

• Use length() to access the number of members in a list

length(my_list)

## [1] 3

In class exercise 5

• Create a list new_list with the following members
  • 1st member: a vector of length 10 from uniform distribution from -2 to 2
  • 2nd member: a matrix from 1:10, with 2 rows, 5 columns, fill by row
  • 3rd member: the running data.frame
• Operations on new_list
  • Add 2 to each element of the first member of new_list
  • Calculate the sum of the 2nd member of new_list
  • Remove the 3rd member of new_list

new_list = list(runif(10, -2, 2), matrix(1:10, 2, 5, byrow = TRUE), running)
new_list

## [[1]]
##  [1] -0.77500241  1.50246652  1.39566400  0.18635356 -0.24914866
##  [6] -1.71086730 -0.10150976  0.63850541 -0.07045173 -1.14813332
## 
## [[2]]
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    2    3    4    5
## [2,]    6    7    8    9   10
## 
## [[3]]
##    Name Gender TenK PR Qualified HalfMarathon
## 1 Sally      F   55 52     FALSE          120
## 2  Mike      M   46 44      TRUE          100
## 3 Carol      F   62 58     FALSE          140
## 4  Sage      M   40 42      TRUE           81

new_list[[1]] = new_list[[1]] + 2
sum(new_list[[2]])

## [1] 55

new_list[[3]] <- NULL

Factor

• Factors are used for categorical objects
• Categorical objects only have a limited number of different values
• Factor categorize data with limited number of unique values and store it as levels
• When you use the data.frame() function, character variables are imported as factors
• Useful in data analysis for statistical modeling since categorical variables enter into statistical models differently than continuous variables
• Use factor() to construct from a vector

Why we use factors

• Factors represent a very efficient way to store character values
• Each unique character value is stored only once
• Data itself is stored as a vector of integers

Demo:Factor

• Create a character vector

direction = c("North", "West", "North", "East", "South", "West", "North", "South")  #create a character vector
direction

## [1] "North" "West"  "North" "East"  "South" "West"  "North" "South"

class(direction)

## [1] "character"

• Use factor() to transform a vector to factor

factor_direction = factor(direction)  # create a factor of direction
factor_direction

## [1] North West  North East  South West  North South
## Levels: East North South West

class(factor_direction)

## [1] "factor"

• Use levels() to access the unique value of a factor

levels(factor_direction)

## [1] "East"  "North" "South" "West"

• Use table() to count the instances for each factor

table(factor_direction)

## factor_direction
##  East North South  West 
##     1     3     2     2

• Create an ordered factor

seasons = c("Spring", "Fall", "Summer", "Spring", "Fall", "Winter", "Winter")

factor_seasons = factor(seasons, levels = c("Spring", "Summer", "Fall", "Winter"), 
    ordered = TRUE)
factor_seasons[1] < factor_seasons[2]

## [1] TRUE

factor_seasons[2] < factor_seasons[3]

## [1] FALSE

• Create a factor from continous value with cut()
• women is a built in data.frame of height&weight of women

head(women)

##   height weight
## 1     58    115
## 2     59    117
## 3     60    120
## 4     61    123
## 5     62    126
## 6     63    129

• Let’s look at the height of women

women$height

##  [1] 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

• We want to create a factor corresponding to height, with three equally-spaced levels

factor_height = cut(women$height, 3)
table(factor_height)

## factor_height
##   (58,62.7] (62.7,67.3]   (67.3,72] 
##           5           5           5

• Use labels=argument in cut() to specify the levels of factors

factor_height = cut(women$height, 3, labels = c("Low", "Medium", "High"))
table(factor_height)

## factor_height
##    Low Medium   High 
##      5      5      5

In class exercise 6

• Create a factor from character
  • Create a ordered factor mons from the following character vector: c(“March”,“April”,“January”,“November”,“January”, “September”,“October”,“September”,“November”,“August”, “January”,“November”,“November”,“February”,“May”,“August”, “July”,“December”,“August”,“August”,“September”,“November”, “February”,“April”)
  • Count the occurance of each month
• Create a factor from continous number
  • Create a factor factor_weight with the weight of women of 2 levels
  • Assign levels of “Low” and “High” to the factor

mons = factor(c("March", "April", "January", "November", "January", "September", 
    "October", "September", "November", "August", "January", "November", "November", 
    "February", "May", "August", "July", "December", "August", "August", "September", 
    "November", "February", "April"), levels = c("January", "February", "March", 
    "April", "May", "June", "July", "August", "September", "October", "November", 
    "December"), ordered = TRUE)
table(mons)

## mons
##   January  February     March     April       May      June      July 
##         3         2         1         2         1         0         1 
##    August September   October  November  December 
##         4         3         1         5         1

factor_weight = cut(women$weight, 2, labels = c("Low", "High"))
factor_weight

##  [1] Low  Low  Low  Low  Low  Low  Low  Low  Low  High High High High High
## [15] High
## Levels: Low High

table(factor_weight)

## factor_weight
##  Low High 
##    9    6

Q&A

Any Questions?

See you tomorrow 8:30am