Get to know R
As we discussed in class, R revolves around objects, e.g., test <- 123.
As we discussed in class, R revolves around objects, e.g., test <- 123.
Note You can also assign values to objects via =, e.g., test = 123.
As we discussed in class, R revolves around objects, e.g., test <- 123.
Note You can also assign values to objects via =, e.g., test = 123.
Objects have types/classes.
As we discussed in class, R revolves around objects, e.g., test <- 123.
Note You can also assign values to objects via =, e.g., test = 123.
Objects have types/classes.
1, 2/3, and are numeric.As we discussed in class, R revolves around objects, e.g., test <- 123.
Note You can also assign values to objects via =, e.g., test = 123.
Objects have types/classes.
1, 2/3, and are numeric.
"Hello" and 'cruel world' are both character.
As we discussed in class, R revolves around objects, e.g., test <- 123.
Note You can also assign values to objects via =, e.g., test = 123.
Objects have types/classes.
1, 2/3, and are numeric.
"Hello" and 'cruel world' are both character.
TRUE, T, FALSE, and F are logical (as is the result of 3 > 2).
As we discussed in class, R revolves around objects, e.g., test <- 123.
Note You can also assign values to objects via =, e.g., test = 123.
Objects have types/classes.
1, 2/3, and are numeric.
"Hello" and 'cruel world' are both character.
TRUE, T, FALSE, and F are logical (as is the result of 3 > 2).
The class(x) function tells you the class of object x.
1#> [1] 1"Clever/funny example words?"#> [1] "Clever/funny example words?"3 < 2#> [1] FALSE"Warriors" > "Bucks"#> [1] TRUE1#> [1] 1"Clever/funny example words?"#> [1] "Clever/funny example words?"3 < 2#> [1] FALSE"Warriors" > "Bucks"#> [1] TRUEclass(1)#> [1] "numeric"class("Clever/funny example words?")#> [1] "character"class(3 < 2)#> [1] "logical"class("Warriors" > "Bucks")#> [1] "logical"In addition to having types/classes, objects have some type of structure.
1:3, c(1, 2), and seq(2, 8, 2) each produce a numeric-class vector.In addition to having types/classes, objects have some type of structure.
1:3, c(1, 2), and seq(2, 8, 2) each produce a numeric-class vector.
c("Alright", "already") produces a vector of character class.
In addition to having types/classes, objects have some type of structure.
1:3, c(1, 2), and seq(2, 8, 2) each produce a numeric-class vector.
c("Alright", "already") produces a vector of character class.
c(1, 3, T, "Hello") produces a vector of character class.
In addition to having types/classes, objects have some type of structure.
1:3, c(1, 2), and seq(2, 8, 2) each produce a numeric-class vector.
c("Alright", "already") produces a vector of character class.
c(1, 3, T, "Hello") produces a vector of character class.
matrix(data = 1:15, ncol = 5) creates a matrix with class from data.
In addition to having types/classes, objects have some type of structure.
1:3, c(1, 2), and seq(2, 8, 2) each produce a numeric-class vector.
c("Alright", "already") produces a vector of character class.
c(1, 3, T, "Hello") produces a vector of character class.
matrix(data = 1:15, ncol = 5) creates a matrix with class from data.
data.frame(x = 1:2, y = c("a", "b"), z = T) produces a data.frame with three columns and two rows. The first column (x) is numeric; the second column (y) is character, and the third column (z) is logical.
Our matrix
matrix(data = 1:15, ncol = 5)#> [,1] [,2] [,3] [,4] [,5]#> [1,] 1 4 7 10 13#> [2,] 2 5 8 11 14#> [3,] 3 6 9 12 15Our matrix
matrix(data = 1:15, ncol = 5)#> [,1] [,2] [,3] [,4] [,5]#> [1,] 1 4 7 10 13#> [2,] 2 5 8 11 14#> [3,] 3 6 9 12 15Our first data.frame!
data.frame(x = 1:3, y = T)#> x y#> 1 1 TRUE#> 2 2 TRUE#> 3 3 TRUEOur matrix
matrix(data = 1:15, ncol = 5)#> [,1] [,2] [,3] [,4] [,5]#> [1,] 1 4 7 10 13#> [2,] 2 5 8 11 14#> [3,] 3 6 9 12 15Our first data.frame!
data.frame(x = 1:3, y = T)#> x y#> 1 1 TRUE#> 2 2 TRUE#> 3 3 TRUENotice how R helps 'fill' out the columns when lengths don't match.
R can help you check object's type.
class(matrix(1:9, ncol = 3))#> [1] "matrix"is.matrix(matrix(1:9, ncol = 3))#> [1] TRUEis.data.frame(matrix(1:9, ncol = 3))#> [1] FALSER can help you check object's type.
class(matrix(1:9, ncol = 3))#> [1] "matrix"is.matrix(matrix(1:9, ncol = 3))#> [1] TRUEis.data.frame(matrix(1:9, ncol = 3))#> [1] FALSEclass(data.frame(x = 1:3))#> [1] "data.frame"is.matrix(data.frame(x = 1:3))#> [1] FALSEis.data.frame(data.frame(x = 1:3))#> [1] TRUEQ What happens when we mix classes, e.g., c(12, "B", F)?
Q What happens when we mix classes, e.g., c(12, "B", F)?
A R applies the class that can apply to all objects.
c(12, "B")#> [1] "12" "B"c(12, F)#> [1] 12 0c("B", F)#> [1] "B" "FALSE"c(12, "B", F)#> [1] "12" "B" "FALSE"Change numbers to characters.
as.character(1:3)#> [1] "1" "2" "3"Change logical to numeric.
as.numeric(c(T, F))#> [1] 1 0Change vector to matrix.
as.matrix(1:3)#> [,1]#> [1,] 1#> [2,] 2#> [3,] 3Straight out of the box, R has a ton of useful features, but it really gets its power from the additional packages (libraries) that users create.
Open-source greatness Users find needs and create amazing solutions.
Caveat utilitor There are a lot of packages, each with a lot of functions. Mistakes can happen.
Open-source greatness2 Again, R is open source: Check the code!
Straight out of the box, R has a ton of useful features, but it really gets its power from the additional packages (libraries) that users create.
Open-source greatness Users find needs and create amazing solutions.
Caveat utilitor There are a lot of packages, each with a lot of functions. Mistakes can happen.
Open-source greatness2 Again, R is open source: Check the code!
(Maybe. Sometimes it's very hard.)
Straight out of the box, R has a ton of useful features, but it really gets its power from the additional packages (libraries) that users create.
Open-source greatness Users find needs and create amazing solutions.
Caveat utilitor There are a lot of packages, each with a lot of functions. Mistakes can happen.
Open-source greatness2 Again, R is open source: Check the code!
(Maybe. Sometimes it's very hard.)
Examples ggplot2 (plotting), dplyr (data work that can link with SQL), sf and raster (geospatial work), lfe (high-dimensional fixed-effect regression), data.table (fast and efficient data work)
Once you find a function/package that you need to install,† you'll typically install it via install.packages("newAmazingPackage").††
† Tool #1: Google. †† The quotation marks are important.
We'll use the package dplyr throughout the course. Let's install it.
# Install 'dplyr' packageinstall.packages("dplyr")Once you find a function/package that you need to install,† you'll typically install it via install.packages("newAmazingPackage").††
† Tool #1: Google. †† The quotation marks are important.
We'll use the package dplyr throughout the course. Let's install it.
# Install 'dplyr' packageinstall.packages("dplyr")Aside Notice the comment above the actual code (R uses # for comments).
Once you find a function/package that you need to install,† you'll typically install it via install.packages("newAmazingPackage").††
† Tool #1: Google. †† The quotation marks are important.
We'll use the package dplyr throughout the course. Let's install it.
# Install 'dplyr' packageinstall.packages("dplyr")Aside Notice the comment above the actual code (R uses # for comments).
While not necessary for R to work, comments are necessary for research.
Once you install a package, it is on your machine.
You don't need to install it again—though you probably should update them from time to time.
Once you install a package, it is on your machine.
You don't need to install it again—though you probably should update them from time to time.
To load a package, use the library(package) function†, e.g., to load dplyr
† Notice library() doesn't need quotation marks. I know...
# Load 'dplyr'library(dplyr)Once you install a package, it is on your machine.
You don't need to install it again—though you probably should update them from time to time.
To load a package, use the library(package) function†, e.g., to load dplyr
† Notice library() doesn't need quotation marks. I know...
# Load 'dplyr'library(dplyr)Now all functions contained in dplyr are available (until you close R).
All of this installing, loading, updating, checking-for-existance-and-then-loading can get old.
As can typing library(pacakge1), library(package2), ...
All of this installing, loading, updating, checking-for-existance-and-then-loading can get old.
As can typing library(pacakge1), library(package2), ...
[Enter] The pacman package... for package management, of course.
All of this installing, loading, updating, checking-for-existance-and-then-loading can get old.
As can typing library(pacakge1), library(package2), ...
[Enter] The pacman package... for package management, of course.
After installing (install.packages("pacman")), you can
Install and load packages via p_load(package1, ..., packageN)
Update packages via p_update()
The p_load paradigm is especially helpful for collaboarations or projects across multiple machines.
Basic algebra: scalars a and b
# Additiona + b# Subtractiona - b# Multiplicationa * b# Divisiona / b# Moda %% b# Integer divisiona %/% b# Exponentsa^bBasic algebra: scalars a and b
# Additiona + b# Subtractiona - b# Multiplicationa * b# Divisiona / b# Moda %% b# Integer divisiona %/% b# Exponentsa^bMatrix algebra: matrices A and B
# AdditionA + B# SubtractionA - B# MultiplicationA %*% B# Inversesolve(A)# Transposet(A)# Diagonaldiag(A)# Dimensionsdim(A); nrow(A); ncol(A)One great feature in R: vectorization.
With vectorization, R automatically applies functions to each element of a vector—no iteration required.
# Multiply a scalar by a scalar3 * 4#> [1] 12# Multiply a scalar by a vector3 * c(4, 5, 6)#> [1] 12 15 18# Multiply a vector by a vector1:3 * c(4, 5, 6)#> [1] 4 10 18Vectorization can be confusing.
c(0.5, 0.9) + c(1, 2, 3)#> [1] 1.5 2.9 3.5R will send you a warning, but it won't stop you.
Summaries for samples x and y
# Meanmean(x)# Medianmedian(x)# Std. dev. and variancesd(x)var(x)# Min. and max.min(x)max(x)# Correlation/covariancecor(x, y)cov(x, y)# Quartiles and meansummary(x)Summaries for samples x and y
# Meanmean(x)# Medianmedian(x)# Std. dev. and variancesd(x)var(x)# Min. and max.min(x)max(x)# Correlation/covariancecor(x, y)cov(x, y)# Quartiles and meansummary(x)Sampling
# Set the seedset.seed(246)# 4 random draws from N(3,5)rnorm(n = 4, mean = 3, sd = sqrt(5))# CDF for N(0,1) at z=1.96pnorm(q = 1.96, mean = 0, sd = 1)# Sample 5 draws from x w/ repl.sample( x = x, size = 5, replace = T)# First and last 3head(x, 3)tail(x, 3)Because vectors are so central to R, being able to index your vectors is important. Note: Vectors have one dimension.
Take the vector x (e.g., x <- c(2, 4, 6, 9)).
x[3] will give us the third element of the vector—i.e., 6.x[2:3] will give us the second and third elements—i.e., c(4, 6).x[-1] returns all elements except the first—i.e., c(4, 6, 9).x[2] <- 0 replaces the second element with 0—i.e., c(2, 0, 6, 9).Because vectors are so central to R, being able to index your vectors is important. Note: Vectors have one dimension.
Take the vector x (e.g., x <- c(2, 4, 6, 9)).
x[3] will give us the third element of the vector—i.e., 6.x[2:3] will give us the second and third elements—i.e., c(4, 6).x[-1] returns all elements except the first—i.e., c(4, 6, 9).x[2] <- 0 replaces the second element with 0—i.e., c(2, 0, 6, 9).Lists, e.g., list(1, 2, 3), are similar but use double brackets, e.g., y[[3]].
Because matrices (and data frames) have two dimensions, we need to index both dimensions.
For matrix A (e.g., A <- matrix(1:9, ncol = 3))
A[3,1] references the element in the 3rd row and 1st column.A[3,] references all elements in the 3rd row (across all columns).A[,1] references all elements in the 1st column (across all rows).A[-2,] returns all elements in A except for the 2nd row.A[2,3] <- 0 replaces the element A[2,3] with zero.Because matrices (and data frames) have two dimensions, we need to index both dimensions.
For matrix A (e.g., A <- matrix(1:9, ncol = 3))
A[3,1] references the element in the 3rd row and 1st column.A[3,] references all elements in the 3rd row (across all columns).A[,1] references all elements in the 1st column (across all rows).A[-2,] returns all elements in A except for the 2nd row.A[2,3] <- 0 replaces the element A[2,3] with zero.You can also name rows/columns in matrices—and can use these names for referencing.
"Special" values
Inf is ∞, i.e., 1/0. -Inf is -∞.NA is missing.NaN is not a number.NULL is null."Special" values
Inf is ∞, i.e., 1/0. -Inf is -∞.NA is missing.NaN is not a number.NULL is null.Standard logical operators
== for equality!= is not equal.>, >=, <, <=& is and; | is or."Special" values
Inf is ∞, i.e., 1/0. -Inf is -∞.NA is missing.NaN is not a number.NULL is null.Standard logical operators
== for equality!= is not equal.>, >=, <, <=& is and; | is or.R orders by number, lowercase, then uppercase.
# Ordering1 < "a"#> [1] TRUENAFinally, NA contains no information in R
NA == NA#> [1] NANA != NA#> [1] NANA > 0#> [1] NANA + 0#> [1] NAis.vector(NA)#> [1] TRUEIn general, a function takes some arguments, performs some internal tasks, and returns some output.
Typical function in R: some_fun(arg1, arg2, arg3 = 0)
For some_fun to run, you must define arg1 and arg2, e.g., some_fun(arg1 = 12, arg2 = -1)
Optional arguments If you do not assign a value for arg3, then some_fun defaults to arg3 = 0
some_fun(arg1 = 12, arg2 = -1)some_fun(arg1 = 12, arg2 = -1, arg3 = 0)Functions in R are flexible.
Examples
c(arg1, arg2, ... argN) returns a vector of the inputted arguments
Note c() takes many inputs and returns one output.
ls() lists all user-defined objects in the current environment
Note ls works without any inputs and returns a character vector.
rm(obj) removes the object obj from the current environment
Note rm can take many inputs and returns no output.
R makes it easy to define your own functions.†
† We'll delve more deeply into this topic soon.
Standard example A function that returns the product of three numbers.
# Our function 'our_product' takes three argumentsour_product <- function(num1, num2, num3) { # Calculate the product tmp_product <- num1 * num2 * num3 # Return the answer return(tmp_product)}You could get away without using return() but that's not recommended.
Our function in action...
our_product(1, 2, 3)#> [1] 6our_product(1, 2, NA)#> [1] NAUsing the tools we've covered, generate a dataset (n=50) such that yi=12+1.5xi+εi where xi∼N(3,7) and εi∼N(0,1).
Estimate the relationship via OLS using only matrix algebra. Recall ˆβOLS=(X′X)−1X′y
Harder Write a function that estimates OLS coefficients using matrix algebra. Compare your results with the canned function from R (lm).
Hardest Bring it all together: Use your DGP (1) and function (3) to run a simulation that illustrates the unbiasedness of OLS.
Introduction to R
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