---
title: "Getting to know .mono[R]"
subtitle: "EC 425/525, Lab 1"
author: "Edward Rubin"
date: "`r format(Sys.time(), '%d %B %Y')`"
output:
  xaringan::moon_reader:
    css: ['default', 'metropolis', 'metropolis-fonts', 'my-css.css']
    # self_contained: true
    nature:
      highlightStyle: github
      highlightLines: true
      countIncrementalSlides: false
---
class: inverse, middle

```{R, setup, include = F}
# devtools::install_github("dill/emoGG")
library(pacman)
p_load(
  broom, tidyverse,
  latex2exp, ggplot2, ggthemes, ggforce, viridis, extrafont, gridExtra,
  kableExtra, snakecase, janitor,
  data.table, dplyr, estimatr,
  lubridate, knitr, parallel,
  lfe,
  here, magrittr
)
# Define pink color
red_pink <- "#e64173"
turquoise <- "#20B2AA"
orange <- "#FFA500"
red <- "#fb6107"
blue <- "#3b3b9a"
green <- "#8bb174"
grey_light <- "grey70"
grey_mid <- "grey50"
grey_dark <- "grey20"
purple <- "#6A5ACD"
slate <- "#314f4f"
# Dark slate grey: #314f4f
# Knitr options
opts_chunk$set(
  comment = "#>",
  fig.align = "center",
  fig.height = 7,
  fig.width = 10.5,
  warning = F,
  message = F
)
opts_chunk$set(dev = "svg")
options(device = function(file, width, height) {
  svg(tempfile(), width = width, height = height)
})
options(knitr.table.format = "html")
```

# Prologue

---
name: schedule

# Schedule

## Today

Get to know .mono[R]

1. Basic features of .mono[R]
2. Fun with functions
3. OLS (canned and custom)
4. Simulations
---
layout: true
# .mono[R] intro
---
name: types

## Object types/classes

As we discussed in class, .mono[R] revolves around objects, _e.g._, `test <- 123`.
--

<br>.hi-slate[*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`.
---

## Object types/classes

.pull-left[
```{R, ex_class, split = T}
1
"Clever/funny example words?"
3 < 2
"Warriors" > "Bucks"
```
]
--
.pull-right[
```{R, ex_class2, split = T}
class(1)
class("Clever/funny example words?")
class(3 < 2)
class("Warriors" > "Bucks")
```
]
---
name: structure

## Structure

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.
---

## Object types

.pull-left[

Our `matrix`

```{R, ex_matrix}
matrix(data = 1:15, ncol = 5)
```


]

--

.pull-right[

Our first `data.frame`!

```{R, ex_df}
data.frame(x = 1:3, y = T)
```

]

--

Notice how .mono[R] helps 'fill' out the columns when lengths don't match.
---

## Object types

.mono[R] can help you check object's type.

.pull-left[
```{R, ex_matrix2}
class(matrix(1:9, ncol = 3))
is.matrix(matrix(1:9, ncol = 3))
is.data.frame(matrix(1:9, ncol = 3))
```
]
--
.pull-right[
```{R, ex_df2}
class(data.frame(x = 1:3))
is.matrix(data.frame(x = 1:3))
is.data.frame(data.frame(x = 1:3))
```
]
---
name: mix

## Object types/classes

.hi-slate[Q] What happens when we mix classes, _e.g._, `c(12, "B", F)`?

--

.hi-slate[A] .mono[R] applies the class that can apply to all objects.

.pull-left[
```{R, ex_type1}
c(12, "B")
c(12, F)
```
]
.pull-right[
```{R, ex_type2}
c("B", F)
c(12, "B", F)
```
]
---
name: change

## Changing types and classes

.pull-left[
Change numbers to characters.
```{R, num2chr}
as.character(1:3)
```
]
.pull-right[
Change logical to numeric.
```{R, log2num}
as.numeric(c(T, F))
```
]

.pull-left[
Change vector to matrix.
```{R, vec2mat}
as.matrix(1:3)
```
]
---
name: packages

## Packages

Straight out of the box, .mono[R] has a ton of useful features, but it really gets its power from the additional packages (libraries) that users create.

- .hi-slate[Open-source greatness] Users find needs and create amazing solutions.

- .hi-slate[*Caveat utilitor*] There are a lot of packages, each with a lot of functions. Mistakes can happen.

- .hi-slate[Open-source greatness.sub[2]] Again, .mono[R] is open source: Check the code!
--
<br>(Maybe. Sometimes it's very hard.)

--

.hi-slate[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)

---

## Installing packages


Once you find a function/package that you need to install,.super[.pink[†]] you'll typically install it via `install.packages("newAmazingPackage")`..super[.pink[††]]

.footnote[.pink[†] Tool \#1: Google.  .pink[††] The quotation marks are important.]

We'll use the package `dplyr` throughout the course. Let's install it.

```{R, ex_install_dplyr, eval = F}
# Install 'dplyr' package
install.packages("dplyr")
```
--
.hi-slate[*Aside*] Notice the comment above the actual code (.mono[R] uses `#` for comments).
--
<br>While not necessary for .mono[R] to work, comments are necessary for research.
---

## Using packages

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 .hi-slate[load a package], use the `library(package)` function.super[.pink[†]], _e.g._, to load `dplyr`

.footnote[.pink[†] Notice `library()` doesn't *need* quotation marks. I know...]

```{R, eval = F}
# Load 'dplyr'
library(dplyr)
```

--

Now all functions contained in `dplyr` are available (until you close .mono[R]).
---

## Package management

All of this installing, loading, updating, checking-for-existance-and-then-loading can get old.


As can typing `library(pacakge1)`, `library(package2)`, ...

--

.slate[*[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.
---
name: math

## Math in .mono[R]

.pull-left[
.hi-slate[Basic algebra:] scalars `a` and `b`
```{R, math_algebra, eval = F}
# Addition
a + b
# Subtraction
a - b
# Multiplication
a * b
# Division
a / b
# Mod
a %% b
# Integer division
a %/% b
# Exponents
a^b
```
]
--
.pull-right[
.hi-pink[Matrix algebra:] matrices `A` and `B`
```{R, matrix_algebra, eval = F}
# Addition
A + B
# Subtraction
A - B
# Multiplication
A %*% B
# Inverse
solve(A)
# Transpose
t(A)
# Diagonal
diag(A)
# Dimensions
dim(A); nrow(A); ncol(A)
```
]
---
name: vectorization

## Vectorization

One **great** feature in .mono[R]: vectorization.

With vectorization, .mono[R] automatically applies functions to each element of a vector—no iteration required.

---

## Vectorization

.pull-left[
```{R, ex_vec}
# Multiply a scalar by a scalar
3 * 4
# Multiply a scalar by a vector
3 * c(4, 5, 6)
# Multiply a vector by a vector
1:3 * c(4, 5, 6)
```
]
.pull-right[
Vectorization can be confusing.
```{R, ex_vec_error}
c(0.5, 0.9) + c(1, 2, 3)
```
.mono[R] will send you a warning, but it won't stop you.
]
---
name: stat

## Statistics in .mono[R]

.pull-left[
.hi-slate[Summaries] for samples `x` and `y`
```{R, stat_functions, eval = F}
# Mean
mean(x)
# Median
median(x)
# Std. dev. and variance
sd(x)
var(x)
# Min. and max.
min(x)
max(x)
# Correlation/covariance
cor(x, y)
cov(x, y)
# Quartiles and mean
summary(x)
```
]
--
.pull-right[
.hi-pink[Sampling]
```{R, sampling_functions, eval = F}
# Set the seed
set.seed(246)
# 4 random draws from N(3,5)
rnorm(n = 4, mean = 3, sd = sqrt(5))
# CDF for N(0,1) at z=1.96
pnorm(q = 1.96, mean = 0, sd = 1)
# Sample 5 draws from x w/ repl.
sample(
  x = x,
  size = 5,
  replace = T
)
# First and last 3
head(x, 3)
tail(x, 3)
```
]
---
name: indexing

## Indexing vectors

Because vectors are so central to .mono[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]]`.

---

## Indexing matrices

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 3.super[rd] row and 1.super[st] column.
- `A[3,]` references all elements in the 3.super[rd] row (across all columns).
- `A[,1]` references all elements in the 1.super[st] column (across all rows).
- `A[-2,]` returns all elements in `A` except for the 2.super[nd] 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.
---

## Other

.pull-left[
"Special" values

- `Inf` is ∞, _i.e._, 1/0. `-Inf` is -∞.
- `NA` is missing.
- `NaN` is *not a number*.
- `NULL` is null.
]
--
.pull-right[
Standard logical operators

- `==` for equality
- `!=` is not equal.
- `>`, `>=`, `<`, `<=`
- `&` is *and*; `|` is *or*.
]

--

.mono[R] orders by number, lowercase, then uppercase.
```{R, ex_order}
# Ordering
1 < "a"
```
---
name: more

## `NA`

Finally, `NA` contains no information in .mono[R]

.pull-left[
```{R, ex_na}
NA == NA
NA != NA
NA > 0
```
]
.pull-right[
```{R, ex_na2}
NA + 0
is.vector(NA)
```
]
---
name: functions

## Functions

In general, a function takes some arguments, performs some internal tasks, and returns some output.

.hi-slate[*Typical function in* .mono[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`
  - Omitted: `some_fun(arg1 = 12, arg2 = -1)`
  - Equivalent: `some_fun(arg1 = 12, arg2 = -1, arg3 = 0)`

---

## Functions

Functions in .mono[R] are flexible.

.hi-slate[*Examples*]

- `c(arg1, arg2, ... argN)` returns a vector of the inputted arguments
<br>*Note* `c()` takes many inputs and returns one output.

- `ls()` lists all user-defined objects in the current environment
<br>*Note* `ls` works without any inputs and returns a character vector.

- `rm(obj)` removes the object `obj` from the current environment
<br>*Note* `rm` can take many inputs and returns no output.
---
name: user_fun

## User-defined functions

.mono[R] makes it easy to define your own functions.<sup>.pink[†]</sup>

.footnote[.pink[†] We'll delve more deeply into this topic soon.]

.hi-slate[*Standard example*] A function that returns the product of three numbers.

```{R, ex_fun}
# Our function 'our_product' takes three arguments
our_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.
---

## User-defined functions

Our function in action...

```{R, ex_our_fun}
our_product(1, 2, 3)
```

```{R, ex_our_fun2}
our_product(1, 2, NA)
```
---
name: exercise

## Exercises

1. Using the tools we've covered, generate a dataset $\left( n=50 \right)$ such that
$$
\begin{align}
  y_i = 12 + 1.5 x_i + \varepsilon_i
\end{align}
$$
where $x_i\sim N(3,7)$ and $\varepsilon_i\sim N(0,1)$.

2. Estimate the relationship via OLS using only matrix algebra. Recall
$$
\begin{align}
  \hat{\beta}_\text{OLS} = \left( {X}^\prime {X} \right)^{-1} {X}^\prime {y}
\end{align}
$$

3. .hi-slate[*Harder*] Write a function that estimates OLS coefficients using matrix algebra. Compare your results with the canned function from .mono[R] (`lm`).

4. .hi-slate[*Hardest*] Bring it all together: Use your DGP (1) and function (3) to run a simulation that illustrates the unbiasedness of OLS.
---
layout: false

# Table of contents

.hi-slate[Introduction to .mono[R]]
.smaller[

1. [Schedule](#schedule)
1. [Object types and classes](#types)
  - [Data structures](#structure)
  - [Mixing types/classes](#mix)
  - [Changing](#change)
1. [Packages](#packages)
1. [Math in .mono[R]](#math)
1. [Vectorization](#vectorization)
1. [Statistics and simulation](#stat)
1. [Indexing](#indexing)
1. [`NA` and logical operators](#more)
1. [Functions](#functions)
1. [User-defined functions](#user_fun)
1. [Exercise](#exercise)

]
---
exclude: true

```{R, generate pdfs, include = F, eval = T}
source("../../ScriptsR/unpause.R")
unpause("01RBasics.Rmd", ".", T, T)
```