2-RMarkdown.Rmd

---
title: "R Markdown"
author: "Devin Judge-Lord"
date: "`r format(Sys.time(), '%d %B, %Y')`"
output:
  html_document:
    toc: yes
  pdf_document:
    toc: yes
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)

if(!"here" %in% rownames(installed.packages())){
install.packages("here", repos = "https://cloud.r-project.org/" )}
library(here)
library(tidyverse)
library(magrittr)

# source(here(setup.R))
```

![](http://www.phdcomics.com/comics/archive/phd101212s.gif)

***This is why don't copy and paste numbers, table, or figures into a paper.**

---

## R Markdown

Markdown is just **plain text** that can be rendered as HTML, PDF, or even Microsoft Word. Rstudio's "Knit" button will make the selected document.

We can use various syntaxes, like $\LaTeX$ and **R** as needed inline with the rest of our text, which we write in [markdown syntax](https://bookdown.org/yihui/rmarkdown/markdown-syntax.html). For example, typing "\$`y = \alpha + X\beta`\$" gives us "$y = \alpha + X\beta$" and typing "\{`r` `nchar("hello world")`\}" gives us "`r  nchar("hello world")`"---pretty cool. For more, see <http://rmarkdown.rstudio.com>, especially this [cheatsheet](http://rmarkdown.rstudio.com), and this [tutorial](https://www.markdowntutorial.com/).

<blockquote>
"use tools that give you more control over the process of data analysis and writing." - [The Plain Person’s Guide to Plain Text Social Science by Kieran Healy](http://plain-text.co/)
</blockquote>
--- 

We can embed a chunk of R code like this:
```{r pressure}
# a dataset built into R
head(pressure)
```

In [the .Rmd file](https://github.com/judgelord/PS811/blob/master/2-RMarkdown.Rmd), you'll see that the above chunk of R code begins with "\`\`\`\{r pressure\}", which tells the computer that this chunk is `r` code and names this chunk "pressure." 

Give code chunks informative names! If your chunk produces figures, they will be saved with this name.

---

If we don't want our code chunk in the output, only the results, we add `echo = FALSE` to the header:

```{r pressure_echo_false, echo = FALSE}
head(pressure)
```

We can set defaults for the whole document (e.g. `knitr::opts_chunk$set(echo = TRUE)`). See the above "setup" chunk in this .Rmd file.

Problem sets and papers will use `echo = FALSE` to display just the output. For notes, we may want to see our code `echo = TRUE`. Or, if our output is HTML, hide our code; try knitting to HTML after adding `code_folding: hide` to the YAML header in this .Rmd file like this:
```output: 
  html_document:
      latex_engine: pdflatex
      code_folding: hide
```

To display code we don't want to run, we add `eval = FALSE`.

```{r, code_not_run, eval = FALSE }
This code will not run. 
```

For example, if you want to share code that does not work on your 811 page, use `eval = FALSE`.

---

It is safer to use `cache = FALSE`, which re-computes all results each time and will thus update if your data have changed. If computing is taking a long time, you can use `cache = TRUE` to knit faster, but this will only run chunks where the *code* has changed. 

---

## Including Plots

We can also embed plots. For example:

```{r pressure_plot}
library(ggplot2);
ggplot(data = pressure, aes(x = temperature, y = pressure)) + 
  geom_point() + 
  geom_line()
```

Note that we needed to load the library `ggplot2` because knitting uses a new **R** session. Your .Rmd file must load any required libraries, functions, and data. The upshot of this is that knitting is self-contained. It starts fresh; not depending on whatever you may have done in **R** previously.

We can adjust the size by adding `fig.width = 3, fig.height= 2` to get a $4\times3$ inch figure.

```{r pressure_size, echo=FALSE, fig.width = 3, fig.height = 2}
ggplot(data = pressure, aes(x = temperature, y = pressure)) + 
  geom_point() + 
  geom_line()
```

---

Let us also center `fig.align='center` and add a caption, `fig.cap = "Plotting Temperature vs. Pressure"`:

```{r pressure_cap, echo=FALSE, fig.cap = "Plotting Temperature vs. Pressure", fig.width = 3, fig.height = 2, fig.align='center'}
ggplot(data = pressure, aes(x = temperature, y = pressure)) + 
  geom_point() + 
  geom_line()
```

---

<!--
We can link to figures in the text of the document by adding `\\label{fig:pressure}` to the caption.
Typing `\ref{fig:pressure}` will now always correctly reference figure \ref{fig:pressure} regardless of how many figures are added above it.

```{r pressure_cap_size_ling, echo=FALSE, fig.cap = "\\label{fig:pressure}Plotting Temperature vs. Pressure with a label", fig.width = 3, fig.height = 2, fig.align='center'}
ggplot(data = pressure, aes(x = temperature, y = pressure)) + 
  geom_point() + 
  geom_line() 
```
-->

---

# Two ways to code

#### 1. Get code working in a .R file (e.g. in your /scratchpad subfolder), then copy the final code into .Rmd file chunks. 

#### 2. Workshop code in .Rmd file chunks. 
#### You may want to change RStudio settings (gear button) to `Chunk Output in Consol`

Either way, press command/control+enter to run **a line or highlighted section** locally. If using a remote server, command/control+option/alt+enter will send it to the terminal/bash.

\newpage
---

# Writing Math
We can use MathJax and/or $\LaTeX$ to write nice-looking math.  For example, we can write out a regression equation as $y = \alpha + X\beta + \varepsilon$, without having to copy, paste, or insert special symbols. To write out anything math related, we enclose it in dollar signs $\$$`math`$\$$. The regression equasion above, for example, is $\$$ `y = \alpha + X\beta + \varepsilon` $\$$. If we want to index something by adding subscripts $x_{1}, x_{2}$ etc, the code is $\$$`x_{1}, x_{2}`$\$$. Fractions are written such that $\$$`\frac{1}{2}`$\$$ is $\frac{1}{2}$, and exponents ($2^{2}$) are written $\$$`2^{2}`$\$$.

---

The Greek letters have a slash before them which tells $\LaTeX$ or MathJax to print that as a Greek letter. Similarly $2 \times 2$ is written $\$$ `2 \times 2` $\$$. See guides to special characters and formatting in $\LaTeX$ [here](https://users.dickinson.edu/~richesod/latex/latexcheatsheet.pdf) and MathJax [here](https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference). I regularly google symbols.

---

## Matrices

To write a matrix:
$$ 
\left[
\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6\\
7 & 8 & 0
\end{array}
\right] 
$$
we write:
```{r, matrix_demo_no comments, echo = TRUE, eval = FALSE}
$$ 
\left[
\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6\\
7 & 8 & 0
\end{array}
\right] 
$$
```

where:
```{r, matrix_demo, echo = TRUE, eval = FALSE}
$$ % start Latex mode
\left[ %creates the left bracket, the "\left" command scales the bracket "["
\begin{array}{ccc} % Creates the "array" (matrix), {ccc} defines the number of columns
1 & 2 & 3 \\ % "&" divides the columns, "\\" creates a new line
4 & 5 & 6\\
7 & 8 & 0
\end{array} % ends the matrix
\right] %creates the left bracket, the "\right" command scales the bracket "]"
$$ % ends LaTeX mode
```

### Matrix multiplication

$$
\left[
\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6\\
7 & 8 & 0
\end{array}
\right] 
\times 
\left[
\begin{array}{ccc}
1 \\
1 \\
1
\end{array}
\right] 
= 
\left[
\begin{array}{ccc}
1 + 2 + 3 \\
4 + 5 + 6\\
7 + 8 + 0
\end{array}
\right] 
= 
\left[
\begin{array}{ccc}
5 \\
15\\
15
\end{array}
\right]
$$

$$
\left[
\begin{array}{ccc}
1 & 1 & 1
\end{array}
\right] 
\times
\left[
\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6\\
7 & 8 & 0
\end{array}
\right] 
= 
\left[
\begin{array}{ccc}
1 + 4 + 7 & 2 + 5 + 8 &  3 + 6 + 0
\end{array}
\right] 
= 
\left[
\begin{array}{ccc}
12 & 15 & 9
\end{array}
\right]
$$

\newpage
---

# Example Notes

### Linear regression with fixed effects:
$$ y_{i} = \alpha_{0} + \alpha_{j} + x_{i} \beta + \varepsilon $$
Where $\alpha_{0}$ is the intercept, 

$\alpha_{j}$ are fixed effects (effects that do not vary by $x$, i.e. intercept shifts) for each group $j$, 

$x$ and $y$ are vectors of observations, and

$\varepsilon$ is the error.

### OLS estimation 

Data:
$$
X = 
\left[
\begin{array}{cc}
x_{1, 1} & x_{1, 2} \\
x_{2, 1} & x_{2, 2} \\
\end{array}
\right],
\\
y = 
\left[
\begin{array}{cc}
y_{1}\\
y_{2}\\
\end{array}
\right]
$$

OLS equation
$$
\hat{\beta} = (X'X)^{-1}(X'y)
$$

### Logistic link function:
$$ Pr(y_{i} = 1) = \frac{1}{1 + e^{-x_{i} \beta}} $$

### Poisson PMF:
$$
      \frac{\lambda^k}{k!} e^{-\lambda}
$$

### Gaussian (normal) PDF:
$$ \frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}} $$