An Introduction to R

# An Introduction to R
## ED 217 B Week 2 
### Daniel Katz
### 1/12/2021

---

### General Strategy

+ My goal is to get us up and running - doing is the best learning

+ Provide you with some quality resources for continuing to learn via links like [_**this**_](https://stackoverflow.com/tags/r/info)
  
+ I won't emphasize code-style best practices except in a few cases (but these will only be for cases that make life easier)

+ I think it's important to focus on ideas and functions

+ For more on style/best practices, [_**click here**_](http://adv-r.had.co.nz/Style.html)

+ Learning how to trouble shoot is important

---
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## General Outline for Today
.pull-left[

1. What is the relationship between probability, odds, and log odd (logits)?

1. Intro: How should I think about and use R and Rstudio?

1. R Basics

1. Reading in data, subsetting, intro to dplyr (and piping)
]

---
## Next few weeks

1. Next week - more on plotting, more on working with data frames.

1. Using `Rmarkdown`

1. Getting introduced to TAM

--
.pull-right[There's a **TON** to R. I don't expect expertise after this session, but I hope you know where to start!

<img src="poppins_bag.gif" style="display: block; margin: auto;" />
]

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# What is R?

+ R is a software and scripting language

+ Like any other language it has syntax (for now think, "rules" of language)

+ R comes with a variety of built-in functions  
  
  
+ R is desiged for statistics, but you can do lots with it 
  + build websites
  + write documents in Latex
  + Create slides for presentations, etc.
---
class: middle
  
# You can learn R!

+ It is quickly becoming the statistical language of choice in academic and non-academic circles

--
  
+ `R Packages` are making tasks more accessible to non-programmers like me

--
  
+ R allows for sharing code: we won't cover Github, but please [_**check it out**_](https://happygitwithr.com/rstudio-git-github.html)

--
  
+ Scripting forces us to slow down and think

+ We can do everything in one place (data cleaning, plotting, modeling, etc)

---

# It makes really (fairly?) cool visualizations

---

---
class: middle

# Probability, odds, logits

+ In this class, we'll be operating a lot with probability, odds, and log odds  
  
  
--

+ As mentioned in course slides, the link function in logistic regression (and the Rasch model is a special case) is the logit link

- We still want to work in the linear model framework
- we do this with the log of the odds

`$$\log(\frac{p_i}{1-p_i}) = \beta_0 + \sum_{n=1}^N \beta_n x_{in}$$`
---
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# Solving for `$p_i$`

Writing, `$\beta_0 + \sum_{n=1}^N \beta_n x_{in}$` as `$\theta$` so `$$\log(\frac{p_i}{1-p_i}) = \theta$$`

1. Exponentiate both sides.

2. Multiply both sides by `${1-p_i}$`

3. Distribut the left side

4. Add `$e^\theta*p_i$`

5. Factor out `$p_i$` on the left

6. Divide both sides by `$1+e^\theta$` 
]
.pull-right[
1. `$\frac{p_i}{1-p_i} =e^\theta$`

2. `$p_i = e^\theta(1-p_i)$`

3. `$p_i = e^\theta-e^\theta*p_i$`

4. `$p_i + e^\theta*p_i = e^\theta$`

5. `$p_i(1+e^\theta)= e^\theta$`

6. `$p_i = \frac{e^\theta}{1+e^\theta}$`
]
---

Probability

+ Perhaps the most basic defintion (frequency/long run frequency)

+ proportion of times an event occurs given a number of trials
  + Often not that simple to interpret  
  + Cannot be outside the range, [0,1]

+ `p` is the probability of an event occurring

+ `1-p` is the probability of an even not occurring

+ What does it mean to say a coin has a 50% chance of landing heads? Or a student has a 30% chance of answering an item correctly?

+ Usually invoking the long run

---

---

# Odds

+ Odds are basically the ratio of an event happening to an event not happening

+ Formally `odds = p/(1-p)`

+ If `p = .6`

+ Odds are `1.5 (.6/.4)` - the event (a candidate winning an election) is 1.5 times more likely to happen than not

+ What are the odds if the probability is .5?

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# Log of the odds -logits

+ Take the natural log (ln) of the odds

+ `$log_{e}(odds)$` or `$ln(odds)$`

+ Most commonly (and in R): `$log(odds)$`

+ Odds range from `$(0, \infty)$` not great for linear modeling

+ log odds range from `$(-\infty, \infty)$`

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# Formulas for going the other way: logits to probability

1. Exponentiate - `$$e^{logit} = e^{log_e(odds)} = odds$$`

2. Get the probability `$$\frac{odds}{1+odds}$$`

---

## Open Up RStudio
---

background-image: url(introconsole.png)  
background-size: contain
background-position: center

---

background-image: url(scriptconsole.png)  
background-size: contain
background-position: center

---

## Introducing "Scripts"

+ Scripts are (essentially) RStudio's text editor. **Work in Scripts**. They're saved text that you _can_ edit

+ Code in the console doesn't get saved and you _cannot_  edit  
  
--

+ The primary aim of working in scripts is reproducability, transparency, being able to run code from start-to-finish without intervening

--
+ Rely on being able to re-run your script as if you have no memory of what you had done before when you return to the script the next day (or whatever)

---

# Running the code in a script

---

## Creating a new script in RStudio

.pull-left[
1. File > New File > R Script 
 + Or, ctrl+shft+N
 + Or, below file, hit the icon that looks like:
<img src="createscript.jpg" width="51" />

2. To run a line of code in a script
+ put your cursor on that line, 
+ run it, via ctrl/cmd + enter. 
+ Or the `run` button in the top right of the script
]

--
.pull-right[Make sure it works: 3. Type `1+1` in a script and run it.
  + What happens? Where does it output?

4. There are multiple ways to run more than one line of code at a time
  + Highlight the relevant code, run
  + Or select the various options under "Run"]
--
  
.center[Write two lines of code (such as `1+1` and `2+2`)]

---

## Commenting

*Commenting is essential.*

+ R will recognize any line after `#` as a comment

For instance:

```r
# I ran this to see what would happen

factorial(4)
```

```
## [1] 24
```

+ Add more comments than you think you need
---

# Vocabulary
          
| R Word   | Translation
|----------|------------------
| Script   | Document containing code to be run
| Console  | Output Window/Printer (but you can also run code here)
| Environment| The place where things you create in R, live (metaphorically)
| Working Directory| The folder where your current R session lives, where output files go
  
---

## Working Directory (We'll return to this in more detail later)
+ The notion of the working directory isn't unique to R

+ Directories are just folders on your computer with a certain `path`
  + For instance, your `desktop` is a directory
  + A folder within `Documents` is a directory

+ A `working directory` is just where you tell `R` that you'll be working
  + when you load files, it knows to look to a certain folder
  + When you export files, `R` exports automatically to the working directory

---

## File paths

+ A path to a Word doc on my desktop looks like: `C:/Users/katzd/Desktop/myfile.docx`

+ A path to a file in a folder called, `thesis` in the `Documents directory` looks like `C:/Users/katzd/Documents/thesis/myfile.docx`

+ But these are long!

+ Instead, we'll tell `R` where to read files from, where to export, etc, via `projects`
---

## File Paths: Getting the Wd...

+ To see the currect working directory, simply run the code `getwd()`

+ To set the working directory `setwd("filepath")` (the filepath has to be in quotes)

+ It's often useful to set the working directory at the top of your script

**via menu options**: Session ➡️ Set Working Directory ➡️ Choose Directory (copy and paste outputted code to the top of your script)

+ Some people don't like this practice: [**Link**](https://whattheyforgot.org/safe-paths.html)

+ Run: `getwd()`

---

.middle[### If you've made any comments or would like to save your current script, please go ahead an do-so now (file ➡️  save ➡️  where you want to save it ➡️  name)]

---

## Creating RStudio Projects
### Projects are an RStudio staple

2. New Directory ➡️  New Project ➡️  Create Project as a Subdirectory of: click `browse`.
  
3. Choose where you'd like to put this session's R work (for instance, on your desktop in a folder called, `ED217B Lab 1`) - or even one level down in a new folder within `ED217B Lab 1`)

4. `Directory Name` ➡️  Name this R project - `IntroR` (no spaces; It'll make your life easier) ➡️ Create Project.]

# Setting up a nice working directory
--

1. There are various philosophies about setting up your working directory. Within your working directory...

1. Set up a folder called "scripts" or similar

1. Set up a folder called "data"

1. Set up a folder called "output" or similar

Finally...time to get our feet wet...

---

# Getting set up.

1. Download the R script `Intro_to_R1.R`

1. Place `Intro_to_R1.R` in your `scripts` subdirectory.

---
## Variable Assignment
1. One of the most fundamental aspects of R (really any language) is assigning `variables` or `objects`, 
 + giving something a name so you can 
 + store it 
 + work with it in R.
 + R uses `<-` (you can also use for Windows: "alt" and "-" or on a Mac: "option" and "-")

2. Now, we can store objects in R and work with the objects!

3. Note, none of this requires an external package, just through `base R`. For a nice base R cheat sheet, [_**Click**_](https://paulvanderlaken.files.wordpress.com/2017/08/base-r-cheetsheat.pdf)

4. When we start assigning variables, note what changes in your R session (where do you see the variables go?)

---

```r
x <- 2
```

```r
#What's the value of y?
y <- x+2
```

1. What is in your Global Environment, now? 
2. What was outputted in the console?
3. Now run `x <- 3`. What is the value of x? What is the value of `x+2`
4. Just type `x` and run

---

## The Environment

+ In the right corner, under `Global Environment`, you should now see where R is "storing" `x` and `y` and their values.

+ The environment is also where we'll see what datasets, in R speak, `dataframes` that we have loaded or created, or other objects

+ If you don't assign something to a variable, it won't be stored

---

---
  
# R and Packages
+ Think of `packages` as very specialized bundles of software. 
  + They're collections of functions developed by the "community"

--
+ These packages have documentation if they're on `CRAN: The Comprehensive R Archive Network` (and even sometimes if they're not)

+ You don't need all the packages!

--
+ Packages add functions to base R

+ For instance, the `psych` package is built with tools commonly needed in the social sciences

---
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## Packages, cont'd
+ When you `install.packages()`, R will search for a package on `CRAN` and download it to your computer (have to be connected to the internet)

+ To see where it's downloaded, run `.libpaths()`

+ Each time you start a new R session, you have to load a package via `library()` but you don't have to install each time

---
## Getting help
+ First and foremost, you can see installed packages in the bottom-right pane:

+ Click on a package to see the documentation
---
## Other Help

+ You can also type `?packagename` such as `?dplyr`

+ To get help with a base R function, you can type ?function

+ To get help with a package function, you can type: `?packagename::function` such as `?dplyr::select` where select is a particular function in R.

+ Under the Help tab in R studio (next to `Tools` at the top), exists a few resources as well, including "cheat sheets"

+ Also, Google (we'll talk about this more)!

---
# Run the examples in documentation, usually at the bottom of the section to see how something works!

---

# Operators in R
|Operation|Operator in R |Example|
|---------|------|-------|-------|
|Addition |`+` |`4+3`
|Subtraction|`-`| `4-3`
|Multiplication|`*`| `4*3`
|Exponentiation | `**`| `4**3`
|Division | `/`| `12/4`
|Matrix multiplication|`%*%`| `a %*% b`|

**Challenge: Aside from the matrix multiplication, make sure all of these work in `R`** (use a script!)

---

## Output
+ R `returns a value` in the `console`

+ It'll look like this:
<img src="output_slides.jpg" width="1809" />

***Challenge***: Order of operations: Run `(4+3)*(4-3)` and then `4+3*4-3` in the console (for experimentation). What happens?

### This is one of those necessary evils, so you know how R works
- To select individual elements in a vector, use `[2]` and the numeric position that you would like to extract.

- For instance, run: `v6 <- v5[c(2,3)]`

- This is also how one may pull out individual columns, rows, or specific rows and columns in a dataframe in R using base R

- We can also get descriptives or compute across a vector, or specific vector elements

- Working with datasets or matrices, we can subset rows, columns or both
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#### Rows: `df[1, ]` (gets just the first row)
#### Columnn `df[,1]` or `df[1]` (gets just the first column)
#### Both `df[1,1]`
#### Can Select multiple `df[1:5, 1:6]` or `df[c(1,3, 8), c(1, 9, 2)]`

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