Explanatory Statistical Modeling in R

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.title[
# Explanatory Statistical Modeling in R
]
.subtitle[
## Introduction and R Fundamentals
]
.author[
### Keith McNulty
]

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## Good morning and welcome!

What I hope you can say at the end of this workshop:

&#129489;&#8205;&#127891; You've learned a lot about some important methods for your work  
&#127881; You've had fun  
&#128075; You've met a few interesting people who work on similar things to you

---
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## Set up Posit Cloud account and access workspace

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# About this workshop

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## Introducing ourselves

Let's find out:

1.  Who you are
2.  Where you are from
3.  What you do
4.  What you hope to get from this morning's sessions

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## Explanatory modeling: what is it?

Explanatory modeling uses a sample of data to draw inferences about the potential causes of an outcome of interest.  It is also sometimes called *inferential modeling*.

Examples:

* Does working schedule and/or pay rate influence likelihood to leave an organization?
* Does academic performance in earlier years of a program influence academic performance in the final year?
* Do certain demographic factors influence choice of career?

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## Explanatory modeling: what we will learn

We will focus on regression analysis as a way to explain outcomes of interest using data. You will learn:

1.  How to choose an appropriate model type for the problem at hand.
2.  How to prepare your data for your model.
3.  How to execute the model.
4.  How to view a variety of outputs from the model.
5.  How to interpret those outputs against the problem at hand.

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## How we will learn

&#128105;&#8205;&#127979;  Talks and instruction

&#128104;&#127997;&#8205;&#128187; Frequent short coding exercises

&#129337; A small project to take away with you

&#128562; A few other things

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## Don't panic 🤯

We are limited on time today - I'll likely have to skim over some things.

An in-depth treatment of everything we do today (and more!) can always be found in the free online version of my textbook [Handbook of Regression Modeling in People Analytics](https://peopleanalytics-regression-book.org/).

After you leave our session, use this as a reference text for everything we do today.

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# Foundations:  Working with people data in R

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## Data types - numeric

``` r
# numeric double
my_double <- 42.3

# use typeof() to find out the data type of a scalar value
typeof(my_double)
```

```
## [1] "double"
```

``` r
# numeric integer
my_integer <- 42L
typeof(my_integer)
```

```
## [1] "integer"
```

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## Data types - character and logical

``` r
# character is any string in quotes
my_name <- "Keith"
typeof(my_name)
```

```
## [1] "character"
```

``` r
# logical is TRUE or FALSE
at_siop_lec <- TRUE
typeof(at_siop_lec)
```

```
## [1] "logical"
```

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## Data structures - numeric, character and logical vectors

``` r
# vectors are 1-dimensional homogeneous structures (same data type)
first_primes <- c(2, 3, 5, 7, 11)

# use str() to get info about data structures
str(first_primes)
```

```
##  num [1:5] 2 3 5 7 11
```

``` r
# character vector
popstars <- c("Katy Perry", "Taylor Swift", "Harry Styles", "Charli XCX")
str(popstars)
```

```
##  chr [1:4] "Katy Perry" "Taylor Swift" "Harry Styles" "Charli XCX"
```

``` r
# logical vector
popstars_keith_likes <- c(FALSE, FALSE, FALSE, TRUE)
str(popstars_keith_likes)
```

```
##  logi [1:4] FALSE FALSE FALSE TRUE
```

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## Data structures - categorical (factor) vectors

``` r
# categorical or factor vectors store a limited set of categorical values
popstars_factor <- as.factor(popstars)
str(popstars_factor)
```

```
##  Factor w/ 4 levels "Charli XCX","Harry Styles",..: 3 4 2 1
```

``` r
# if the categories have order, you can specify the order
performance <- c("Low", "High", "Medium", "High", "Low")
ordered_performance <- ordered(
 performance, 
 levels = c("Low", "Medium", "High")
)
str(ordered_performance)
```

```
## Ord.factor w/ 3 levels "Low"<"Medium"<..: 1 3 2 3 1
```

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## Data structures - type coercion

``` r
# what happens if we try to put heterogeneous data in a vector
mixed_types_1 <- c(6.75, "Keith")
str(mixed_types_1)
```

```
##  chr [1:2] "6.75" "Keith"
```

``` r
# some form of type coercion occurs
mixed_types_2 <- c(TRUE, 6.3)
str(mixed_types_2)
```

```
##  num [1:2] 1 6.3
```

``` r
# if you add an unknown element to a defined factor vector
new_popstars <- c(popstars_factor, "Lady Gaga")
str(new_popstars)
```

```
##  chr [1:5] "3" "4" "2" "1" "Lady Gaga"
```

``` r
# use type conversion functions to control coercion
new_popstars <- c(as.character(popstars_factor), "Lady Gaga")
str(new_popstars)
```

```
##  chr [1:5] "Katy Perry" "Taylor Swift" "Harry Styles" "Charli XCX" ...
```

---
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## Exercise - data type and type conversion

For our first short exercise, we will do some practice on working with and converting data types.

Go to our [Posit Cloud workspace](https://posit.cloud/spaces/688089/join?access_code=1qJ6zGSp4l9n-zAaGpjXE8OJhS3kwGJQPrDYhwbK) and start **Assignment 01 - R Fundamentals**.

Let's work on **Exercises 1 and 2**.

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## Data structures - named lists

Named lists are the most flexible structures in R.  They can contain any other structures inside them.

``` r
my_list <- list(
 great_tv = c("Ozark", "Mad Men", "Breaking Bad"),
 first_primes = first_primes,
 popstars_factor = popstars_factor
)

str(my_list)
```

```
## List of 3
##  $ great_tv       : chr [1:3] "Ozark" "Mad Men" "Breaking Bad"
##  $ first_primes   : num [1:5] 2 3 5 7 11
##  $ popstars_factor: Factor w/ 4 levels "Charli XCX","Harry Styles",..: 3 4 2 1
```

``` r
# access specific elements
my_list$great_tv
```

```
## [1] "Ozark"        "Mad Men"      "Breaking Bad"
```

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## Data structures - dataframes

Dataframes are named lists of vectors of the same length.  They are the most popular data structure in R - basically the R equivalent of a spreadsheet.

``` r
(popstars_info <- data.frame(
 popstars = popstars_factor,
 keith_likes = popstars_keith_likes
))
```

```
##       popstars keith_likes
## 1   Katy Perry       FALSE
## 2 Taylor Swift       FALSE
## 3 Harry Styles       FALSE
## 4   Charli XCX        TRUE
```

``` r
str(popstars_info)
```

```
## 'data.frame':	4 obs. of  2 variables:
##  $ popstars   : Factor w/ 4 levels "Charli XCX","Harry Styles",..: 3 4 2 1
##  $ keith_likes: logi  FALSE FALSE FALSE TRUE
```

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## Loading and viewing dataframes

All of the data sets we work with will be in online CSV files, so we can load them in from a URL using `read.csv()`.

``` r
url <- "https://peopleanalytics-regression-book.org/data/ugtests.csv"
ugtests <- read.csv(url)
str(ugtests)
```

```
## 'data.frame':	975 obs. of  4 variables:
##  $ Yr1  : int  27 70 27 26 46 86 40 60 49 80 ...
##  $ Yr2  : int  50 104 36 75 77 122 100 92 98 127 ...
##  $ Yr3  : int  52 126 148 115 75 119 125 78 119 67 ...
##  $ Final: int  93 207 175 125 114 159 153 84 147 80 ...
```

Often data is big, so we will use `head()` to look at the first few rows:

``` r
head(ugtests)
```

```
##   Yr1 Yr2 Yr3 Final
## 1  27  50  52    93
## 2  70 104 126   207
## 3  27  36 148   175
## 4  26  75 115   125
## 5  46  77  75   114
## 6  86 122 119   159
```

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## Functions

Functions perform useful operations on objects, returning a transformed object.  They usually exist because there is a task that needs to be performed repeatedly by a user or many users.  We've already seen some functions.

Can you name some functions that we have already seen in previous pages?

We will be using a lot of functions over the next 2 days.  Some of them will be built into base R, like `lm()` or `glm()`, and some will be from add-on packages like `polr()`.

``` r
# example function - substr() extracts characters from a string
substr("Keith", start = 2, stop = 4)
```

```
## [1] "eit"
```

To display help on how to use the `substr` function, use `?substr` or `help(substr)` in the console.

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## Packages

A set of functions that have been created for a specific purpose can be released as a package.  We will be using packages like `dplyr` and `MASS` during this workshop.

All packages have been pre-installed for you on Posit Cloud, but installing packages is easy.  For example `install.packages("MASS")` would install the `MASS` package.

To use the functions in a package, you should load the installed package from your library.  For example, to load `dplyr` you would use `library(dplyr)`.

Sometimes it makes sense to namespace functions in packages so that they are not confused with similarly named functions in other packages.  For example, to use the `filter()` function in `dplyr`, you can namespace using `dplyr::filter()`.

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## The pipe operator

The pipe operator `|>`  helps you write more readable code through avoiding deeply nested functions within functions, allowing you to see the order of operations more clearly. (**Tip:** Use `Cmd/Ctrl+Shift+M` for a shortcut to the pipe).

``` r
library(dplyr)

# without pipe
round(mean(dplyr::pull(dplyr::filter(ugtests, Yr2 < 75), Yr1)), 2)
```

```
## [1] 51.75
```

``` r
# with pipe (note neat coding style)
ugtests |> 
 dplyr::filter(Yr2 < 75) |> 
 dplyr::pull(Yr1) |> 
 mean() |> 
 round(2)
```

```
## [1] 51.75
```

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## Exercise - Dataframes, functions, packages and the pipe operator

For our next short exercise, we will do some practice on working with dataframes, functions, packages and the pipe operator.

Go to our [Posit Cloud workspace](https://posit.cloud/spaces/688089/join?access_code=1qJ6zGSp4l9n-zAaGpjXE8OJhS3kwGJQPrDYhwbK) and continue **Assignment 01 - R Fundamentals**.

Let's work on **Exercises 3 and 4**.

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## Plotting and graphing in base R

Plotting is a big part of any analytical work.  R has a very wide range of options for this.

Base R has functions like `plot()` for simple X-Y plots, and `boxplot()` or `hist()` for specific plot types.

``` r
plot(ugtests$Yr1, ugtests$Final)
```

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## Plotting and graphing in `ggplot2`

For those who know it, `ggplot2` is an incredibly powerful graphing package based on the Grammar of Graphics (Wilkinson, 2005).

``` r
library(ggplot2)

ggplot(ugtests, aes(x = Yr1, y = Final)) +
  geom_point(color = "blue") + 
  labs(x = "Year 1", y = "Final") + 
  theme_minimal()
```

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## Pairplots

Pairplots are very useful summary plots to understand univariate and bivariate patterns in data, and are often a useful precursor to modeling efforts.  It's important for data types to be well defined for pairplots to work effectively.

``` r
library(GGally)

GGally::ggpairs(ugtests)
```

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## Documenting work in Quarto

Quarto allows you to integrate your work into a document with commentary, and is a great way to record the work you have done for future reference and reproducibility.

The assignments in this workshop are all set up in Quarto documents.  When you have finished them you can render them into HTML documents which will remain available in your workspace after this workshop.  Feel free to add your own text commentary or notes to these documents to help remind you of important things.

I **always** use Quarto to record my method and code in one document.

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## Exercise - Plotting and recording your work

For our next short exercise, we will do some practice on plotting and on recording work in Quarto.

Go to our [Posit Cloud workspace](https://posit.cloud/spaces/688089/join?access_code=1qJ6zGSp4l9n-zAaGpjXE8OJhS3kwGJQPrDYhwbK) and continue **Assignment 01 - R Fundamentals**.

Let's work on **Exercises 5 and 6**.

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# &#x1F389; We are ready to start modeling! &#128588;