Types of variables

# Types of variables

---

<div class="my-footer">
<span>
by Dr. Lucy D'Agostino McGowan
</span>
</div>

---

## <i class="fas fa-laptop"></i> `Diamonds`

- Go to RStudio Cloud and open `Diamonds`

---
## Variable types

* There are two major classes of variables
  * numeric (quantitative) 
  * categorical

---

## Variable types

* Recall from the first week of class, you can use the `glimpse()` function to see all of your variables and their types

```r
data("PorschePrice")
glimpse(PorschePrice)
```

```
## Observations: 30
## Variables: 3
## $ Price   <dbl> 69.4, 56.9, 49.9, 47.4, 42.9, 36.9, 83.0, 72.9, 69.9, 67…
## $ Age     <int> 3, 3, 2, 4, 4, 6, 0, 0, 2, 0, 2, 2, 4, 3, 10, 11, 4, 4, …
## $ Mileage <dbl> 21.50, 43.00, 19.90, 36.00, 44.00, 49.80, 1.30, 0.67, 13…
```
]

* What are the variables here?

---

## Variable types

* Recall from the first week of class, you can use the `glimpse()` function to see all of your variables and their types

```r
data("Diamonds")
glimpse(Diamonds)
```

```
## Observations: 351
## Variables: 6
## $ Carat      <dbl> 1.08, 0.31, 0.31, 0.32, 0.33, 0.33, 0.35, 0.35, 0.37,…
## $ Color      <fct> E, F, H, F, D, G, F, F, F, D, E, F, D, D, F, F, D, D,…
## $ Clarity    <fct> VS1, VVS1, VS1, VVS1, IF, VVS1, VS1, VS1, VVS1, IF, V…
## $ Depth      <dbl> 68.6, 61.9, 62.1, 60.8, 60.8, 61.5, 62.5, 62.3, 61.4,…
## $ PricePerCt <dbl> 6693.3, 3159.0, 1755.0, 3159.0, 4758.8, 2895.8, 2457.…
## $ TotalPrice <dbl> 7228.8, 979.3, 544.1, 1010.9, 1570.4, 955.6, 860.0, 8…
```
]

* What are the variables here?

--
* `fct`: "factor" this is a type of categorical variable

---

## Variable types

* Recall from the first week of class, you can use the `glimpse()` function to see all of your variables and their types

```r
glimpse(starwars)
```
]

```
## Observations: 87
## Variables: 5
## $ name       <chr> "Luke Skywalker", "C-3PO", "R2-D2", "Darth Vader", "L…
## $ height     <int> 172, 167, 96, 202, 150, 178, 165, 97, 183, 182, 188, …
## $ mass       <dbl> 77.0, 75.0, 32.0, 136.0, 49.0, 120.0, 75.0, 32.0, 84.…
## $ hair_color <chr> "blond", NA, NA, "none", "brown", "brown, grey", "bro…
## $ skin_color <chr> "fair", "gold", "white, blue", "white", "light", "lig…
```
]

* `chr`: "character" this is a type of categorical variable

---

## Variable types

* So far, our models have only included _numeric_ (_quantitative_) variables
--

* What would the equation be for predicting `$y$` from `$x$` when `$x$` is numeric?
--

* What would happen if `$x$` is categorical?
--

* What would the equation be for predicting `$y$` from `$x$` if `$x$` is categorical with 2 levels?
--

* What would the equation be for predicting `$y$` from `$x$` if `$x$` is categorical with 3 levels?
  
---

## indicator variable

An **indicator variable** uses two values, usually 0 and 1, to indicate whether a data case does (1) or does not (0) belong to a specific category

---

```r
data("Diamonds")
```

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class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>TotalPrice<\/th>\n      <th>Color<\/th>\n      <th>Carat<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"columnDefs":[{"className":"dt-right","targets":[1,3]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

---

## Indicator variables

```r
Diamonds <- Diamonds %>%
  mutate(
*   ColorD = ifelse(Color == "D", 1, 0),
    ColorE = ifelse(Color == "E", 1, 0),
    ColorF = ifelse(Color == "F", 1, 0),
    ColorG = ifelse(Color == "G", 1, 0),
    ColorH = ifelse(Color == "H", 1, 0),
    ColorI = ifelse(Color == "I", 1, 0),
    ColorJ = ifelse(Color == "J", 1, 0)
  )
```

---

## Indicator variables

```r
Diamonds <- Diamonds %>%
  mutate(
    ColorD = ifelse(Color == "D", 1, 0), 
*   ColorE = ifelse(Color == "E", 1, 0),
    ColorF = ifelse(Color == "F", 1, 0),
    ColorG = ifelse(Color == "G", 1, 0),
    ColorH = ifelse(Color == "H", 1, 0),
    ColorI = ifelse(Color == "I", 1, 0),
    ColorJ = ifelse(Color == "J", 1, 0)
  )
```

---

## Indicator variables

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## Indicator variables

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class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>TotalPrice<\/th>\n      <th>Carat<\/th>\n      <th>Color<\/th>\n      <th>ColorD<\/th>\n      <th>ColorE<\/th>\n      <th>ColorF<\/th>\n      <th>ColorG<\/th>\n      <th>ColorH<\/th>\n      <th>ColorI<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":5,"columnDefs":[{"className":"dt-right","targets":[1,2,4,5,6,7,8,9]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>
]

---

## Indicator variables

```r
lm(TotalPrice ~ ColorD + ColorE + ColorF + ColorG + ColorH + ColorI + ColorJ,
   data = Diamonds)
```

```
## 
## Call:
## lm(formula = TotalPrice ~ ColorD + ColorE + ColorF + ColorG + 
##     ColorH + ColorI + ColorJ, data = Diamonds)
## 
## Coefficients:
## (Intercept)       ColorD       ColorE       ColorF       ColorG  
##        1936         3632         2423         7224         7623  
*##      ColorH       ColorI       ColorJ  
*##        6732         5704           NA
```
]

* When including indicator variables in a model for `k` categories, always include `k-1` 
--

* The one that is left out is the "reference" category

---

## Indicator variables

```r
lm(TotalPrice ~ ColorD + ColorE + ColorF + ColorG + ColorH + ColorI,
   data = Diamonds)
```

```
## 
## Call:
## lm(formula = TotalPrice ~ ColorD + ColorE + ColorF + ColorG + 
##     ColorH + ColorI, data = Diamonds)
## 
## Coefficients:
## (Intercept)       ColorD       ColorE       ColorF       ColorG  
##        1936         3632         2423         7224         7623  
##      ColorH       ColorI  
##        6732         5704
```
]

* **Interpretation:** A diamond with Color `D` compared to color `J` increases the expected total price by 3632.
--

* **Interpretation:** A diamond with Color `E` compared to color `J` increases the expected total price by 2423

---

## Indicator variables

```r
lm(TotalPrice ~ ColorD + ColorE + ColorF + ColorG + ColorH + ColorI,
   data = Diamonds)
```

* **Interpretation:** A diamond with Color `D` compared to color `J` increases the expected total price by 3632.
* What is the interpretation for a diamond with Color `F`?

---

## R is smart

```r
lm(TotalPrice ~ Color, data = Diamonds)
```

```
## 
## Call:
## lm(formula = TotalPrice ~ Color, data = Diamonds)
## 
## Coefficients:
## (Intercept)       ColorE       ColorF       ColorG       ColorH  
##        5569        -1209         3592         3990         3100  
##      ColorI       ColorJ  
##        2071        -3632
```
]

---

## R is smart

```r
lm(TotalPrice ~ Color, data = Diamonds)
```

* What is the interpretation for Color `E` now?

--
* What if we wanted a different referent category?

--
  * We could code the indicators ourselves
  
--
  * We could use the **forcats**

---

## forcats

* R uses factors to handle categorical variables, variables that have a fixed and known set of possible values. 
* The **forcats** package is loaded with the **tidyverse**, it helps you do things like order your factors

Source: [forcats.tidyverse.org](forcats.tidyverse.org)

---

## forcats

```r
levels(Diamonds$Color)
```

```
## [1] "D" "E" "F" "G" "H" "I" "J"
```

```r
new_levels <- c("J", "D", "E", "F", "G", "H", "I")
Diamonds <- Diamonds %>%
  mutate(Color = fct_relevel(Color, new_levels))
```

```r
levels(Diamonds$Color)
```

```
## [1] "J" "D" "E" "F" "G" "H" "I"
```

---

## R is smart

```r
lm(TotalPrice ~ Color, data = Diamonds)
```

```
## 
## Call:
## lm(formula = TotalPrice ~ Color, data = Diamonds)
## 
## Coefficients:
## (Intercept)       ColorD       ColorE       ColorF       ColorG  
##        1936         3632         2423         7224         7623  
##      ColorH       ColorI  
##        6732         5704
```
]

---

## R is smart

```r
lm(TotalPrice ~ Color, data = Diamonds)
```

---

## What if the variable is **binary**

* A **binary** variable is a special type of categorical variable with **two levels**

---

## ICU example

* A sample of 200 patients in an ICU unit
* Want to see if the patient's heart rate is related to whether they were admitted via the emergency room 
--

* y: Heart rate (beats per minute)
  * x: indicator for emergency room admission
--

* Aside: Is this inference or prediction?

---

## Binary x variable

```r
data("ICU")
lm(Pulse ~ Emergency, data = ICU)
```

```
## 
## Call:
## lm(formula = Pulse ~ Emergency, data = ICU)
## 
## Coefficients:
## (Intercept)    Emergency  
##       91.11        10.63
```

* How can we interpret `$\hat{\beta}_0$` now?
--

* How can we interpret `$\hat{\beta}_1$`?

---

## <i class="fas fa-laptop"></i> `Diamonds`

- Go to RStudio Cloud and open `Diamonds`

---