Visualizing numerical data 🔢

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layout: true
  
<div class="my-footer">
<span>
<a href="https://DataScience4Psych.github.io/DataScience4Psych/" target="_blank">Data Science for Psychologists</a>
</span>
</div>

---

# Terminology

---

## Number of variables involved

- Univariate data analysis - distribution of single variable
- Bivariate data analysis - relationship between two variables
- Multivariate data analysis - relationship between many variables at once, 
  - usually focusing on the relationship between two while conditioning for others

---

## Types of variables

- **Numerical variables** can be classified as **continuous** or **discrete** based on whether or not the variable can take on an infinite number of values or only non-negative whole numbers, respectively.
- If the variable is **categorical**, we can determine if it is **ordinal** based on whether or not the levels have a natural ordering.

---

# Data

---

## Data: Lending Club

- Thousands of loans made through the Lending Club,
  - a platform that allows individuals to lend to each other
- Not all loans are created equal 
  - ease of getting a loan depends on (apparent) ability to repay the loan
- Data includes loans *made* 
  - (these data are not loan applications)
]
.pull-right-narrow[
<img src="img/lending-club.png" width="100%" style="display: block; margin: auto;" />
]

---

## Take a peek at data

``` r
library(openintro)
glimpse(loans_full_schema)
```

```
## Rows: 10,000
## Columns: 55
## $ emp_title                        <chr> "global config enginee…
## $ emp_length                       <dbl> 3, 10, 3, 1, 10, NA, 1…
## $ state                            <fct> NJ, HI, WI, PA, CA, KY…
## $ homeownership                    <fct> MORTGAGE, RENT, RENT, …
## $ annual_income                    <dbl> 90000, 40000, 40000, 3…
## $ verified_income                  <fct> Verified, Not Verified…
## $ debt_to_income                   <dbl> 18.01, 5.04, 21.15, 10…
## $ annual_income_joint              <dbl> NA, NA, NA, NA, 57000,…
## $ verification_income_joint        <fct> , , , , Verified, , No…
## $ debt_to_income_joint             <dbl> NA, NA, NA, NA, 37.66,…
## $ delinq_2y                        <int> 0, 0, 0, 0, 0, 1, 0, 1…
## $ months_since_last_delinq         <int> 38, NA, 28, NA, NA, 3,…
## $ earliest_credit_line             <dbl> 2001, 1996, 2006, 2007…
...
```

---

## Selected variables

``` r
loans <- loans_full_schema %>%
  select(loan_amount, interest_rate, term, grade, 
         state, annual_income, homeownership, debt_to_income)
glimpse(loans)
```

```
## Rows: 10,000
## Columns: 8
## $ loan_amount    <int> 28000, 5000, 2000, 21600, 23000, 5000, 2…
## $ interest_rate  <dbl> 14.07, 12.61, 17.09, 6.72, 14.07, 6.72, …
## $ term           <dbl> 60, 36, 36, 36, 36, 36, 60, 60, 36, 36, …
## $ grade          <ord> C, C, D, A, C, A, C, B, C, A, C, B, C, B…
## $ state          <fct> NJ, HI, WI, PA, CA, KY, MI, AZ, NV, IL, …
## $ annual_income  <dbl> 90000, 40000, 40000, 30000, 35000, 34000…
## $ homeownership  <fct> MORTGAGE, RENT, RENT, RENT, RENT, OWN, M…
## $ debt_to_income <dbl> 18.01, 5.04, 21.15, 10.16, 57.96, 6.46, …
```

---

## Selected variables

<br>

.midi[
variable        | description
----------------|-------------
`loan_amount`   |	Amount of the loan received, in US dollars
`interest_rate` |	Interest rate on the loan, in an annual percentage
`term`	        | The length of the loan, which is always set as a whole number of months
`grade`	        | Loan grade, which takes a values A through G and represents the quality of the loan and its likelihood of being repaid
`state`         |	US state where the borrower resides
`annual_income` |	Borrower’s annual income, including any second income, in US dollars
`homeownership`	| Indicates whether the person owns, owns but has a mortgage, or rents
`debt_to_income` | Debt-to-income ratio
]

---

## Variable types

<br>

variable        | type
----------------|-------------
`loan_amount`   |	numerical, continuous
`interest_rate` |	numerical, continuous
`term`	        | numerical, discrete
`grade`	        | categorical, ordinal
`state`         |	categorical, not ordinal
`annual_income` |	numerical, continuous
`homeownership`	| categorical, not ordinal
`debt_to_income` | numerical, continuous

---

# Wrapping Up...

---

# Visualizing numerical data

---

## Describing shapes of numerical distributions

- shape:
    - skewness: right-skewed, left-skewed, symmetric (skew is to the side of the longer tail)
    - modality: unimodal, bimodal, multimodal, uniform
- center: mean (`mean`), median (`median`), mode (not always useful)
- spread: range (`range`), standard deviation (`sd`), inter-quartile range (`IQR`)
- unusual observations

---

# Histogram

---

## Histogram

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_histogram()
```

```
## `stat_bin()` using `bins = 30`. Pick better value with
## `binwidth`.
```

---

## Histograms and binwidth

+ binwidth = 1000

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_histogram(binwidth = 1000)
```

---

## binwidth = 5000

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_histogram(binwidth = 5000)
```

---

## binwidth = 20000

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_histogram(binwidth = 20000)
```

---

## Customizing histograms

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-9-1.png" width="100%" style="display: block; margin: auto;" />

]
.pull-right[.small[

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_histogram(binwidth = 5000) +
* labs(
*   x = "Loan amount ($)",
*   y = "Frequency",
*   title = "Amounts of Lending Club loans"
* )
```
]
]

---

## Fill with a categorical variable

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-10-1.png" width="100%" style="display: block; margin: auto;" />
]
.pull-right[.small[

``` r
ggplot(loans, aes(x = loan_amount, 
*                 fill = homeownership)) +
  geom_histogram(binwidth = 5000,
*                alpha = 0.5) +
  labs(
    x = "Loan amount ($)",
    y = "Frequency",
    title = "Amounts of Lending Club loans"
  )
```
]
]

---

## Facet with a categorical variable

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-11-1.png" width="100%" style="display: block; margin: auto;" />
]
.pull-right[.small[

``` r
ggplot(loans, aes(x = loan_amount, fill = homeownership)) + 
  geom_histogram(binwidth = 5000) +
  labs(
    x = "Loan amount ($)",
    y = "Frequency",
    title = "Amounts of Lending Club loans"
  ) +
* facet_wrap(~ homeownership, nrow = 3)
```
]
]

---

# Density plot

---

## Density plot

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_density()
```

---

## Density plots and adjusting bandwidth

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_density(adjust = 0.5)
```

<img src="d05_viznum_files/figure-html/unnamed-chunk-13-1.png" width="50%" style="display: block; margin: auto;" />
]
.pull-right[
+ adjust = 1

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_density(adjust = 1) # default bandwidth
```

<img src="d05_viznum_files/figure-html/unnamed-chunk-14-1.png" width="50%" style="display: block; margin: auto;" />
]
---

# adjust = 2

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_density(adjust = 2)
```

---

## Customizing density plots

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-16-1.png" width="100%" style="display: block; margin: auto;" />
]
.pull-right[.small[

``` r
ggplot(loans, aes(x = loan_amount)) +
  geom_density(adjust = 2) +
* labs(
*   x = "Loan amount ($)",
*   y = "Density",
*   title = "Amounts of Lending Club loans"
* )
```
]
]

---

## Adding a categorical variable

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-17-1.png" width="100%" style="display: block; margin: auto;" />
]
.pull-right[.small[

``` r
ggplot(loans, aes(x = loan_amount, 
*                 fill = homeownership)) +
  geom_density(adjust = 2, 
*              alpha = 0.5) +
  labs(
    x = "Loan amount ($)",
    y = "Density",
    title = "Amounts of Lending Club loans", 
*   fill = "Homeownership"
  )
```
]
]

---

# Box plot

---

## Box plot

``` r
ggplot(loans, aes(x = interest_rate)) +
  geom_boxplot()
```

---

## Box plot and outliers

``` r
ggplot(loans, aes(x = annual_income)) +
  geom_boxplot()
```

---

## Customizing box plots

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-20-1.png" width="100%" style="display: block; margin: auto;" />
]
.pull-right[.small[

``` r
ggplot(loans, aes(x = interest_rate)) +
  geom_boxplot() +
  labs(
    x = "Interest rate (%)",
    y = NULL,
    title = "Interest rates of Lending Club loans"
  ) +
* theme(
*   axis.ticks.y = element_blank(),
*   axis.text.y = element_blank()
* )
```
]
]

---

## Adding a categorical variable

.pull-left[
<img src="d05_viznum_files/figure-html/unnamed-chunk-21-1.png" width="60%" style="display: block; margin: auto;" />
]
.pull-right[.small[

``` r
ggplot(loans, aes(x = interest_rate,
*                 y = grade)) +
  geom_boxplot() +
  labs(
    x = "Interest rate (%)",
    y = "Grade",
    title = "Interest rates of Lending Club loans",
*   subtitle = "by grade of loan"
  )
```
]
]

---

# Relationships numerical variables

---

## Scatterplot

``` r
ggplot(loans, aes(x = debt_to_income, y = interest_rate)) +
  geom_point()
```

---

## Hex plot

``` r
ggplot(loans, aes(x = debt_to_income, y = interest_rate)) +
  geom_hex()
```

---

## Hex plot

``` r
ggplot(loans %>% filter(debt_to_income < 100), 
       aes(x = debt_to_income, y = interest_rate)) +
  geom_hex()
```

---

# Sources

- Mine Çetinkaya-Rundel's Data Science in a Box ([link](https://datasciencebox.org/))