Programming with Data

class: center, middle, inverse, title-slide

# Programming with Data
## Session 7: Forecasting with Logistic Regressions
### Dr. Wang Jiwei
### Master of Professional Accounting

---

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# Binary outcomes

---

## What are binary outcomes?

- Thus far we have talked about events with continuous outcomes
    - Revenue, earnings, ROA, etc
- Binary outcomes only have two possible outcomes
    - Did something happen, *yes* or *no*?
    - Is a statement *true* or *false*?

- Financial accounting:
    - Will the company's earnings meet analysts' expectations?
    - Will the company have positive earnings?
- Managerial accounting:
    - Will we have problem with our supply chain?
    - Will our customer go bankrupt?
- Audit:
    - Is the company committing fraud?
- Taxation:
    - Is the company too aggressive in their tax positions?
- Management and strategy
    - Does the business model change?

> We can assign a probability to any of these

---

## Binary classficiation algos

- Popular algorithms that can be used for [binary classification](https://en.wikipedia.org/wiki/Binary_classification) include:
    - Logistic Regression (today's session)
    - Decision Trees (to be covered)
    - [k-Nearest Neighbors](https://www.datacamp.com/community/tutorials/machine-learning-in-r)
    - [Support Vector Machine](http://uc-r.github.io/svm)
    - [Naive Bayes](https://uc-r.github.io/naive_bayes)

---

## Logistic regression

- When modeling a binary outcome, we use logistic regression
    - A.k.a. logit model
- The *logit* function is `$logit(p) = \text{log}\left(\frac{p}{1-p}\right)$`
    - Also called *log odds*, see next slide

$$
\text{log}\left(\frac{\text{Prob}(y=1|X)}{1-\text{Prob}(y=1|X)}\right)=\alpha + \beta_1 x_1 + \beta_2 x_2 + \ldots + \varepsilon
$$

- The **sign** of the coefficients means the same as before
    - **+**: *increases* the likelihood of `$y$` occurring
    - **-**: *decreases* the likelihood of `$y$` occurring

.center[<img src = "../../../Figures/LogitLayout.png" height = "200px">]

---

## Odds vs probability

.center[<img src="../../../Figures/odds.png" height="500px">]

---
class: inverse, middle, center

# Logistic regression interpretation

---

## Interpreting logit values

- The level of the coefficient is different
    - The relationship isn't linear between `$x_i$` and `$y$` now
    - Instead, coefficient is in *log odds*
        - Thus, `$e^{X\beta}$` gives you the *odds*, `$o=\frac{p}{1-p}$`
        - To get probability, `$p$`, we can calculate `$p=\frac{o}{1+o}$`
- Interpretation: for a one-unit increase in `$x_i$`
    - the *log odds* for `$y$` = 1 increase by `$\beta$` (same as the OLS), holding others at a fixed value
    - the *odds* for `$y$` = 1 increase by `$(e^\beta-1)$` times of baseline odds (ie, odds before the change), holding others at a fixed value
        - `$log(o2) - log(o1) = \beta$`
        - `$log(o2/o1) = \beta$`
        - `$o2/o1 = e^\beta$`
        - `$o2 - o1 = (e^\beta - 1) * o1$`
    - you need to sum all relevant log odds before converting to probability
    - <a target="_blank" href="https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/">Click here for a review</a>

---

## Implement logit regression

- The logistic model is related to our previous linear models as such:

> Both linear and logit models are under the class of General Linear Models (GLMs)

- To regress a GLM, we use the `glm()` command.

- To run a logit regression:

```r
mod <- glm(y ~ x1 + x2 + x3 + ..., data = df, family = binomial)

summary(mod)
```

> `family = binomial` is what sets the model to be a logit

- In fact, the `lm()` we have been using is actually `glm()` when you specify the option `family = gaussian`

---

## Example logit regression

> Do holidays increase the likelihood that a department more than doubles its store's average weekly sales across departments?

```r
# Create the binary variable from Walmart sales data
df$double <- ifelse(df$Weekly_Sales > df$store_avg * 2, 1, 0)
model1 <- glm(double ~ IsHoliday, data = df, family = binomial)
tidy(model1)
```

```
## # A tibble: 2 x 5
##   term          estimate std.error statistic  p.value
##   <chr>            <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)     -3.45    0.00924    -373.  0       
## 2 IsHolidayTRUE    0.539   0.0278       19.4 1.09e-83
```

> Holidays increase the odds...  but by how much?

- There are two ways to interpret this:
    1. Coefficient by coefficient
    2. In total

---

## Interpretting specific coefficients

$$
logodds(Double~sales) = -3.45 + 0.54 IsHoliday
$$

- Interpreting specific coefficients is easiest done manually
- Odds for the `$IsHoliday$` coefficient are `exp(0.54) = 1.72`
    - This means that having a holiday modifies the baseline (i.e., non-Holiday) odds by 1.72 to 1
        - Where 1 to 1 is considered no change (`exp(0) = 1`)
    - Baseline `exp(-3.45)` is 0.032 to 1

```r
# Automating the above:
exp(coef(model1))
```

```
##   (Intercept) IsHolidayTRUE 
##    0.03184725    1.71367497
```

---

## Interpretting in total

- It is important to note that log odds are additive
    - So, calculate a new log odd by plugging in values for variables and adding it all up
        - Holiday: `$-3.45 + 0.54 * 1 = -2.91$`
        - No holiday: `$-3.45 + 0.54 * 0 = -3.45$`
- Then calculate odds and log odds like before
    - With holiday: `exp(-2.91) = 0.055`
    - Without holiday: `exp(-3.45) = 0.032`
    - Ratio of holiday to without: 1.72!
        - This is the individual log odds for holiday

> We need to specify values to calculate log odds in total

---

## Converting to probabilities

- We can calculate a probability at any given point using the log odds

$$
Probability = \frac{odds}{odds + 1}
$$

- Probability of double sales...
    - With a holiday: `0.055 / (0.055 + 1) = 0.052`
    - Without a holiday: `0.032 / (0.032 + 1) = 0.031`

> These are easier to interpret, but require specifying values

---

## Using predict() to simplify it

- `predict()` can calculate log odds and probabilities for us with minimal effort
    - Specify `type = "response"` to get probabilities

```r
IsHoliday <- c(FALSE, TRUE)
test_data <- as.data.frame(IsHoliday)
predict(model1, test_data)  # log odds if no type = "response"
```

```
##         1         2 
## -3.446804 -2.908164
```

```r
predict(model1, test_data, type = "response")  #probabilities
```

```
##          1          2 
## 0.03086431 0.05175146
```

- Here, we see the baseline probability is 3.1%
- The probability of doubling sales on a holiday is higher, at 5.2%

---

## R practice: Logit

- A continuation of last session's practices answering:
    - Is Walmart more likely to see a year over year decrease in quarterly revenue during a recession?
- Practice using `mutate()` and `glm()`
- Do exercises 1 and 2 in the practice file
    - <a target="_blank" href="Session_7s_Exercise.html">R Practice</a>

---

## What about more complex model?

```r
model2 <- glm(double ~ IsHoliday + Temperature + Fuel_Price,
              data = df, family = binomial)
tidy(model2)
```

```
## # A tibble: 4 x 5
##   term          estimate std.error statistic   p.value
##   <chr>            <dbl>     <dbl>     <dbl>     <dbl>
## 1 (Intercept)    -1.78    0.0673       -26.4 1.93e-153
## 2 IsHolidayTRUE   0.370   0.0284        13.0 8.80e- 39
## 3 Temperature    -0.0108  0.000470     -23.0 1.70e-117
## 4 Fuel_Price     -0.309   0.0196       -15.8 6.20e- 56
```

```r
# Odds
exp(coef(model2))
```

```
##   (Intercept) IsHolidayTRUE   Temperature    Fuel_Price 
##     0.1692308     1.4483570     0.9892316     0.7340376
```

> We need to specify values for all inputs to determine probabilities, ie, the impact of each input depends on the values of the others!

---

## Probabilities

```r
# Average probability in September
hday_sep    <- mean(predict(model2, filter(df, IsHoliday, month == 9),
                            type = "response"))
no_hday_sep <- mean(predict(model2, filter(df, !IsHoliday, month == 9),
                            type = "response"))
# Average probability in December
hday_dec    <- mean(predict(model2, filter(df, IsHoliday, month == 12),
                            type="response"))
no_hday_dec <- mean(predict(model2, filter(df, !IsHoliday, month == 12),
                            type="response"))

html_df(data.frame(Month=c(9, 9, 12, 12), IsHoliday=c(FALSE, TRUE, FALSE, TRUE),
                   Probability=c(no_hday_sep, hday_sep, no_hday_dec, hday_dec)))
```

<table class="table table-striped table-hover" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Month </th>
   <th style="text-align:center;"> IsHoliday </th>
   <th style="text-align:center;"> Probability </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 9 </td>
   <td style="text-align:center;"> FALSE </td>
   <td style="text-align:center;"> 0.0266789 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 9 </td>
   <td style="text-align:center;"> TRUE </td>
   <td style="text-align:center;"> 0.0374761 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 12 </td>
   <td style="text-align:center;"> FALSE </td>
   <td style="text-align:center;"> 0.0398377 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 12 </td>
   <td style="text-align:center;"> TRUE </td>
   <td style="text-align:center;"> 0.0586483 </td>
  </tr>
</tbody>
</table>

---

## A bit easier: Marginal effects

> Marginal effects tell us the change in our output for a change of 1 unit to an input

- Marginal effects are partial derivatives (slope of the tangent line) of a regression equation with respect to each variable in the model for each unit in the data
    - In OLS regression with no interactions or higher-order term (such as polynomial functions with quadratic terms `$x^2$`), the estimated coefficients are marginal effects
- Using [`package:margins`](https://github.com/leeper/margins), we can calculate marginal effects
- There are a few types that we could calculate:
    - An *Average Marginal Effect* tells us what the average effect of an input is across all values in our data
        - This is the default method in the package
    - We can also specify a specific value to calculate marginal effects at

---

## Logistic 2D/3D curve

> Marginal effect means the partial derivative of any given point on the surface

.pull-left[
.center[<img src = "../../../Figures/logistic_3d.png">]
]
.pull-right[
.center[<img src = "../../../Figures/logistic_2d.png">]
]

---

## Marginal effects in action

```r
# Calculate Average Marginal Effects (AME)
# It will take a while
library(margins)
m <- margins(model2)
m
```

```
##  Temperature Fuel_Price IsHoliday
##   -0.0003377  -0.009644   0.01334
```

- By default, the margins() returns the Average Marginal Effect (AME)
- A holiday increases the probability of doubling by a flat 1.33%
    - Not too bad when you consider that the probability of doubling is 3.23%
- If the temperature goes up by 1°F (0.55°C), the probability of doubling changes by -0.03%
- If the fuel price increases by 1 USD for 1 gallon of gas, the probability of doubling changes by -0.96%

---

## `package:margins` niceties

- We can get some extra information about our marginal effects through `summary()`:

```r
summary(m) %>%
  html_df()
```

- Those p-values work just like with our linear models
- We also get a confidence interval

---

## Plotting marginal effects

```r
# Note: The `which...` part is absolutely necessary at the moment
# due to a bug in the package (mismatch of factors and AME values
# you may try to remove `which...` to see what happened
plot(m, which = summary(m)$factor)
```

---

## Marginal effects at a specified value

```r
margins(model2, at = list(IsHoliday = c(TRUE, FALSE)),
        variables = c("Temperature", "Fuel_Price")) %>%
  summary() %>%
  html_df()
```

<table class="table table-striped table-hover" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> factor </th>
   <th style="text-align:center;"> IsHoliday </th>
   <th style="text-align:center;"> AME </th>
   <th style="text-align:center;"> SE </th>
   <th style="text-align:center;"> z </th>
   <th style="text-align:center;"> p </th>
   <th style="text-align:center;"> lower </th>
   <th style="text-align:center;"> upper </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Fuel_Price </td>
   <td style="text-align:center;"> FALSE </td>
   <td style="text-align:center;"> -0.0093401 </td>
   <td style="text-align:center;"> 0.0005989 </td>
   <td style="text-align:center;"> -15.59617 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> -0.0105139 </td>
   <td style="text-align:center;"> -0.0081664 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Fuel_Price </td>
   <td style="text-align:center;"> TRUE </td>
   <td style="text-align:center;"> -0.0131335 </td>
   <td style="text-align:center;"> 0.0008717 </td>
   <td style="text-align:center;"> -15.06650 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> -0.0148420 </td>
   <td style="text-align:center;"> -0.0114250 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Temperature </td>
   <td style="text-align:center;"> FALSE </td>
   <td style="text-align:center;"> -0.0003271 </td>
   <td style="text-align:center;"> 0.0000146 </td>
   <td style="text-align:center;"> -22.46024 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> -0.0003556 </td>
   <td style="text-align:center;"> -0.0002985 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Temperature </td>
   <td style="text-align:center;"> TRUE </td>
   <td style="text-align:center;"> -0.0004599 </td>
   <td style="text-align:center;"> 0.0000210 </td>
   <td style="text-align:center;"> -21.92927 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> -0.0005010 </td>
   <td style="text-align:center;"> -0.0004188 </td>
  </tr>
</tbody>
</table>

- specify the values through *at* argument, *variables* for the features of changes

> On a holiday, if fuel price changes by 1 unit, the probability of doubling changes by -1.31%

---

## Marginal effects at a specified value

```r
margins(model2, at = list(Temperature = c(0, 20, 40, 60, 80)),
        variables = c("IsHoliday")) %>%
  summary() %>%
  html_df()
```

<table class="table table-striped table-hover" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> factor </th>
   <th style="text-align:center;"> Temperature </th>
   <th style="text-align:center;"> AME </th>
   <th style="text-align:center;"> SE </th>
   <th style="text-align:center;"> z </th>
   <th style="text-align:center;"> p </th>
   <th style="text-align:center;"> lower </th>
   <th style="text-align:center;"> upper </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> IsHoliday </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0.0234484 </td>
   <td style="text-align:center;"> 0.0020168 </td>
   <td style="text-align:center;"> 11.62643 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0.0194955 </td>
   <td style="text-align:center;"> 0.0274012 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> IsHoliday </td>
   <td style="text-align:center;"> 20 </td>
   <td style="text-align:center;"> 0.0194072 </td>
   <td style="text-align:center;"> 0.0016710 </td>
   <td style="text-align:center;"> 11.61387 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0.0161320 </td>
   <td style="text-align:center;"> 0.0226824 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> IsHoliday </td>
   <td style="text-align:center;"> 40 </td>
   <td style="text-align:center;"> 0.0159819 </td>
   <td style="text-align:center;"> 0.0013885 </td>
   <td style="text-align:center;"> 11.51001 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0.0132604 </td>
   <td style="text-align:center;"> 0.0187033 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> IsHoliday </td>
   <td style="text-align:center;"> 60 </td>
   <td style="text-align:center;"> 0.0131066 </td>
   <td style="text-align:center;"> 0.0011592 </td>
   <td style="text-align:center;"> 11.30623 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0.0108345 </td>
   <td style="text-align:center;"> 0.0153786 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> IsHoliday </td>
   <td style="text-align:center;"> 80 </td>
   <td style="text-align:center;"> 0.0107120 </td>
   <td style="text-align:center;"> 0.0009732 </td>
   <td style="text-align:center;"> 11.00749 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0.0088046 </td>
   <td style="text-align:center;"> 0.0126193 </td>
  </tr>
</tbody>
</table>

> At 0 temperature, a holiday will result in 2.34% increase of probability of doubling.

---
class: inverse, center, middle

# Today's Application: Shipping delays

---

## The question

> Can we leverage global weather data to predict shipping delays?

.center[<img src="../../../Figures/Singapore_port.jpg" height="400px">]

---

## A bit about shipping data

- WRDS doesn't have shipping data
- There are, however, vendors for shipping data, such as:

- They pretty much have any data you could need:
    - Over 650,000 ships tracked using ground and satellite based AIS 
        - AIS: Automatic Identification System
    - Live mapping
    - Weather data
    - Fleet tracking
    - Port congestion
    - <a target="_blank" href="https://www.inmarsat.com/">Inmarsat</a> support for ship operators

---

## What can we see from naval data?

.pull-left[
Cruise: Quantum of the Seas

.center[<img src="../../../Figures/Ships_Quantum_Seas.JPG" width = "400px">]

Oil tankers in the Persian gulf

.center[<img src="../../../Figures/Ships_persiangulf_oil.png" width = "400px">]
]

.pull-right[
Busiest port for transshipment (Singapore)

Busiest ports by containers and tons (Shanghai & Ningbo-Zhoushan, China)
<img src="../../../Figures/Ships_Ningbo-Zhoushan_busy-tonnage.png" height = "200px">
]

---

## Singaporean owned ships

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---

## Code for last slide's map

```r
library(plotly)  # for plotting
library(RColorBrewer)  # for colors
# plot with boats, ports, and typhoons
# Note: geo is defined in the code file -- it controls layout
palette = brewer.pal(8, "Dark2")[c(1, 8, 3, 2)]
p <- plot_geo(colors = palette) %>%
  add_markers(data = df_ports, x = ~port_lon, y = ~port_lat, color = "Port") %>%
  add_markers(data = df_Aug31, x = ~lon, y = ~lat, color = ~ship_type,
              text = ~paste('Ship name', shipname)) %>%
  add_markers(data = typhoon_Aug31, x = ~lon, y = ~lat, color="TYPHOON",
              text = ~paste("Name", typhoon_name)) %>%
   layout(showlegend = TRUE, geo = geo,
    title = 'Singaporean owned container and tanker ships, August 31, 2018')
p
```

- `plot_geo()` is from [`package:plotly`](https://plotly-r.com)
- `add_markers()` adds points to the map
- `layout()` adjusts the layout
- Within geo, a list, the following makes the map a globe
    - `projection = list(type = "orthographic")`

---

## What might matter for shipping?

> What observable events or data might provide insight as to whether a naval shipment will be delayed or not?

1. Typhoons

---

## Typhoon Jebi

.center[<iframe width="560" height="315" src="https://www.youtube.com/embed/kH9o1CSs5Rk?rel=0" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>]

- <a target="_blank" href="https://www.youtube.com/embed/kH9o1CSs5Rk?rel=0">click to play on youtube</a>

---

## Typhoon Jebi

.center[<iframe width="800px" height="500px" src="https://earth.nullschool.net/#2018/09/03/2100Z/wind/surface/level/orthographic=-221.34,35.55,806/loc=133.763,27.561"></iframe>]

---

## Typhoons in the data

<div id="htmlwidget-57ce453e1055b357b6a8" style="width:100%;height:360px;" class="plotly html-widget"></div>
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---

## Code for last slide's map

```r
# plot with boats and typhoons
palette = brewer.pal(8, "Dark2")[c(1, 3, 2)]
p <- plot_geo(colors = palette) %>%
  add_markers(data = df_all[df_all$frame == 14,], x = ~lon, y = ~lat,
              color = ~ship_type, text = ~paste('Ship name', shipname)) %>%
  add_markers(data = typhoon_Jebi, x = ~lon,
              y = ~lat, color = "Typhoon Jebi",
              text = ~paste("Name", typhoon_name, "</br>Time: ", date)) %>%
   layout(showlegend = TRUE, geo = geo,
          title = 'Singaporean ships, September 4, 2018, evening')
p
```

- This map is made the same way as the first map

---

## R Practice on mapping

- Practice interactive mapping using typhoon data
    - 1 map using [`package:plotly`](https://plotly-r.com)
- Bonus practice
    - 1 map using [`package:leaflet`](https://rstudio.github.io/leaflet/)
- There is another interactive mapping [`package:sf`](https://rdrr.io/r/base/library.html) but its installation is not friendly on a Mac
- Do exercises 3 and 4 in the practice file
    - <a target="_blank" href="Session_7s_Exercise.html">R Practice</a>

---
class: middle, inverse, center

# Predicting delays due to typhoons

---

## Data

- If the ship will report a delay of at least 3 hours some time in the next 12-24 hours
- What we have:
    - Ship location
    - Typhoon location
    - Typhoon wind speed

> We need to calculate distance between ships and typhoons

---

## Distance for geo

- There are a number of formulas for this
    - <a target="_blank" href="https://en.wikipedia.org/wiki/Haversine_formula">*Haversine*</a> for a simple calculation
    - <a target="_blank" href="https://en.wikipedia.org/wiki/Vincenty's_formulae">*Vincenty's formulae*</a> for a complex, incredibly accurate calculation
        - Accurate within **0.5mm**
- Use `distVincentyEllipsoid()` from `package:geosphere` to get a reasonably quick and accurate calculation
    - Calculates distance between two sets of points, x and y, structured as matrices
    - Matrices must have longitude in the first column and latitude in the second column
    - Provides distance in meters by default

```r
library(geosphere)
x <- as.matrix(df3[ , c("lon", "lat")])  # ship location
y <- as.matrix(df3[ , c("ty_lon", "ty_lat")]) # typhoon location

df3$dist_typhoon <- distVincentyEllipsoid(x, y) / 1000 # convert to KM
```

---

## Clean up

- Some indicators to cleanly capture how far away the typhoon is

```r
df3$typhoon_500 = ifelse(df3$dist_typhoon < 500 & 
                         df3$dist_typhoon >= 0, 1, 0)
df3$typhoon_1000 = ifelse(df3$dist_typhoon < 1000 &
                          df3$dist_typhoon >= 500, 1, 0)
df3$typhoon_2000 = ifelse(df3$dist_typhoon < 2000 &
                          df3$dist_typhoon >= 1000, 1, 0)
```

.center[<img src="../../../Figures/ifelse.png">]

---

## Do typhoons delay shipments?

```r
fit1 <- glm(delayed ~ typhoon_500 + typhoon_1000 + typhoon_2000,
            data = df3, family = binomial)
summary(fit1)
```

```
## 
## Call:
## glm(formula = delayed ~ typhoon_500 + typhoon_1000 + typhoon_2000, 
##     family = binomial, data = df3)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.2502  -0.2261  -0.2261  -0.2261   2.7127  
## 
## Coefficients:
##              Estimate Std. Error  z value Pr(>|z|)    
## (Intercept)  -3.65377    0.02934 -124.547   <2e-16 ***
## typhoon_500   0.14073    0.16311    0.863   0.3883    
## typhoon_1000  0.20539    0.12575    1.633   0.1024    
## typhoon_2000  0.16059    0.07106    2.260   0.0238 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 14329  on 59184  degrees of freedom
## Residual deviance: 14322  on 59181  degrees of freedom
##   (3866 observations deleted due to missingness)
## AIC: 14330
## 
## Number of Fisher Scoring iterations: 6
```

> It appears so!

---

## Interpretation of coefficients

```r
odds1 <- exp(coef(fit1))
odds1
```

```
##  (Intercept)  typhoon_500 typhoon_1000 typhoon_2000 
##   0.02589334   1.15111673   1.22800815   1.17420736
```

- Ships 1,000 to 2,000 km from a typhoon have a 17% increased odds of having a delay

```r
m1 <- margins(fit1)
summary(m1)
```

```
##        factor    AME     SE      z      p   lower  upper
##  typhoon_1000 0.0052 0.0032 1.6322 0.1026 -0.0010 0.0115
##  typhoon_2000 0.0041 0.0018 2.2570 0.0240  0.0005 0.0076
##   typhoon_500 0.0036 0.0042 0.8626 0.3883 -0.0046 0.0117
```

- Ships 1,000 to 2,000 km from a typhoon have an extra 0.41% chance of having a delay (baseline of 2.5%, ie, all x = 0)

---

## Interpretation of coefficients

- Alternatively, we may calculate actual probability by summing up all relevant log odds.

```r
prob_odds1 <- c(exp(coef(fit1)[1]),
                exp(coef(fit1)[c(2, 3, 4)] + coef(fit1)[c(1, 1, 1)]))
probability1 <- prob_odds1 / (1 + prob_odds1)
probability1
```

```
##  (Intercept)  typhoon_500 typhoon_1000 typhoon_2000 
##   0.02523980   0.02894356   0.03081733   0.02950702
```

- Ships 1,000 to 2,000 km from a typhoon have a 3% chance of having a delay (baseline of 2.5%)

- Note the calculation of odds for each scenario:
    - all typhoon_ = 0: `$\alpha$`
    - typhoon_500 = 1: `$\alpha+\beta1$`
    - typhoon_1000 = 1: `$\alpha+\beta2$`
    - typhoon_2000 = 1: `$\alpha+\beta3$`

---

## What about typhoon intensity?

- Hong Kong's typhoon classification: <a target="_blank" href="https://www.weather.gov.hk/en/informtc/class.htm">Official source</a>
    1. 41-62 km/h: Tropical depression
    2. 63-87 km/h: Tropical storm
    3. 88-117 km/h: Severe tropical storm
    4. 118-149 km/h: **Typhoon**
    5. 150-184 km/h: **Severe typhoon**
    6. 185+km/h: **Super typhoon**

```r
# 1 knot (nautical mile/h) = 1.852 km/h
# cut() makes a categorical variable out of a numerical variable
# using specified bins
df3$Super <- ifelse(df3$intensity_vmax * 1.852 >= 185, 1, 0)
df3$Moderate <- ifelse(df3$intensity_vmax * 1.852 >= 88 &
                         df3$intensity_vmax * 1.852 < 185, 1, 0)
df3$Weak <- ifelse(df3$intensity_vmax * 1.852 >= 41 & 
                   df3$intensity_vmax * 1.852 < 88, 1, 0)
df3$HK_intensity <- cut(df3$intensity_vmax * 1.852, c(-1, 41, 62, 87, 117,
                                                      149, 999))
table(df3$HK_intensity)
```

```
## 
##   (-1,41]   (41,62]   (62,87]  (87,117] (117,149] (149,999] 
##      3398     12039     12615     11527      2255     21141
```

---

## Typhoon intensity and delays

```r
fit2 <- glm(delayed ~ (typhoon_500 + typhoon_1000 + typhoon_2000) : 
              (Weak + Moderate + Super), data = df3,
            family = binomial)
tidy(fit2)
```

```
## # A tibble: 10 x 5
##    term                  estimate std.error statistic p.value
##    <chr>                    <dbl>     <dbl>     <dbl>   <dbl>
##  1 (Intercept)           -3.65       0.0290 -126.     0      
##  2 typhoon_500:Weak      -0.00879    0.213    -0.0413 0.967  
##  3 typhoon_500:Moderate   0.715      0.251     2.86   0.00430
##  4 typhoon_500:Super     -8.91     123.       -0.0726 0.942  
##  5 typhoon_1000:Weak      0.250      0.161     1.55   0.121  
##  6 typhoon_1000:Moderate  0.123      0.273     0.451  0.652  
##  7 typhoon_1000:Super    -0.0269     0.414    -0.0648 0.948  
##  8 typhoon_2000:Weak      0.182      0.101     1.80   0.0723 
##  9 typhoon_2000:Moderate  0.0253     0.134     0.189  0.850  
## 10 typhoon_2000:Super     0.311      0.136     2.29   0.0217
```

> Moderate storms predict delays when within 500km

> Super typhoons predict delays when 1,000 to 2,000km away

---

## Interpretation of coefficients

```r
odds2 <- exp(coef(fit2))
odds2[c(1, 3, 10)]
```

```
##          (Intercept) typhoon_500:Moderate   typhoon_2000:Super 
##           0.02589637           2.04505487           1.36507575
```

- Ships within 500km of a moderately strong storm have 104% higher *odds* of being delayed
- Ships 1,000 to 2,000km from a super typhoon have 36% higher *odds*

---

## Interpretation of coefficients

```r
prob_odds2 <- c(exp(coef(fit2)[1]),
                exp(coef(fit2)[c(3, 10)] + coef(fit2)[c(1, 1)]))
probability2 <- prob_odds2 / (1 + prob_odds2)
probability2
```

```
##          (Intercept) typhoon_500:Moderate   typhoon_2000:Super 
##           0.02524268           0.05029586           0.03414352
```

- Ships within 500km of a moderately strong storm have a 5% chance of being delayed (baseline: 2.5%)
- Ships 1,000 to 2,000km from a super typhoon have a 3.4% chance

---

## Marginal effects

```r
m2 <- margins(fit2)
summary(m2) %>%
  html_df()
```

<table class="table table-striped table-hover" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> factor </th>
   <th style="text-align:center;"> AME </th>
   <th style="text-align:center;"> SE </th>
   <th style="text-align:center;"> z </th>
   <th style="text-align:center;"> p </th>
   <th style="text-align:center;"> lower </th>
   <th style="text-align:center;"> upper </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Moderate </td>
   <td style="text-align:center;"> 0.0007378 </td>
   <td style="text-align:center;"> 0.0006713 </td>
   <td style="text-align:center;"> 1.0990530 </td>
   <td style="text-align:center;"> 0.2717449 </td>
   <td style="text-align:center;"> -0.0005779 </td>
   <td style="text-align:center;"> 0.0020535 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Super </td>
   <td style="text-align:center;"> -0.0050241 </td>
   <td style="text-align:center;"> 0.0860163 </td>
   <td style="text-align:center;"> -0.0584087 </td>
   <td style="text-align:center;"> 0.9534231 </td>
   <td style="text-align:center;"> -0.1736129 </td>
   <td style="text-align:center;"> 0.1635647 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> typhoon_1000 </td>
   <td style="text-align:center;"> 0.0035473 </td>
   <td style="text-align:center;"> 0.0036186 </td>
   <td style="text-align:center;"> 0.9802921 </td>
   <td style="text-align:center;"> 0.3269420 </td>
   <td style="text-align:center;"> -0.0035450 </td>
   <td style="text-align:center;"> 0.0106396 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> typhoon_2000 </td>
   <td style="text-align:center;"> 0.0039224 </td>
   <td style="text-align:center;"> 0.0017841 </td>
   <td style="text-align:center;"> 2.1985908 </td>
   <td style="text-align:center;"> 0.0279070 </td>
   <td style="text-align:center;"> 0.0004257 </td>
   <td style="text-align:center;"> 0.0074191 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> typhoon_500 </td>
   <td style="text-align:center;"> -0.0440484 </td>
   <td style="text-align:center;"> 0.6803640 </td>
   <td style="text-align:center;"> -0.0647424 </td>
   <td style="text-align:center;"> 0.9483791 </td>
   <td style="text-align:center;"> -1.3775373 </td>
   <td style="text-align:center;"> 1.2894405 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Weak </td>
   <td style="text-align:center;"> 0.0009975 </td>
   <td style="text-align:center;"> 0.0005154 </td>
   <td style="text-align:center;"> 1.9353011 </td>
   <td style="text-align:center;"> 0.0529534 </td>
   <td style="text-align:center;"> -0.0000127 </td>
   <td style="text-align:center;"> 0.0020077 </td>
  </tr>
</tbody>
</table>

- Delays appear to be driven mostly by 2 factors:
    1. A typhoon 1,000 to 2,000 km away from the ship
    2. Weak typhoons

---
class: inverse, center, middle

# Summary of Session 7

---

## For next week

- Try to replicate the code
- Continue your Datacamp career track
- Continue with your project
    - You can start to explore models

---

## R Coding Style Guide

Style is subjective and arbitrary but it is important to follow a generally accepted style if you want to share code with others. I suggest the [The tidyverse style guide](https://style.tidyverse.org/) which is also adopted by [Google](https://google.github.io/styleguide/Rguide.html) with some modification
- Highlights of **the tidyverse style guide**:
    - *File names*: end with .R
    - *Identifiers*: variable_name, function_name, try not to use "." as it is reserved by Base R's S3 objects
    - *Line length*: 80 characters
    - *Indentation*: two spaces, no tabs (RStudio by default converts tabs to spaces and you may change under global options)
    - *Spacing*: x = 0, not x=0, no space before a comma, but always place one after a comma
    - *Curly braces {}*: first on same line, last on own line
    - *Assignment*: use `<-`, not `=` nor `->`
    - *Semicolon(;)*: don't use, I used once for the interest of space
    - *return()*: Use explicit returns in functions: default function return is the last evaluated expression
    - *File paths*: use [relative file path](https://www.w3schools.com/html/html_filepaths.asp) "../../filename.csv" rather than absolute path "C:/mydata/filename.csv". Backslash needs `\\`

---

## R packages used in this slide

This slide was prepared on 2021-09-08 from Session_7s.Rmd with R version 4.1.1 (2021-08-10) Kick Things on Windows 10 x64 build 18362 🙋.

The attached packages used in this slide are:

```
##    geosphere RColorBrewer       plotly      margins        rlang        broom 
##     "1.5-10"      "1.1-2"    "4.9.4.1"     "0.3.26"     "0.4.11"      "0.7.9" 
##    lubridate      forcats      stringr        dplyr        purrr        readr 
##     "1.7.10"      "0.5.1"      "1.4.0"      "1.0.7"      "0.3.4"      "2.0.1" 
##        tidyr       tibble      ggplot2    tidyverse   kableExtra        knitr 
##      "1.1.3"      "3.1.3"      "3.3.5"      "1.3.1"      "1.3.4"       "1.33"
```