Trees vs. Lines

So far in the labs, we’ve learned how we can fit linear models to our data and use them to make predictions.
In this lab, we’ll learn how to make predictions by growing trees.
- Instead of creating a line, we split our data into branches based on a series of yes or no questions.
- The branches help sort our data into leaves which can then be used to make predictions.
Start by loading the titanic data.

Our first tree

(1) Write and run code using the tree() function to create a classification tree that predicts whether a person survived the Titanic based on their sex.
- A classification tree tries to predict which category a categorical variable would belong to based on other variables.
- The syntax for tree is similar to that of the lm() function.
- Assign this model the name tree1.
(2) Why can’t we just use a linear model to predict whether a passenger on the Titanic survived or not based on their sex?

(3) To actually look at and interpret our tree1, write and run code placing the model into the treeplot function.
- (4) Write down the labels of the two branches.
- (5) Write down the labels of the two leaves.
Answer the following, based on the treeplot:
- (6) Which sex does the model predict will survive?
- (7) Where does the plot tell you the number of people that get sorted into each leaf? How do you know?
- (8) Where does the plot tell you the number of people that have been sorted incorrectly in each leaf?

(9) Similar to how you included multiple variables for a linear model, write and run code creating a tree that predicts whether a person survived based on their sex, age, class, and where they embarked.
- Assign this model the name tree2.
(10) Write and run code creating a treeplot for this model and answer the following questions:
- (11) Mrs. Baxter was a 50-year-old female with a 1st class ticket from Cherbourg. Does the model predict that she survived?
- (12) Which variable ended up not being used by tree2?

By default, the tree() function will fit a tree model that will make good predictions without needing lots of branches.
We can increase the complexity of our trees by changing the complexity parameter, cp, which equals 0.01 by default.
We can also change the minimum number of observations needed in a leaf before we split it into a new branch using minsplit, which equals 20 by default.
(13) Using the same variables that you used in tree2, write and run code creating a model named tree3 but include cp = 0.005 and minsplit = 10 as arguments.
- (14) How is tree3 different from tree2?

Just like with linear models, we can use cross-validation to measure how well our classification trees perform on unseen data.
First, we need to compute the predictions that our model makes on test data.
- Use the data function to load the titanic_test data.
- (15) Fill in the blanks below to predict whether people in the titanic_test data survived or not using tree1.
- Note: the argument type = "class" tells the predict function that we are predicting a categorical variable and not a numerical variable.

titanic_test <- mutate(____, prediction = predict(____, newdata = ____, type = "class"))

Similar to how we use the mean squared error to describe how well our model predicts numerical variables, we use the misclassification rate to describe how our model predicts categorical variables.
- The misclassification rate (MCR) is the number of people who were predicted to be in one category but were actually in another.
Run the following command to see a side-by-side comparison of the actual outcome and the predicted outcome:

View(select(titanic_test, survived, prediction))

In order to tally up the total number of misclassifications, we need to create a function that compares the actual outcome with the predicted outcome. The not equal to operator != will be useful here.
(17) Fill in the blanks to create a function to calculate the MCR.
- Hint: sum(____!=____) will count the number of times that the left-hand side does not equal the right-hand side.
- We want to count the number of times that actual does not equal predicted and then divide by the total number of observations.

calc_mcr <- function(actual, predicted) {
  sum(____ != ____) / length(actual)
}

summarize(titanic_test, mcr = calc_mcr(survived, prediction))

(18) In your own words, explain what the misclassification rate is.
(19) Which model (tree1, tree2, or tree3) had the lowest misclassification rate for the titanic_test data?
(20) Write and run code creating a 4th model using the same variables used in tree2. This time though, change the complexity parameter to 0.0001. Then answer the following:
- (21) Does creating a more complex classification tree always lead to better predictions? Why not?
A regression tree is a tree model that predicts a numerical variable.
(22) Write and run code creating a regression tree model to predict the Titanic’s passengers’ ages and calculate the MSE.
- Plots of regression trees are often too complex to plot.