Lab 6 - Logistic regression

Lab
Important

This lab is due Monday, March 27 at 5:00pm.

Packages

You’ll need the following packages for today’s lab.

library(tidyverse)
library(tidymodels)
library(dsbox)

Data

The data can be found in the dsbox package, and it’s called gss16. Since the data set is distributed with the package, we don’t need to load it separately; it becomes available to us when we load the package.

If you would like to explicitly load the data into your environment so you can view it, you can do so by running this code.

gss16 <- gss16

You can find out more about the data set by inspecting its documentation, which you can access by running ?gss16 in the Console or using the Help menu in RStudio to search for gss16. You can also find this information here.

Exercises

Exercise 1 - Data wrangling

Important

Remember: For each exercise, you should choose one person to type. All others should contribute to the discussion, but only one person should type up the answer, render the document, commit, and push to GitHub. All others should not touch the document.

  1. Create a new data frame called gss16_advfront that includes the variables advfront, educ, polviews, and wrkstat. Then, use the drop_na() function to remove rows that contain NAs from this new data frame.

  2. Transform the advfront variable such that it has two levels: "Strongly agree" and "Agree" should both be mapped to "Agree" and the remaining levels should all be relabeled "Not agree". Make sure the resulting levels are in the following order: "Agree" and "Not agree".

Hint: use the factor() function inside a mutate() statement to relabel the original levels. Be sure to list the levels in order so that they are correctly ordered after relabeling.

  1. Similarly to part b, combine the levels of the polviews variable such that levels that have the word “liberal” in them are lumped into a level called "Liberal" and those that have the word “conservative” in them are lumped into a level called "Conservative". Make sure the levels are in the following order: "Conservative" , "Moderate", and "Liberal". Finally, count() how many times each new level appears in the polviews variable.

Hint: be careful if you manually type out the levels in the original polviews variable to note that there are typos in two of the original levels “slightly conservative” and “extremely conservative” are both misspelled, and so you will need to match those misspellings in your call to factor().

Important

After the team member working on Exercise 1 renders, commits, and pushes, all other team members should pull. Then, choose a new team member to write the answer to Exercise 2. (And so on for the remaining exercises.)

Exercise 2 - Train and test sets

Now, let’s split the data into training and test sets so that we can evaluate the models we’re going to fit by how well they predict outcomes on data that wasn’t used to fit the models.

Specify a random seed of 1234 (i.e., include set.seed(1234) at the beginning of your code chunk), and then split gss16_advfront randomly into a training set train_data and a test set test_data. Do this so that the training set contains 80% of the rows of the original data.

Exercise 3 - Logistic Regression

  1. Using the training data, fit a logistic regression model that predicts advfront using educ. In particular, the model should predict the probability that advfront has value "Not agree". Name this model model1. Report the tidy model output.

  2. Write out the fitted model equation in proper notation. State the meaning of any variables in the context of the data.

  3. Using your fitted model, report the estimated probability of agreeing with the following statement: Even if it brings no immediate benefits, scientific research that advances the frontiers of knowledge is necessary and should be supported by the federal government (Agree in advfront) if you have an education of 7 years.

Exercise 4 - Another model

  1. Again using the training data, fit a new logistic regression model that adds the additional explanatory variable of polviews. Name this model model2. Report the tidy output.

  2. Now, report the estimated probability of agreeing with the following statement: Even if it brings no immediate benefits, scientific research that advances the frontiers of knowledge is necessary and should be supported by the federal government (Agree in advfront) if you have an education of 7 years and are Conservative.

Exercise 5 - Evaluating models with AIC

  1. Report the AIC values for each of model1 and model2.

  2. Based on your results in part a, does it appear that including political views in addition to years of education is useful for modeling whether employees agree with the statement “Even if it brings no immediate benefits, scientific research that advances the frontiers of knowledge is necessary and should be supported by the federal government”? Explain.

Exercise 6 - Evaluating models using test data

  1. For each of model1 and model2, report the number of false positive and false negatives when making predictions on the test_data with a decision boundary of 0.5.

  2. Do these results provide much information about which model you would prefer for a prediction task? If so, which model would you choose?

  3. Do you think a decision boundary of 0.5 makes sense here or would you adjust it?

Submission

Warning

Before you wrap up the assignment, make sure all documents are updated on your GitHub repo. We will be checking these to make sure you have been practicing how to render and push changes.

You must turn in a PDF file to the Gradescope page by the submission deadline to be considered “on time”. Only one team member should submit to Gradescope, but they should add all other team members to the submission.

Make sure your data are tidy! That is, your code should not be running off the pages and spaced properly. See: https://style.tidyverse.org/ggplot2.html.

To submit your assignment:

  • Go to http://www.gradescope.com and click Log in in the top right corner.
  • Click School Credentials \(\rightarrow\) Duke NetID and log in using your NetID credentials.
  • Click on your STA 199 course.
  • Click on the assignment, and you’ll be prompted to submit it.
  • Mark all the pages associated with exercise. All the pages of your lab should be associated with at least one question (i.e., should be “checked”). If you do not do this, you will be subject to lose points on the assignment.
  • Select all pages of your .pdf submission to be associated with the “Workflow & formatting” question.

Grading

Component Points
Ex 1 8
Ex 2 3
Ex 3 10
Ex 4 5
Ex 5 5
Ex 6 14
Workflow & formatting 5
Total 50
Note

The “Workflow & formatting” grade is to assess the reproducible workflow. This includes:

  • linking all pages appropriately on Gradescope

  • putting your team and member names in the YAML at the top of the document

  • committing the submitted version of your .qmd to GitHub

  • Are you under the 80 character code limit? (You shouldn’t have to scroll to see all your code). Pipes %>%, |> and ggplot layers + should be followed by a new line

  • You should be consistent with stylistic choices, e.g. only use 1 of = vs <- and %>% vs |>

  • All binary operators should be surrounded by space. For example x + y is appropriate. x+y is not.