Problem Set 3: Analyzing the 2016 Presidential Election

Background

The outcome of the 2016 U.S. presidential election was surprising to most observers. To get a better sense of what happened, we will analyze a data set that compiles various sources from the Census, election outcomes, and Bureau of Labor Statistics.

Question 1 (4 points)

You’ve been hired by a political consultant to figure out what happened in the 2016 election. The first task is to see where the losses occurred in terms of the outcome of the 2012 election.

Load the pres2016.csv file into a data frame called pres2016. Create a new variable in the data frame called dem_change that is the difference between Clinton’s vote share in 2016 (dem_share_2016) and Obama’s vote share in 2012 (dem_share_2012). Use this new variable to create a scatter plot of the Obama-Clinton vote share change on the share of Obama’s vote in 2012. Be sure to use informative axis labels.

Did the largest losses for Clinton relative to Obama occur in Obama strongholds, Romney strongholds, or in counties that were relatively competitive in 2012?

Rubric: 1 autograder point for calculating dem_change, 2 pdf points for plot, 1 pdf point for explanation.

Question 2 (4 points)

Your boss asks you to create a prediction model for the change in Democratic vote share, but says you can only use Obama vote share as an independent variable. Your boss wants a linear relationship, but you think a nonlinear fit might be better.

Fit two regression models to the data both using dem_change as the dependent variable. First, save a model called obama_fit that uses dem_share_2012 as the independent variable. Second, save a model called obama_sq_fit that includes dem_share_2012 and its square as independent variables.

Compare the adjusted \(R^2\) of these two regressions. Interpret these two values and say which is the more predictive model.

Rubric: 1 autograder point for obama_fit; 1 autograder point for obama_sq_fit; 1 PDF point for \(R^2\) presentation in text; 1 point for description/interpretation.

Question 3 (5 points)

Now, your boss actually can’t read regression coefficients and certainly doesn’t understand a nonlinear term. Thus, you need to create a plot to show the predictions from each model over the scatter plot you created earlier.

Recreate the scatter plot from Question 1, but now add the two fitted value lines/curves from the obama_fit and obama_sq_fit models. For the linear fit, use the abline() function for base R or the geom_abline() function for ggplot. For the nonlinear fit, use the predict() function to get predicted values for the model and then plot them using the points() function in base R or the geom_line() function for ggplot.

Rubric: 2 PDF points for correct linear fit on plot, 3 PDF points for correct nonlinear fit on plot.

Question 4 (6 points)

Another of your bosses correctly identified that the close races in Wisconsin, Michigan, and Pennsylvania tipped the election to Trump, so he wants to identify the relationship between Rust Belt counties and the change in Democratic vote share. But you worry that the demographics of those counties might be different than the rest of the country. So you prepare two regressions.

Create a new variable called rust_belt that is 1 if the county is in the following states: Ohio (OH), Michigan (MI), Pennsylvania (PA), Wisconsin (WI), Indiana (IN), or Illinois (IL). The variable should be 0 for all other counties. Run two regressions:

• Save a regression of dem_change as the dependent variable on rust_belt as the independent variable as fit_1.
• Save a regression of dem_change as the dependent variable on rust_belt and whprop_2010 as the independent variables as fit_2.

This boss prefers to see regression tables. Pass these tables to the function stargazer::stargazer() to make a nicely formatted regression table. NOTE: For the R chunk that calls stargazer, please use the option results = 'asis' or else the formatting will be off. When calling stargazer::stargazer(), use the following format:

stargazer::stargazer(fit_1, fit_2, tile = "An Informative Title",
                     covariate.labels = c("Covariate 1", "Covariate 2"),
                     dep.var.labels = "Informative name of the dependent variable",
                     header = FALSE)

The last line suppresses some ugly output from the function. Finally, answer these questions about the resulting models:

1. Interpret the coefficient on rust_belt from fit_1 in the substantive context of this example.
2. Interpret the coefficient on rust_belt from fit_2 in the substantive context of this example.
3. In a sentence, describe why the relationship between rust_belt and dem_change might be different between these two models.

Rubric: 1 autograder point for fit_1; 1 autograder point for fit_2; 1 PDF point for regression table; 3 PDF points for interpretations/discussion.

Question 5 (4 points)

Now we will see if the relationship between demographics and the change in the Democratic vote share is the same for the Rust Belt and non-Rust Belt states. Create two subsets of the data, one called rb for the rust belt states and one called non_rb for the non-Rust belt states. Run a regression of dem_change on whprop_2010 in each of these subsets, saving them as rb_fit and non_rb_fit, respectively. Make a plot of the two regression lines, distinguishing them by color. In the text, describe which line corresponds to which group and briefly describe which group of states has a stronger relationship with the outcome (that is, steeper regression line).

Rubric: 1 autograder point for rb_fit; 1 autograder point for non_rb_fit; 2 PDF points for plot and discussion.

Question 6 (2 points)

Let’s investigate how this subset approach relates to interaction terms. In the entire pres2016 data, run a regression of dem_change on rust_belt, whprop_2010, and the interaction between these two variables. Save this model as int_fit. In the text, interpret the coefficient on the interaction in the context of the plot from Question 5: how does this coefficient relate to the two lines you plotted there?

Rubric: 1 autograder point for int_fit; 1 PDF point for interpretation/discussion.