Spending your data

Lecture 20

Author

Affiliation

Prof. Mine Çetinkaya-Rundel

Duke University
STA 199 - Fall 2026

Published

November 9, 2026

Warm-up

While you wait: Participate 📱💻

Describe logistic regression and identify one aspect of it you are confused about / would like more clarity on.

Go to wooclap.com and use the code OMEXALN.

Announcements

My office hours moved to Tuesday, Josh’s office hours are also updated:
- Josh: Tuesday 2-3 pm + Wednesday 4-5 pm
- Mine: Tuesday 3-4:30 pm (I’m giving a talk at the R+AI conference on Wednesday, check it out if you’re interested!)
HW 6 due Wednesday 11:59 pm
Project write-up due Friday 11:59 pm
Week 12 nudges will be coming throughout the week, please make sure to read and don’t hesitate to reach out with any questions!

From last time: Dem flips

Packages

library(tidyverse) # data wrangling and visualization
library(tidymodels) # modeling

Today’s data

2026 House results and projections from Decision Desk HQ (as of 2026-11-04, 11:14 am), merged with 2024 results (from the gerrymander dataset we worked with earlier in the semester):

midterm_26_raw <- read_csv("data/midterm-2026-11-04-11-14.csv")

glimpse(midterm_26_raw)

Rows: 443
Columns: 18
$ district       <chr> "AK-00", "AL-01", "AL-02", "AL-03", "AL-04", "AL-05", "…
$ state_abb      <chr> "AK", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AR", "…
$ state          <chr> "Alaska", "Alabama", "Alabama", "Alabama", "Alabama", "…
$ house_rep_20   <chr> "Don Young", "Jerry Carl", "Barry Moore", "Mike Rogers"…
$ house_party_20 <chr> "Republican", "Republican", "Republican", "Republican",…
$ house_rep_22   <chr> "Mary Sattler Peltola", "Jerry L Carl", "Barry Moore", …
$ house_party_22 <chr> "Democrat", "Republican", "Republican", "Republican", "…
$ house_rep_24   <chr> "Nick Begich", "Barry Moore", "Shomari Figures", "Mike …
$ house_party_24 <chr> "Republican", "Republican", "Democrat", "Republican", "…
$ harris_24      <dbl> 41.41, 21.89, 53.52, 26.18, 15.96, 34.20, 29.68, 61.45,…
$ trump_24       <dbl> 54.54, 76.94, 45.31, 72.71, 83.02, 64.02, 68.47, 37.50,…
$ gerry_22       <chr> NA, "F", "F", "F", "F", "F", "F", "F", "C", "C", "C", "…
$ gerry_24       <chr> NA, "B", "B", "B", "B", "B", "B", "B", "C", "C", "C", "…
$ gerry_26       <chr> NA, "B", "B", "B", "B", "B", "B", "B", "C", "C", "C", "…
$ rating_26      <chr> "Lean R", "Safe R", "Lean R", "Safe R", "Safe R", "Safe…
$ leader_26      <chr> "Republican", "Republican", "Democrat", "Republican", "…
$ margin_26      <dbl> 9.00, 18.00, 8.00, 28.00, 50.00, 7.00, 15.00, 39.00, 35…
$ called_26      <chr> "uncalled", "called", "called", "called", "called", "ca…

Data prep

A seat flips to Democrat if it was held by a Republican after 2024 and a Democrat leads in 2026:

midterm_26 <- midterm_26_raw |>
  mutate(
    flip_dem_24_26 = case_when(
      called_26 == "uncalled" ~ NA,
      called_26 == "called" & house_party_24 == "Republican" & leader_26 == "Democrat" ~ "1",
      called_26 == "called" & house_party_24 == "Republican" & leader_26 == "Republican" ~ "0",
      called_26 == "called" & house_party_24 == "Democrat" ~ "0",
    ),
    flip_dem_24_26 = as.factor(flip_dem_24_26)
  ) |>
  filter(!is.na(called_26))

Data split:

midterm_26_called <- midterm_26 |> filter(called_26 == "called")
midterm_26_uncalled <- midterm_26 |> filter(called_26 == "uncalled")

Goal

Predict whether a seat flips to Democrat based on Trump’s 2024 vote share for uncalled seats, using data from called seats.

Code

ggplot(
  midterm_26,
  aes(x = trump_24, y = flip_dem_24_26, fill = flip_dem_24_26)
) +
  geom_jitter(
    shape = "circle filled",
    height = 0.2,
    alpha = 0.7,
    size = 3,
    show.legend = FALSE,
    color = "white"
  ) +
  scale_fill_manual(
    values = c("0" = "darkgray", "1" = "#0015BC"),
    na.value = "#A3B18A"
  ) +
  scale_x_continuous(
    limits = c(10, 90),
    breaks = seq(0, 100, 10),
    labels = label_percent(scale = 1)
  ) +
  labs(
    x = "Trump's 2024 vote share (%)",
    y = "Flipped to Democrat",
    title = "2026 House elections",
    caption = "Data from Decision Desk HQ, as of 2026-11-04 at 11:14 am"
  ) +
  facet_wrap(~called_26, nrow = 2, scales = "free_y")

Fitting a logistic model

flip_fit <- logistic_reg() |>
  fit(flip_dem_24_26 ~ trump_24, data = midterm_26_called)

tidy(flip_fit)

# A tibble: 2 × 5
  term        estimate std.error statistic      p.value
  <chr>          <dbl>     <dbl>     <dbl>        <dbl>
1 (Intercept)  -3.48      0.648      -5.37 0.0000000805
2 trump_24      0.0244    0.0117      2.08 0.0372

Remember

In logistic regression, we predict the log odds of the probability of success, \(\log\left(\frac{\hat{p}}{1-\hat{p}}\right)\).

Output \(\rightarrow\) model

Output

tidy(flip_fit)

# A tibble: 2 × 5
  term        estimate std.error statistic      p.value
  <chr>          <dbl>     <dbl>     <dbl>        <dbl>
1 (Intercept)  -3.48      0.648      -5.37 0.0000000805
2 trump_24      0.0244    0.0117      2.08 0.0372

. . .

Fitted model:

\[ \log\left(\frac{\hat{p}}{1-\hat{p}}\right) = -3.48 + 0.0244\times trump\_24 \]

The intercept

If trump_24 = 0, then

\[ \begin{aligned} \log\left(\frac{\hat{p}}{1-\hat{p}}\right) &= b_0 + b_1 \times 0 \\ &= b_0 \\ \end{aligned} \]

. . .

Exponentiating both sides:

\[ \begin{aligned} e^{\log\left(\frac{\hat{p}}{1-\hat{p}}\right)} &= e^{b_0} \\ \frac{\hat{p}}{1-\hat{p}} &= e^{b_0} \end{aligned} \]

Interpreting the intercept

\[ \log\left(\frac{\hat{p}}{1-\hat{p}}\right) = -3.48 + 0.0244\times trump\_24 \]

. . .

\[ e^{-3.48} = 0.03 \]

. . .

Seats where Trump got 0% of the vote in 2024 are predicted, on average, to have a 3% odds of flipping to Democrat.
Since Trump’s vote share in called seats ranges from 10.6% to 83%, so this is an extrapolation and not meaningful.

The slope I

Find log odds when the predictor is equal to \(x\):

\[ log(odds_1) = {b_0} + {b_1x} \]

. . .

Increase \(x\) by one unit and find log odds when the predictor is equal to \(x + 1\):

\[ log(odds_2) = {b_0} + {b_1(x + 1)} \]

The slope II

Difference between the two log odds:

\[ \begin{aligned} log(odds_2) - log(odds_1) &= ({b_0} + {b_1 (x + 1)}) - ({b_0} + {b_1x}) \\ log\Big(\frac{odds_2}{odds_1}\Big) &= b_0 + b_1x + b_1 - b_0 - b_1x \\ log\Big(\frac{odds_2}{odds_1}\Big) &= b_1 \end{aligned} \]

The slope III

Difference between the odds, by exponentiating both sides:

\[ \begin{aligned} log\Big(\frac{odds_2}{odds_1}\Big) &= b_1 \\ \frac{odds_2}{odds_1} &= e^{b_1} \end{aligned} \]

Interpreting the slope

\[ \log\left(\frac{\hat{p}}{1-\hat{p}}\right) = -3.48 + 0.0244\times trump\_24 \]

. . .

\[ e^{0.0244} \approx 1.02 \]

. . .

Seats where Trump’s 2024 vote share was one percentage point higher are predicted to have odds of flipping to Democrat that are higher by a factor of \(e^{0.0244}\approx 1.02\), on average.

Classification
(prediction by another name…)

Predict

How well did our model do for predicting already called house seats?

midterm_26_called_aug <- augment(flip_fit, new_data = midterm_26_called)

midterm_26_called_aug |>
  count(flip_dem_24_26, .pred_class)

# A tibble: 2 × 3
  flip_dem_24_26 .pred_class     n
  <fct>          <fct>       <int>
1 0              0             353
2 1              0              38

Terrible!

Is that surprising?

Predict for uncalled seats

midterm_26_uncalled_aug <- augment(flip_fit, new_data = midterm_26_uncalled)

midterm_26_uncalled_aug |>
  select(district, trump_24, house_party_24, starts_with(".pred_"), leader_26) |>
  print(n = 44)

# A tibble: 44 × 7
   district trump_24 house_party_24 .pred_class .pred_0 .pred_1 leader_26 
   <chr>       <dbl> <chr>          <fct>         <dbl>   <dbl> <chr>     
 1 AK-00        54.5 Republican     0             0.895  0.105  Republican
 2 AZ-01        50.9 Republican     0             0.903  0.0967 Democrat  
 3 AZ-02        56.9 Republican     0             0.890  0.110  Democrat  
 4 AZ-05        59.2 Republican     0             0.884  0.116  Republican
 5 AZ-08        57.5 Republican     0             0.888  0.112  Republican
 6 CA-04        32.8 Democrat       0             0.936  0.0645 Democrat  
 7 CA-05        57.6 Republican     0             0.888  0.112  Republican
 8 CA-07        33.4 Democrat       0             0.935  0.0652 Democrat  
 9 CA-11        14.1 Democrat       0             0.958  0.0418 Democrat  
10 CA-14        30.4 Democrat       0             0.939  0.0609 Democrat  
11 CA-23        57.1 Republican     0             0.889  0.111  Republican
12 CA-34        22.4 Democrat       0             0.949  0.0508 Democrat  
13 CA-40        49.5 Republican     0             0.906  0.0938 Republican
14 CO-03        53.6 Republican     0             0.897  0.103  Republican
15 CO-04        57.9 Republican     0             0.887  0.113  Democrat  
16 CO-05        53.2 Republican     0             0.898  0.102  Democrat  
17 FL-07        55.6 Republican     0             0.893  0.107  Republican
18 FL-09        47.6 Democrat       0             0.910  0.0900 Democrat  
19 FL-26        67.0 Republican     0             0.863  0.137  Republican
20 FL-27        56.7 Republican     0             0.890  0.110  Republican
21 LA-05        67.4 Republican     0             0.862  0.138  Democrat  
22 LA-06        41.8 Democrat       0             0.921  0.0790 Democrat  
23 ME-02        53.8 Democrat       0             0.897  0.103  Republican
24 MI-04        51.9 Republican     0             0.901  0.0989 Democrat  
25 MI-07        49.8 Republican     0             0.906  0.0945 Democrat  
26 MI-10        52.2 Republican     0             0.900  0.0996 Democrat  
27 MN-01        55.1 Republican     0             0.894  0.106  Democrat  
28 NC-03        60.3 Republican     0             0.881  0.119  Republican
29 NC-05        58.2 Republican     0             0.886  0.114  Democrat  
30 NC-07        56.3 Republican     0             0.891  0.109  Republican
31 NC-08        59.1 Republican     0             0.884  0.116  Republican
32 NC-10        58.2 Republican     0             0.887  0.113  Republican
33 NY-01        54.3 Republican     0             0.896  0.104  Republican
34 NY-02        56.8 Republican     0             0.890  0.110  Republican
35 NY-17        49.4 Republican     0             0.907  0.0935 Democrat  
36 NY-21        60.1 Republican     0             0.882  0.118  Republican
37 TN-04        71.2 Republican     0             0.851  0.149  Democrat  
38 TX-02        61.3 Republican     0             0.879  0.121  Republican
39 TX-22        58.7 Republican     0             0.885  0.115  Republican
40 TX-27        64.4 Republican     0             0.871  0.129  Republican
41 TX-38        59.4 Republican     0             0.883  0.117  Republican
42 WA-03        50.0 Democrat       0             0.905  0.0947 Democrat  
43 WA-04        58.7 Republican     0             0.885  0.115  Republican
44 WA-05        53.6 Republican     0             0.897  0.103  Republican

Application exercise

Go to your ae project in Positron.
If you haven’t yet done so, make sure all of your changes up to this point are committed and pushed, i.e., there’s nothing left in your source control pane.
If you haven’t yet done so, pull to get today’s application exercise file: ae-11-dem-flips-logistic.qmd.
Work through the application exercise in class, and render, commit, and push your edits by the end of class.

Warm-up

While you wait: Participate 📱💻

Announcements

From last time: Dem flips

Packages

Today’s data

Data prep

Goal

Fitting a logistic model

Output \(\rightarrow\) model

The intercept

Interpreting the intercept

The slope I

The slope II

The slope III

Interpreting the slope

Classification (prediction by another name…)

Predict

Predict for uncalled seats

Application exercise

Classification
(prediction by another name…)