Spending your data

Lecture 20

Prof. Mine Çetinkaya-Rundel

Duke University
STA 199 - Fall 2026

November 9, 2026

Warm-up

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

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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

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

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

  1. 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.