Week 5
Data Analysis
Soci—316
Our Case
Image can be retrieved here.
Let’s Use Our Model
Counterfactual Predictions—With Our Truncated Sample
Show the underlying code
library(marginaleffects)
avg_predictions(survival_truncated, variables = "age") |>
as_tibble() |>
ggplot(mapping = aes(x = age, y = estimate)) +
geom_line(colour = "#b7a5d3", linewidth = 1.5) +
geom_ribbon(mapping = aes(ymin = conf.low,
ymax = conf.high),
fill = "lightgrey",
alpha = 0.2) +
theme_bw()
Let’s Use Our Model
Counterfactual Predictions—With the Full Sample
Show the underlying code
survival_full <- lm(survived ~ age, data = titanic)
avg_predictions(survival_full, variables = "age") |>
as_tibble() |>
ggplot(mapping = aes(x = age, y = estimate)) +
geom_line(colour = "#b7a5d3", linewidth = 1.5) +
geom_ribbon(mapping = aes(ymin = conf.low,
ymax = conf.high),
fill = "lightgrey",
alpha = 0.2) +
theme_bw()
An Invitation
Click to Expand Flyer
Supervised Machine Learning (SML)
An Illustration
# A tibble: 80,000 × 6
fruit shape weight_g colour texture origin
<chr> <chr> <dbl> <chr> <chr> <chr>
1 apple spherical 150 red crispy china
2 banana curved 120 yellow creamy ecuador
3 orange spherical 148 orange juicy egypt
4 watermelon spherical 4500 green juicy spain
5 strawberry conical 13 red juicy mexico
6 grape spherical 5 green juicy chile
7 mango ellipsoidal 240 yellow juicy india
8 pineapple conical 2100 yellow juicy costa rica
9 apple spherical 140 green crispy usa
10 banana curved 110 yellow creamy ecuador
# ℹ 79,990 more rows
# A tibble: 1 × 6
fruit shape weight_g colour texture origin
<chr> <chr> <int> <chr> <chr> <chr>
1 <NA> conical 6 red juicy china # A tibble: 8 × 2
fruit probability
<chr> <dbl>
1 apple 0.03
2 banana 0
3 orange 0.05
4 watermelon 0
5 strawberry 0.71
6 grape 0.21
7 mango 0
8 pineapple 0 # A tibble: 1 × 1
prediction
<chr>
1 strawberry
Unsupervised Machine Learning (UML)
An Illustration
Karim and Lukk’s The Radicalization of Mainstream Parties in the 21st Century
Bias-Variance Tradeoff
Image can be retrieved here.
Bias
Emerges when we build SML algorithms that fail to sufficiently map the patterns—or pick up the empirical signal–linking X and Y. Think: underfitting.
Variance
Arises when our algorithms not only pick up the signal linking X and Y, but some of the noise in our data as well. Think: overfitting.
The Goal
To strike the optimal balance between bias and variance.
k-Fold Cross-Validation
Unlike conventional approaches to sample partition, v or k-fold cross-validation allows us to learn from all our data.
k-fold cross-validation proceeds as follows:
- We randomly divide our overall sample into k subsets or folds.
- We train our algorithm on k - 1 folds, holding just one group out for model assessment.
- We repeat this process k times—every fold is held out once and used to fit the model k - 1 times.
- We then pool or average the evaluation metrics (e.g., predictive accuracy) for all the held-out runs.
Stratified k-fold cross-validation ensures that the distribution of class labels—or for numeric targets, the mean—is relatively constant across folds.
Stylized example of five-fold cross-validation
Gender Typicality
Figure 8 from Mittleman (2022).
Gendered Stereotypes in Print Media
Figure 8 from Boutyline and colleagues (2023)
