From Hypotheses to Models

This module introduces the fundamental concepts of statistical modeling in political science research. We have already explored our data, visualized distributions, and examined relationships between variables. Now, we ask:

• How can we formalize patterns in data?
• How can we make confident claims that go beyond mere observation?

Modeling is the bridge between descriptive insights and data-driven inference. It allows us to quantify uncertainty, test hypotheses, and predict outcomes. Think of models as tools that help you reason rigorously about your data instead of relying solely on intuition.

By the end of this module, you will have a conceptual understanding of modeling and practical skills to begin building your first statistical models.

Theory

Suggested Conceptual Reading & Discussion

• Argyle, L. P., Busby, E. C., Fulda, N., Gubler, J. R., Rytting, C., & Wingate, D. (2023). Out of one, many: Using language models to simulate human samples. Political Analysis, 31(3), 337-351.

What is a Model?

A model is a simplified representation of reality that allows us to:

1. Summarize relationships between variables
2. Estimate effects while accounting for uncertainty
3. Make predictions for new data

For example, let's say we recorded the time I take to come to the Sciences Po Bordeaux. You might ask: What is the actual time I take to come to work?

Code: Live Demo & Hands-on Lab

Student Group Live Demo (Group 3)

• Topic: Linear Regression & Categorical Predictors (Specifying DV ~ IV, adding C(category), interpreting slopes, reference levels & R²).
• Review the Live Demo Guidelines & Schedule.

Modeling with Words

Even without code, practice conceptual modeling:

1. Identify your outcome variable (dependent variable) - Y (here it's time_to_iep)
2. Identify potential predictors (independent variables) - Xs
3. Ask: How do other predictors explain variation in outcomes?

Conceptual modeling is essential before jumping to formulas. Models without theory are often misleading.

Common pitfalls to avoid

• Modeling before understanding the data
• Neglecting measurement validity
• Misinterpreting statistical significance

Code to reproduce the figure

# !pip install "altair[all]"
import altair as alt
import pandas as pd

df = pd.DataFrame(
    {
        'time_to_iep': [
            16.93, 19.49, 18.21, 19.09, 17.67, 18.48, 16.37, 17.57, 19.18,
            18.74, 17.15, 17.76, 17.2, 19.78, 18.34, 17.93, 18.09, 17.14,
            19.41, 17.99, 16.54, 18.42, 16.65, 19.83, 18.32, 18.13, 16.72,
            18.05, 18.5, 19.45, 17.22, 17.32, 19.48, 18.93, 18.69, 18.78,
            18.58, 18.8, 18.28, 20.06, 18.12, 18.64, 18.16, 17.44, 18.96,
            17.55, 19.09, 17.95, 21.01, 18.19
        ]
    }
)

mean_val = df["time_to_iep"].mean()

hist = alt.Chart(df, title="Distribution of Time to IEP").mark_bar().encode(
    x=alt.X("time_to_iep:Q", bin=alt.Bin(maxbins=10), title="Time to IEP"),
    y="count()"
)

mean_line = alt.Chart(pd.DataFrame({"x":[mean_val]})).mark_rule(
    color="red", strokeDash=[6,4]
).encode(x="x:Q")

mean_text = alt.Chart(pd.DataFrame({"x":[mean_val]})).mark_text(
    text=f"{mean_val:.2f}",
    dx=20, dy=250, color="red"
).encode(x="x:Q", y=alt.value(0))

hist + mean_line + mean_text

Application

We will work from 07_intro_to_modeling.py and 09_categorical_models.py in the Course Materials.

Tip

To run Python scripts in VS Code, follow 📘 Running Python Scripts in VS Code

Focus on understanding how each IV (predictors) is related to the DV (outcome). Ask yourself:

• How does each variable help me explain the outcome (DV)?
• What is the causal mechanism behind it?
• What is the hypothetical direction of the effect (+/-)?

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Get Ready for Next Session: Think. Explore. Practice.

Think

• What happens to your primary coefficient ($\beta_1$) when you introduce demographic and political controls side by side? Does your finding survive controlling for confounders?
• How will you format and present multiple regression models side by side in an academic publication-ready table in Typst?
• Suggested Reading: King, G., Tomz, M., & Wittenberg, J. (2000). Making the most of statistical analyses: Improving interpretation and presentation. American Journal of Political Science, 44(2), 347-361. - The seminal classic on converting raw statistical regression output into meaningful, substantive quantities of interest for social science readers.

Explore

• Live Demo (Group 4): Multiple Regression Specifications & Exporting Tables (models with controls: Baseline → Demographics → Full model, make_table for Typst). Group 4 prepares a 10–15 min demonstration and shares the handout on WhatsApp before class (groups can book a meeting with the instructor to get direction).
• The class should review the course materials (08_multiple_regression.py) and the Typst Table Formatting Documentation to follow along and lead the peer discussion.

Practice

• Fit your regression models with controls in Python and generate your final Typst regression table.
• Complete Milestone 5 - Modeling (Due Friday, Mar 05 at 08:00 before class via email).