Final Project Essentials

Index Measures and Interaction Terms

Carolina Torreblanca

University of Pennsylvania

Global Development: Intermediate Topics in Politics, Policy, and Data

PSCI 3200 - Spring 2026

Logistics

Agenda

Final project example
Final project essential tools
Final project essentials Workshop

Final project example

Check out workshops/survey_data.(qmd|html)

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bibliography: references.bib
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Research Question

Does moving to a new city reduce the political engagement of young people?

I hypothesize that moving to a new city will reduce young people’s likelihood of engaging in political or civic action
- Youth have low levels of political engagement, often driven by lack of information and experience
- Youth that move have less information and experience with engagement in their new city
- Youth that move probably have fewer social ties, and ties are important for facilitating engagement

Data and Variables

Data

Random sample of 825 AAU students
2 waves (May-June, October-November of 2022)

Variables

Outcome: survey questions measuring political participation
Treatment: whether student is originally from Addis Ababa
Building confidence: feelings of political efficacy, number of years since move, urban or rural origin, SES, etc.

Research Design

Design: Estimate the relationship between whether or not an individual moved to a new city to attend university and their level of political engagement
Assumption: Individuals that moved to a AA would have participated the same amount as those that already lived there
Diagnosis: Unrealistic… even if we condition on observable characteristics
Plan: Build confidence by ruling-out potential differences in baseline propensity to participate among moving and non-moving students

Researh Context

Students at Addis Ababa University (AAU)
- Youth frequently move to a new city in order to obtain education
- AAU is Ethiopia’s top university, and students from around the country move to study there
- Universities are important sites of political socialization

Building Confidence

Conditioning on baseline characteristics

Urban vs rural home
- Students moving from another city will be less different (in their propensity to participate) than students from AA
Socio-Economic Status (SES)
- Students with similar SES will be less different (in their propensity to participate)

Building Confidence

Observable implications of the hypothesis (if it’s causal)

Some types of participation are more likely to be affected by moving
- Those that rely on social ties or information about the environment
- Estimate separate models for high/low types of participation
The effect of moving should decrease over time
- As students become more embedded, the gap between moving and non-moving students should become smaller
- Estimate how the relationship differs depending on # of years since moving

Building Confidence

Placebo tests

Self-efficacy is related to participation
- Moving may affect feelings about your individual efficacy, but not the efficacy of youth in general
Effort is related to moving
- Moving may affect your real-world engagement, but not an opportunity within the survey

Data and Variables

Data

Random sample of 825 AAU students
2 waves (May-June, October-November of 2022)

Variables

Outcome: survey questions measuring political participation
Treatment: whether student is originally from Addis Ababa
Building confidence: feelings of political efficacy, number of years since move, urban or rural origin, SES, etc.

Final Project Essentials

Creating Index Measures

What is an index measure?

When should we create an index measure?

When you have many ways of measuring a single concept
- This is true for outcome measures, treatment measures, and covariates

What does this accomplish?

Simplifies analysis (fewer graphs, tables, etc.)
Reduces number of hypotheses being tested

Additive Scale

What is an additive scale?

Simple sum across columns (index = column_1 + column_2)

When to use an additive scale

Variables are measured on a common scale
Interested in a cumulative amount of something
- Number of times someone engaged in a specific behavior
- Amount of money from several different sources

Additive Scale

Benefits of additive scales

Interpretability: number on the original scale
Simplicity: Just plain addition

Averaged Z-Scores

What is a z-score?

\(Z = (X - \mu) / \sigma\)
Standardized: Mean of 0 and standard deviation of 1

When to use averaged z-scores

When variables are measured on different scales
When variables cannot be summed

Averaged Z-Scores

Benefits of averaged z-scores

Interpretability: Standard deviations from the mean
Outlier detection: abs(3)

Fancier index techniques

Principal Component Analysis
Factor Analysis
Inverse Covariance Weighting

Interaction Terms

What is an interaction term?

Simple linear models assume that the effect of predictors is independent of other factors
Interaction terms allow us to estimate the difference in the slope of a predictor across unit characteristics

\[ Y_i = \alpha + \beta_1 X_{i1} + \beta_2 X_{i2} + \beta_3 X_{i1}*X_{i2} + \epsilon_i \]

Interaction Terms

What are interaction terms used for?

Heterogeneous effects
- Gender
- Education
Difference-in-differences
- Treated and not-treated units

\[ Y_i = \alpha + \beta_1 X_{i1} + \beta_2 X_{i2} + \beta_3 X_{i1}*X_{i2} + \epsilon_i \]

Interaction Terms

\[ Y_i = \alpha + \beta_1 X_{i1} + \beta_2 X_{i2} + \beta_3 X_{i1}*X_{i2} + \epsilon_i \]

Example: Continuous outcome with two binary predictors

\(\alpha\): Intercept when \(X_{i1}\) and \(X_{i2}\) are 0
\(\beta_1\): Slope when \(X_{i2} = 0\)
\(\beta_2\): Difference in \(\alpha\) between \(X_{i2}=0\) and \(X_{i2}=1\)
\(\beta_3\): Difference in \(\beta_1\) between \(X_{i2}=0\) and \(X_{i2}=1\)