POL222 - week 9

Basic Logic of Observational Research

Researchers do not control the independent variable (X), instead, they observe how Y changes naturally across different values of X, and try to identify causal relationships while accounting for confounding variables (Z)

How to examine X and Y’s relationship

Divide observations based on the value of X

Compute the average (mean) of Y for each value of X → conditional mean

Compare conditional means of Y across groups with different X values

How does Y vary on average as X changes?

Conditional Mean

The conditional mean of Y is the average value of Y for a given value of X

Average Treatment Effect

Average difference in Y between groups with different X values after controlling for Z, shows how much Y changes on average when X changes, holding Z constant

Regression Models

Statistical tools used to estimate the conditional mean of Y based on one or more predictors , model how Y changes on average when X changes, controlling for other variables

Linear Regression

method where the relationship between Y and X is estimated by a straight line (linear relationship), used for forecasting, description, and causal questions

Multiple Linear Regression

Extends linear regression to include multiple predictors, estimates how Y varies on average as X changes while controlling for Z

Regression Adjustment

If Z is a confounding variable, multiple regression adjusts the slope (coefficient) of X so that the confounding effect of Z is removed

Slope in Regression

The slope (coefficient) of X represents the magnitude of Y’s change as X increases by one unit, a steeper slope means a stronger effect of X on Y

Steps in Observational Research

Identify causal theory (X → Y, possible Z)

Divide data by values of X (and Z, if controlling)

Compute and compare conditional means of Y

Use regression models to estimate conditional means when multiple variables exist

Interpret slopes to understand causal magnitude/direction