Both multivariate regression and propensity score matching (PSM) are used to adjust for confounding in observational studies, but they differ in methodology, assumptions, and applications.

1. Multivariate Regression in Stata

Overview

• Multivariate regression (typically logistic or linear regression) adjusts for confounders by including them as covariates in a regression model.
• Used when treatment assignment is not random but confounders can be directly included in the model.

Stata Command for Multivariate Regression

Example: Estimating the effect of treatment (treat) on outcome (y), adjusting for covariates (x1, x2, x3):

Linear Regression (Continuous Outcome)
reg y treat x1 x2 x3, robust

Logistic Regression (Binary Outcome)
logit y treat x1 x2 x3, robust

2. Propensity Score Matching (PSM) in Stata

Overview

• PSM estimates the probability (propensity score) of receiving the treatment, then matches treated and untreated individuals with similar scores.
• Reduces selection bias by creating comparable treatment/control groups.

Steps in PSM

1. Estimate the propensity score (logistic regression predicting treatment).
   logit treat x1 x2 x3
   predict pscore
2. Match individuals (1:1, 1:N, nearest neighbor, caliper, etc.).
   ssc install psmatch2
   psmatch2 treat x1 x2 x3, out(y) neighbor(1) caliper(0.05)
3. Check balance (assess covariate distributions between groups).
   pstest x1 x2 x3, graph
4. Estimate treatment effect on the matched sample.
   teffects psmatch (y) (treat x1 x2 x3), atet

Key Differences: Multivariate Regression vs. PSM

Summary

• Use multivariate regression when sample size is small or when you want to adjust for many covariates.
• Use PSM when selection bias is strong and you want a matched control group.
• Combining PSM with regression provides better adjustment.