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PSM

Propensity score matching (PSM) is a statistical technique used to reduce selection bias in observational studies. It attempts to balance observed covariates that may influence both treatment assignment and outcomes. PSM involves estimating propensity scores using logistic regression and matching treated and untreated subjects based on their propensity to receive treatment. Key assumptions are that treatment assignment is strongly ignorable after conditioning on propensity scores, and there is sufficient overlap in propensity scores between treated and untreated groups. Common matching algorithms include nearest neighbor, caliper, and stratified matching. PSM aims to estimate treatment effects by comparing outcomes of matched treated and control groups.

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541 views21 pages

PSM

Propensity score matching (PSM) is a statistical technique used to reduce selection bias in observational studies. It attempts to balance observed covariates that may influence both treatment assignment and outcomes. PSM involves estimating propensity scores using logistic regression and matching treated and untreated subjects based on their propensity to receive treatment. Key assumptions are that treatment assignment is strongly ignorable after conditioning on propensity scores, and there is sufficient overlap in propensity scores between treated and untreated groups. Common matching algorithms include nearest neighbor, caliper, and stratified matching. PSM aims to estimate treatment effects by comparing outcomes of matched treated and control groups.

Uploaded by

sonalz
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Propensity Score Matching

(PSM)
Peeyush Taori
Roberto Vincenzi

Introduction
Consider the model
Y=a+bD+cX+e
We observe

X could affect both D and Y.


We could run an OLS
But it imposes a specific structural form
Many times, we are not aware of exact
functional form

PSM
Estimation based on propensity
scores can deal with such situations
Attempts to reduce selection bias
due to confounding variables
Create treatment and control groups
that are similar in terms of observed
covariates
Compare the difference in outcomes
between two groups to estimate
effect of treatment

PSM
Matching is (relatively) easy when
covariates are less
Dimensionality issue

PSM reduces dimensionality to a scalar


(propensity score)
Propensity score is the probability that an
individual receives treatment based on
observed covariates
Matching done on propensity score rather
than covariates

Assumptions
Two key assumptions:
A1: Only observable covariates affect
outcome variable and treatment
variable.
PST states that Y1 and Y0 are
conditionally independent of
treatment if we condition on
propensity score of individual.

Assumptions
A2: Common Support
For each X, probability of treated as
well as untreated is positive.
Ensures an overlap in treated and
non-treated individuals based on
characteristics.

Under these two assumptions,


treatment assignment is considered
as strongly ignorable (Rosenbaum
and Rubin, 1983).

PSM Implementation
Run logistic regression of treatment
variable on the confounding
variables, and obtain propensity
scores.
Match observations in the treatment
and control group based on matching
algorithm
Ensure that propensity scores and
covariates are balanced between the
two groups.

Example
Example dataset of clinics in village
(treatment), infant moratlity
(outcome), and covariates.
Imrate

Povrate Pcdocs

10

.5

.01

15

.6

.02

22

.7

.01

19

.6

.02

25

.6

.01

19

.5

.02

.1

.04

.3

.05

.2

.04

Step 1
Run logit regression of T on povrate,
pcdocs Imrat T
Povra Pcdoc Pscor
e

te

10

.5

.01

.416

15

.6

.02

.735

22

.7

.01

.928

19

.6

.02

.735

25

.6

.01

.752

19

.5

.02

.395

.1

.04

.001

.3

.05

.026

.2

.04

.008

Step 2
Match observations in treatment to
control
Based on propensity score
Match 1 with 6
Match 2, 3, 4 with 5

New control group now has only 5


and 6.

Step 3
Compare average outcome between
two groups
(10+15+22+19) (19+25+25+25)
= -7

Matching can be done in many


different ways that will change the
results.

Matching Algorithms
Factors to consider
With or without replacement
Closeness of match
1:1 or N:1 match
Weighting of outcome variable

No single method suits all situations


Trade-off between efficiency and bias

Matching Algorithms
Mahalanobis Distance
Mahalanobis distance computed for each pair
Observations matched based on least
distance

Nearest Neighbour
Objective to minimize absolute difference
between propensity scores.

Matching Algorithms
Caliper Matching
Similar to nearest neighbour matching
Use a caliper
Many to one match

Stratified Matching
Create strata based on propensity scores
Calculate ATE by comparing outcomes
across different strata

How well is matching done


Good knowledge of institutional
settings
Data should come from similar
sources
Irrelevant variables should be
excluded
Matching quality should be good
Balanced groups
Compare distributions (propensity score
and covariates)

Matching vs Regression
Both attempt to solve the same
problem. Why not control for
covariates in regression?
Matching advantages
Not dependent on specific functional
form
Easier to assess how matching is
performing
Removes observations that are not
comparable

Matching vs Regression
Regression advantages
Estimate effect of a continuous treatment
variable
Assess effect of all covariates
Interaction of treatment with covariates
Allows extrapolation of results

Sometimes PSM can result in loss of a


large number of observations (can be
detrimental for drawing inferences)

PSM Limitations
Unobserved confounders
Unobserved variables that affect both
treatment and outcome
Good amount of overlap needed
between groups in terms of observable
characteristics
Situations where high propensity score
gets treatment and low score does not

Software Packages
Stata
psmatch2
teffects psmatch (Stata 13)
pscore

R
MatchIt

Thank You

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