Michael Massoglia
Department of Sociology
University of Wisconsin Madison
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The logic of propensity models
Application based discussion of some of the
key features
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Emphasis on working understanding use of models
Brief formal presentation of the models
Empirical example
Questions and discussion
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Please interrupt with questions and clarifications
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Not an advocate nor a detractor
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Try to understand the strengths and weakness
 The research is vastly expanding in this area
 Focus on 1 statistics program -- 2 modules
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Used in published work
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Level of talk
Data is often problematic in social science
research
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Propensity models
 One tool that can help with data limitations
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Net of controls, the estimate is based upon
mean differences on some outcome between
those who experienced the event or treatment –
marriage, incarceration, job -- and is assumed
to be an average effect generalizable to the
entire population
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Under conditions in which
 1) The treatment is random and the
 2) Population is homogeneous (prior)
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Often unlikely in the social sciences
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Many social processes cannot be randomly
designed
Incarceration
 Marriage
 Drug use
 Divorce
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 And the list goes on
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Data limitations
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Cross sectional, few waves, retrospective data, measures
change
Propensity models attempt to replicated
experimental design with statistics
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Rooted in classic experimental design
 Treatment group
 Exposed to some treatment
 Control group
 Not exposed to treatment
 Individuals are statistically randomization into
groups
 Identical (net of covariates)
 Or differ in ways unrelated to outcomes
 Treatment can be seen as random
 Ignorable treatment (conditional independence)
assumption
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PSM: Toward a consideration of counterfactuals
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The counterfactual
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Some people receive treatment -- marriage, incarceration,
job.
“What would have happened to those who, in fact, did
receive treatment, if they had not received treatment (or
the converse)?”
Counterfactuals cannot observed, but we can
create an estimate of them
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Rubin “The fundamental problem…”
 At the heart of PSM
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Calculate the predicted probability of some
treatment
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Assuming the treatment can be manipulated
 Comparatively minor debate in literature
 We have predicted probability (for everything)
Predicted probability is based observed covariates
 Once we know the predicted probability
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 1) Find people who experiences a treatment
 2) Match to people who have same* predicted
probability, but did not experience treatment
 3) Observe differences on some outcome
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All based on matching a treated to a controlled
 1 program 2 modules
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Nearest neighbor matching
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Kernel matching
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Weights for distance
Radius matching
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1-1 match
0.01 around each treated
Stratification matching
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Breaks propensity scores into strata based on region of common
support
 Great visual from Pop Center at PSU
 http://help.pop.psu.edu/help-by-statistical-
method/propensity-matching/Intro%20to%20Pscore_Sp08.pdf/?searchterm=None
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Range of common support
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Balancing Property
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Existence Condition
Ignorable treatment assumption
Observed Covariates
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Reviewers pay attention
 ? More so than other methods
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Important to keep in mind: Cross group models
 Not within person “fixed effects models”
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We use data only from region of common support:
Violates existence condition. Assumption of common
support (1)
Range of
matched
cases.
Participants
Nonparticipants
Predicted Probability
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Among those with the same predicted
probability of treatment, those who get treated
and not treated differ only on their error term
in the propensity score equation.
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But this error term is approximately independent of
the X’s.
 Ignorable treatment assumption
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The reality:
 The same given the covariates
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Propensity models based on observed
covariates
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Much like many other regression based models
 Yet, reviewers pay particular attention
 Models get additional attention
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PSM
 Cannot: Fix out some variables
 Fixed effects models: Hard to measure time stable traits
 Can: Assess the role of unobserved variables with
simulations
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More formally:
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The propensity score for subject i (i = 1, …, N), is the
conditional probability of being assigned to
treatment Zi = 1 vs. control Zi = 0 given a vector xi of
observed covariates:
e(x i )  Pr ( Z i  1 | X i  x i )
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where it is assumed that, given the X’s the Zi’s are
independent
e(x i )  Pr ( Z i  1 | X i  x i )
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Given the X’s the Zi’s are independent (given
covariates)
Moves propensity scores to logic to that of an experiment
Substantively means
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Treatment status is independent of observed variables
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Treatment status occurs at random
Ignorable Treatment Assumption (2)
Stable unit treatment value assumption. The potential
outcomes on one unit should be unaffected by the particular
assignment of treatments to the other units
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Issues of independence
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3 part process
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1)Assign propensity scores
 Create your matching equation
 Some programs do this at the same they estimate
treatment score
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My view is do them separately
 Greater flexibility if you have pp scores independent of
treatment effects
 High, low, females, makes
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2) Create matched sample
 Average treatment effect
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3) Tests of robustness
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Can be done in SAS, S-Plus R, MPLS, SPSS*
Stata
PSMATCH2: Stata module for propensity score matching,
common support graphing, and covariate imbalance
testing
 psmatch2.ado
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PSCORE – same basic features
 More user “friendly”
 pscore.ado
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.net search psmatch2
.net search pscore
.ssc install psmatch2, replace
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Estimation of average treatment effects based
on propensity scores (2002) The Stata Journal
Vol.2, No.4, pp. 358-377.
Walk through the process
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Create propensity score
 From observed covariates in the data
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Use different matching groups
 Estimates
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Test the robustness of effect
 Bias from unobservables
1) tab mypscore
Estimated |
propensity |
score |
Freq. Percent
Cum.
------------+----------------------------------.000416 |
1
0.02
0.02
.000446 |
1
0.02
0.04
.0004652 |
1
0.02
0.05
.0005133 |
1
0.02
0.07
.0005242 |
1
0.02
0.09
.0005407 |
1
0.02
0.11
.0005493 |
1
0.02
0.13
.0005666 |
3
0.05
0.18
.0005693 |
1
0.02
0.20
.0005729 |
1
0.02
0.22
2) Bad Matching Equation: Link back to PSU
3) Link : IU
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gen delta
delta is the difference in treatment effect between treated
and untreated
rbounds delta, gamma (1 (0.1)2)
gamma: log odds of differential assignment due to
unobserved heterogeneity
Rosenbaum bounds takes the difference in the response
variable between treatment and control cases as delta, and
examines how delta changes based on gamma
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LINK TO IU 2
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Propensity models
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Dependent on data
 As are all models
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Reviewers and editors seem to care more
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Yet weakness appear similar traditional regression
models
You can empirically test the role of
unobservables with simulations
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Significant advancement
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A small window into propensity models
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Regression, matched sample, use as covariates, as an
instrument
Longitudinal data perfectly measured on all
variables over time
 Open to an argument preferences
 Fixed effects models
 And variants: Difference in differences
 Do not live in such world
 Propensity models help us through imperfect data
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Questions? (5)
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Preference an open discussion