Propensity Score Matching. Outline. Describe the problem Introduce propensity score matching as one solution Present empirical tests of propensity score estimates as unbiased Illustrate special challenges in practice Discuss any applications from your work. “Work Horse” Design: Description.
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With or without differential attrition, we struggle to rule out:
Simple Regression illustrated with one group
Frequency of such regression in our society
It is a function of all imperfect correlations
Size of Regression gross f(unreliability/population
difference)
Simple oneonone case matching from overlap
visually described
TC
Logic of the design is to compare ES from a randomly created control group with ES from a nonrandomly formed comparison that shares the same treatment group
Portlandsample size smallest and least stable
Detroit vs Grand Rapidsa withinstate but not withincity comparison. Hence, this is not a very local comparison
On SAT/CAT, 2 pretest writing measures, the randomly and nonrandomly formed comparison groups did not differ
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All three figures show the relationship between two variables for each of two groups. The top figure shows two variables that have no measurement error, and so are perfectly correlated. Notice that the regression lines are parallel, that all dots are on the regression line, and that scores at pretest are the same as scores at posttest.
To generalize, the pretest can be a pretest on the posttest, but it can also be any covariate, and the logic in these three figures will apply.
The middle figure shows what happens when we add random measurement error to the pretest but not to the posttest. Now, each dot is displaced horizontally to the right or the left by the error. As a result, the regression lines have different intercepts, when in fact the two groups are not different at all.
To generalize, efforts to use pretest covariates to reduce bias in quasiexperiments are problematic if the covariate has error.
The bottom figure shows the same two groups, this time with errors in the posttest but not in the pretest. Now each dot is displaced vertically either up or down by error. But the two groups still have the same intercept (as they should since there is no effect).
The lesson: Errors in pretest covariates can bias results. So OLS is not good at correcting bias.
Using latent variables can help greatly reduce the biased caused by measurement errors in the pretest.
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However, it does nothing to help reduce the specification error problem. A misspecified latent variable model still yields biased results.
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N = 445 Undergraduate Psychology Students caused by measurement errors in the pretest.
Randomly Assigned to
Observational Study
Randomized Experiment
N = 235
N = 210
Randomly Assigned to
Self

Selected into
Mathematics
Vocabulary
Mathe
matics
Vocabulary
Training
Training
Training
Training
N = 119
N = 116
N = 79
N = 131
Shadish, Clark & Steiner (2008) (WithinStudy Comparison)?
=
ATE
23 constructs in 5 domains
Math Vocab Mean Absolute
Tng Tng Diff Bias
Mean Mean
Unadjusted Randomized Experiment 11.35 7.16 4.19
Unadjusted QuasiExperiment 12.38 7.37 5.01 .82
Vocab Math Mean Absolute
Tng Tng Diff Bias
Mean Mean
Unadjusted Randomized Experiment 16.19 8.08 8.11
Unadjusted QuasiExperiment 16.75 7.75 9.00 .89
with
(proved Rosenbaum & Rubin 1983)
Steps in conducting a PS analysis
Steps in conducting a PS analysis
Steps in conducting a PS analysis
Steps in conducting a PS analysis
LOGISTIC REGRESSION VAR=vm
/METHOD=ENTER vocabpre numbma_r likema_r likeli_r prefli_r pextra pconsc
beck cauc afram age momdeg_r daddeg_r majormi liked avoided selfimpr
/SAVE PRED (ps).
balance after PSadjustment caused by measurement errors in the pretest.
(Im)balance in Covariates and PSlogit (23 covariates)initial imbalance
after PSadjustment caused by measurement errors in the pretest.
Overlap & Balance (PSlogit)before PSadjustment
Steps in conducting a PS analysis
ATT
ATE
ATE
ATE
= .1·.44 + 4.2·.23 + 2.7·.16 + 6.3·.10 + 5.2·.06 = 2.4
ATT
ATT
Steps in conducting a PS analysis
Ruling out hidden bias
Avoiding overt bias
for establishing strong ignorability
PS Methods
Regression Approaches
Advantages
Generalizability
Standard errors
Criteria for model selection
Disadvantages
Funct. form assumptions & extrapolation
No blinding
Model specification ()
Some Other WithinStudy Comparisons caused by measurement errors in the pretest.
How good was the experiment? 2 of 5 sites
Mantra: Selection per se is not the problem – unknown selection is the problem
Primary challenge in matching designs: can never know if we adequately accounted for selection (Rosenbaum & Rubin, 1983)
Covariate selection matters (Steiner, Cook, Shadish, & Clark, in press)
“Backdoor Path”
A
Y
B
X
Z
Outcome
Treatment