I am trying to find any relevant example of researchers combining these two techniques for causal inference. While a lot of studies juxtapose these approaches, I am wondering how matched samples with propensity scores may be used in regression.
Propensity Score Matching vs. Regression
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The Morgan and Winship book is pretty good but the best and most intuitive thing I have read on propensity scores is from an econometrics journal- I think the author is named Caliendo and its called something like "a practical guide to propensity scores".
I don't completely understand the "blending" of regression and propensity scores- I've seen papers were people use the pscore as a weight, like a sampling weight, and others were it is introduced as a control variable. If you find some nice readable resources please share.
****braces for econo-trolls****
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The Morgan and Winship book is pretty good but the best and most intuitive thing I have read on propensity scores is from an econometrics journal- I think the author is named Caliendo and its called something like "a practical guide to propensity scores".
Here's the piece you mention: "Some Practical Guidance for the Implementation of Propensity Score Matching" by Marco Caliendo and Sabine Kopeinig http://onlinelibrary.wiley.com/doi/10.1111/j.1467-6419.2007.00527.x/pdf
In regards to the OP's question, maybe this is relevant: "Second, we present a regression-adjusted matching estimator that combines matching with regression. This can be useful because matching does not address the relation between covariates and outcome. Additionally, if covariates appear seriously imbalanced after propensity score matching (inexact or imperfect matching) a bias-
correction procedure after matching may help to improve estimates" (2008:55). -
The issue I have with PSM is that it doesn't fully replace randomization.
If selection into treatment is influenced by unobserved variables (covariates not included in your dataset), then matching will not produce valid causal estimates (selection is not addressed so these coefficients will be correlated with the error term). Evidence so far is mixed. There are papers that have compared the results you get with PSM and those from randomization and show that PSM can at times produce valid causal estimates, but others have showed that it doesn't. It all depends on how rich are the covariates you have access to. -
^ beakman, your point is valid if you have the option of running an experiment. But there are plenty of social science "treatments" that can't actually be randomized. In those situations, matching techniques + OLS are definitely better than just OLS.
Sure, but the model makes certain assumptions. It only makes sense to know those assumptions, which if violated, would not allow researchers to make causal claims based on matched data.
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^ beakman, your point is valid if you have the option of running an experiment. But there are plenty of social science "treatments" that can't actually be randomized. In those situations, matching techniques + OLS are definitely better than just OLS.
Not sure what you mean by better here. Matching techniques and OLS draw on the same information (measured variables) and suffer from the same limitation (unmeasured variables). You might mean that matching techniques make some of the assumptions more transparent than a standard regression model, but it's not as if a matching estimator somehow makes more of the available information than is possible with a standard regression model.
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^ beakman, your point is valid if you have the option of running an experiment. But there are plenty of social science "treatments" that can't actually be randomized. In those situations, matching techniques + OLS are definitely better than just OLS.
Not sure what you mean by better here. Matching techniques and OLS draw on the same information (measured variables) and suffer from the same limitation (unmeasured variables). You might mean that matching techniques make some of the assumptions more transparent than a standard regression model, but it's not as if a matching estimator somehow makes more of the available information than is possible with a standard regression model.Have you read Gary King's work? He has a different take on matching than you.