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Michael Massoglia Department of Sociology University of Wisconsin Madison The logic of propensity models Application based discussion of some of the key features Emphasis on working understanding use of models Brief formal presentation of the models Empirical example Questions and discussion Please interrupt with questions and clarifications Not an advocate nor a detractor Try to understand the strengths and weakness The research is vastly expanding in this area Focus on 1 statistics program -- 2 modules Used in published work Level of talk Data is often problematic in social science research Propensity models One tool that can help with data limitations 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 Under conditions in which 1) The treatment is random and the 2) Population is homogeneous (prior) Often unlikely in the social sciences Many social processes cannot be randomly designed Incarceration Marriage Drug use Divorce And the list goes on Data limitations Cross sectional, few waves, retrospective data, measures change Propensity models attempt to replicated experimental design with statistics 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 PSM: Toward a consideration of counterfactuals The counterfactual 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 Rubin “The fundamental problem…” At the heart of PSM Calculate the predicted probability of some treatment 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 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 All based on matching a treated to a controlled 1 program 2 modules Nearest neighbor matching Kernel matching Weights for distance Radius matching 1-1 match 0.01 around each treated Stratification matching 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 Range of common support Balancing Property Existence Condition Ignorable treatment assumption Observed Covariates Reviewers pay attention ? More so than other methods Important to keep in mind: Cross group models Not within person “fixed effects models” 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 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. But this error term is approximately independent of the X’s. Ignorable treatment assumption The reality: The same given the covariates Propensity models based on observed covariates Much like many other regression based models Yet, reviewers pay particular attention Models get additional attention PSM Cannot: Fix out some variables Fixed effects models: Hard to measure time stable traits Can: Assess the role of unobserved variables with simulations More formally: 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 ) 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 ) Given the X’s the Zi’s are independent (given covariates) Moves propensity scores to logic to that of an experiment Substantively means Treatment status is independent of observed variables 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 Issues of independence 3 part process 1)Assign propensity scores Create your matching equation Some programs do this at the same they estimate treatment score My view is do them separately Greater flexibility if you have pp scores independent of treatment effects High, low, females, makes 2) Create matched sample Average treatment effect 3) Tests of robustness 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 PSCORE – same basic features More user “friendly” pscore.ado .net search psmatch2 .net search pscore .ssc install psmatch2, replace Estimation of average treatment effects based on propensity scores (2002) The Stata Journal Vol.2, No.4, pp. 358-377. Walk through the process Create propensity score From observed covariates in the data Use different matching groups Estimates 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 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 LINK TO IU 2 Propensity models Dependent on data As are all models Reviewers and editors seem to care more Yet weakness appear similar traditional regression models You can empirically test the role of unobservables with simulations Significant advancement A small window into propensity models 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 Questions? (5) Preference an open discussion