2 Matching Annotations
- Jul 2020
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humboldt-wi.github.io humboldt-wi.github.io
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If control units are matched exactly to treated units such that Xi = Xj then we can say that this is the estimated Average Treatment Effect (ATE) where ATE = E [Y(1) - Y(0)].
Fair enough, but this does ignore the fact the Controls ... were not treated!
It's seldom addressed that for all the effort to match on observed covariates, there is some reason somewhere why the Case was treated and the Control was not.
Rosenbaum (elsewhere) says this can be collapsed to one unmeasured covariate but practically, there'll be a host of reasons the why the Control was 'wrongly' not treated (or indeed, the Case was 'wrongly' treated),
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- Sep 2019
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www.theanalysisfactor.com www.theanalysisfactor.com
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The numerator is the same as that of a probability, but the denominator here is different. It’s not a measure of events out of all possible events. It’s a ratio of events to non-events. You can switch back and forth between probability and odds—both give you the same information, just on different scales. If O1 is the odds of event in the Treatment group and O2 is the odds of event in the control group then the odds ratio is O1/O2. Just like the risk ratio, it’s a way of measuring the effect of the tutoring program on the odds of an event.
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