Dear Carlos,
conditional ignorability will be violated if two units with the same
observed covariate values have differing probabilities of receiving the
treatment. Even though the units appear identical in your dataset, they
differ on unobserved characteristics relevant for treatment assignment.
Rosenbaum's sensitivity tests ask ``How would our inferences about
treatment effects be altered by such hidden biases of various magnitudes?''
Suppose you have two units with the same observed covariate values that
nonetheless differ in their probabilities of receiving the treatment.
The odds of unit 1 receiving the treatment are, say, pi_{1}/1-pi_{1},
and the odds of unit 2 receiving the treatment are pi_{2}/1-pi_{2}, and
the odds ratio is the ratio of these odds. Now imagine that we assume
this odds ratio was at most some number Gamma >= 1. If Gamma were 1,
then the odds for units 1 and 2 would be identical and there would not
be any hidden bias. If Gamme = 2, for example, the two units appear
identical but differ in their odds of receiving the treatment by as much
as a factor of 2, i.e., one is up to twice as likely as the other to
receive the treatment. Rosenbaum's sensitivity tests consider several
possible values of Gamma and show how inferences about treatment effects
would change. The larger Gamma before your results vanish, the less
sensitive your results are to hidden bias. Your Stata output will
probably show you confidence levels for your teatment effect estimate
under various magnitudes of Gamma. The larger Gamma has to be before
your results become statistically indistinguishable from zero, the more
robust they are.
cheers,
Holger
Carlos Rodriguez wrote:
> Good afternoon,
>
> I have done propensity score matching and I have run a Rosembaum
> bounds sensitivity analysis as recommended in a textbook to check for
> ignorability, but I am not clear what to make of the STATA output.
> How does one interpret the output of Rosenbaum bounds test?
>
> thanks in advance,
> Regards,
> Carlos
>
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--
Holger Lutz Kern, PhD
Postdoctoral Associate
Yale University
The MacMillan Center
Program on Democracy
34 Hillhouse Avenue
New Haven, CT 06520
http://pantheon.yale.edu/~hlk8/
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