Re: Re: st: Propensity score matching: Must all treated samples have a counterfactual?

["Ariel Linden, DrPH" <ariel.linden@gmail.com>]

Ricky,

You've got a very small sample size here, and by using matching within a
caliper, you're likely to lose some "non-treated" units, simply because
there are not enough similar non-treated units to choose from. 

If it were me, I would probably consider using a weighting mechanism on all
units within a doubly robust approach. You won't lose non-treated units.
Moreover, if either the outcome model or the propensity model is correct,
the doubly robust estimate is unbiased. Again, I will reiterate that you
have a small sample size...

It is up to you to do your due diligence to determine if there is overlap in
covariates used to generate the propensity score (and used in the outcome
model). If there is little or no overlap, it means that you'll be
extrapolating beyond the data. This not a situation you want to find
yourself. You may ultimately decide to use regression with no fanciness, and
call it a day.

In Stata 13 there are doubly robust commands available: -teffects aipw-, and
-teffects iprwa-.

If you are using older versions of Stata, you can implement doubly robust
methods using -dr- (http://personalpages.manchester.ac.uk/staff/mark.lunt)
or -drglm- (http://www.stata-journal.com/software/sj13-1)

Be aware that these two programs provide an ATE, not an ATT estimator as you
would get from matching.

Ariel



Date: Mon, 19 Aug 2013 18:49:15 +0100
From: Ricky Lim <ricky.lim12345@gmail.com>
Subject: Re: st: Propensity score matching: Must all treated samples have a
counterfactual?

Dear Ariel & Sebastian,

Thank you very much for your replies!
They were very helpful.

And thanks for the two articles, Ariel.
I have read one of them today and will read another one tomorrow.
And yes, I meant caliper, not radius.
Sorry for the confusion.

***

Dear Ariel, Sebastian & all Statalisters,

My study is about organisational merger actually.
So there are 2 organisations pre-treatment (pre-merger) and 1
organisation post-treatment (post-merger).

I'm generating the propensity scores based on the per-treatment observables.
The standard deviation for my PS is around 0.06.
20 - 25% of that would be 0.012 - 0.015.

I only have 20 organisations for 9 mergers.
Applying this caliper on my samples would mean that 5 organisations
(one each from a different merger, hence 5 mergers) will have no
counterfactuals.
This leaves me with only 4 mergers which are too small a sample.
I think if one of the constituent organisations do not have a
couunterfactuals pre-merger, I would have to give up the whole merger
case.

Also, each of the constituent organisation for the remaining 4 mergers
have 1 to >10 counterfactuals within the caliper +-0.015.
Is it necessary for each of the treated organisation to have the same
number of counterfactuals?
Can one of them have one, and another one have say, five?

At the moment,
I am more keen to just use 3 nearest neighbour without caliper, just
so that I can still use all 20 organisations / 9 mergers.
But that will involve the assumption that the matches are good enough.

Would be grateful to hear your thoughts / advices.

Thank you very much in advanced.

Regards,
Ricky


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