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re: Re: st: Propensity Score Matching Between 3 Groups

From   "Ariel Linden" <>
To   <>
Subject   re: Re: st: Propensity Score Matching Between 3 Groups
Date   Thu, 27 Feb 2014 09:56:49 -0500

This is a good thought-provoking thread. Let me add in here a few thoughts:

First, in the case of multiple control groups, it makes the most sense to
treat them as separate treatment conditions. Thus, Fernando's second
proposed methodology is the most suitable. That is, estimate the multinomial
logit, with the probability of being in each of the three groups as the
propensity score. I'll take it a bit further now and suggest that rather
than matching, calculate the inverse-probability of treatment weights (IPTW)
for each individual, based on their actual treatment "assignment" and on
their estimated propensity score (taken from -mlogit-). Then you can use
these weights within the context of an outcome regression model (speaking to
Adam's last point).

Lucky for Stata users, in version 13.0 it appears that all the approaches in
-teffects- allow for multiple treatment groups. "The treatment model can be
binary, or it can be multinomial, allowing for  multivalued treatments."

While I have used the various regressions adjustment models with multiple
treatment arms and can attest to their "robustness", I have not played
around with the -teffects psmatch- for this exercise. 

I hope this helps


Date: Wed, 26 Feb 2014 17:15:49 -0500
From: Adam Olszewski <>
Subject: Re: st: Propensity Score Matching Between 3 Groups

It may be worth noting however, that this procedure violates the
principles of causal inference. If Group C resides in a
non-intervention area, then their probability of receiving "treatment"
is zero, and the positivity assumption required by propensity score
analysis is not met. Perhaps this is somehow irrelevant to the study
subject, but if causal inference assumptions are not met, then why not
just use regular regression?

On Wed, Feb 26, 2014 at 4:54 PM, Austin Nichols <>
> Isobel Williams <>:
> The practical implementation of Fernando's first suggestion depends on
> your data, but if you have exogenous treatment predictors in the local
> `x' and a treatment dummy t, plus a variable group with value labels
> 1="A", 2="B", 3="C" then you can:
> logit t `x' if inlist(group,1,2)
> predict double p if inlist(group,1,3)
> psmatch2 t, p(p) out(y) `options'
> But I am unclear on why you would want to do this, as there is no
> guarantee that this type of matching will produce appropriate balance,
> even in expectation, much less in practice.
> On Wed, Feb 26, 2014 at 2:58 PM, Fernando Rios Avila <>
>> Hi Isobel,
>> So here is what I know about this.
>> If what you want to do is to indeed apply the propensity scores from
>> the A vs B group for the A vs C group, I would run the logit between A
>> and B, and then predict the propensity score for all three groups.
>> Once the propensity score is estimated, you can indicate within the
>> -psmatch2- the specific propensity score you want to use, instead of
>> having it estimate a separately logit model.
>> The other alternative, given that there is nothing that would indicate
>> that people in group B are equal to people in group C, is to estimate
>> the propensity score using a multinomial logit for the three groups,
>> and then proceed with your analysis with each pair group of interest.
>> (for example C vs B with B as treated group) (C vs A) and (B vs A)
>> Hope this helps.
>> Fernando

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