Re: st: Propensity Score Matching Between 3 Groups

[Steve Samuels <sjsamuels@gmail.com>]

I believe that Adam has misinterpreted the "positivity assumption". It
is, according to Stuart (2009):

"2) there is a positive probability of receiving each treatment for all
values of X: 0 < P(T = 1|X) < 1 for all X."

In other words, the conditioning event is not residence in the
non-intervention area (a "treatment"), but on the predictors used for
creating the propensity score.

Reference: Stuart, EA. 2009. Matching Methods for Causal Inference: A
review and a look forward. Statistical Science 
Author Manuscrip available at:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2943670/pdf/nihms200640.pdf

Steve
sjsamuels@gmail.com


On Feb 26, 2014, at 5:15 PM, Adam Olszewski <adam.olszewski@gmail.com> wrote:

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?
AO

On Wed, Feb 26, 2014 at 4:54 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> Isobel Williams <iwilliams24@hotmail.com>:
> 
> 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 <f.rios.a@gmail.com> wrote:
>> 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
>> 
>> 
>> On Wed, Feb 26, 2014 at 2:01 PM, Isobel Williams
>> <iwilliams24@hotmail.com> wrote:
>>> Hi,
>>> 
>>> I am trying to estimate a propensity score and then find the
>>> average treatment effect on the treated. However, my sample has 3
>>> groups:
>>> 
>>> Group A: Resides in intervention area, receives treatment
>>> Group B: Resides in intervention area, doesn't receive treatment
>>> Group C: Resides in non-intervention area, doesn't receive treatment
>>> 
>>> Thisis effectively like having 1 intervention group and 2 control groups: I
>>> want to calculate a propensity score for treatment between Groups A and
>>> B. I then want to apply this propensity score to Groups A and C to find
>>> the average treatment effect on the treated.
>>> 
>>> I have seen this done in several economic papers, but never explained thoroughly. Is it
>>> possible to do this in Stata, and if so, how?
>>> 
>>> If it is relevant, I am using a logit model and -psmatch2- (the user-written SSC programme) to estimate the propensity score.
>>> 
>>> Thanks!
>>> Isobel Williams
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