Re: st: Propensity Score Matching Between 3 Groups

[Alfonso Sánchez-Peñalver <alfonso.statalist@gmail.com>]

Hi,

I would like to add something more even though propensity matching is not really my area of expertise, but I would like to add to the estimation of the probability of being treated.

For the estimation of the probability of treatment a multinomial (probit or logit) estimation would not be entirely appropriate. The reason is that, as Adam indicates, the probability of intervention for the people in Group C is zero. However, the information on the observed variables for the people of Group C can be useful to model the probability of treatment if we don’t know whether a person we select lives or not in a treatment area. Notice that the treatment selection process is really a 2-step selection:

1. You have to belong to a treatment area, and
2. given that you belong to treatment area, then you have to be selected for treatment.

This can be modeled with a nested logit model where there are two nests (in treatment area, not in treatment area) where only the first nest has two more branches (treated, not treated). It can also be modeled with a Heckman sample selection probit model, where the sample selection probit part is whether the individual belongs to a treatment area, and the final probit is whether the person is selected for treatment or not. I personally prefer the nested logit approach, but that may be just me.

Best,

Alfonso Sánchez-Peñalver, PhD

Visiting Assistant Professor
Suffolk University
Senior Instructor
UMass Boston



On Feb 27, 2014, at 9:56 AM, Ariel Linden <ariel.linden@gmail.com> wrote:

> 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
> 
> Ariel
> 
> Date: Wed, 26 Feb 2014 17:15:49 -0500
> From: Adam Olszewski <adam.olszewski@gmail.com>
> 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?
> 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
> 
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