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Re: st: St : Regression discontinuity with Dichotomous dependent variable


From   Nick Sanders <sandersn@stanford.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: St : Regression discontinuity with Dichotomous dependent variable
Date   Tue, 3 Jan 2012 15:05:59 -0600

I bow to those with greater knowledge, but I imagine one could simply specify (assuming the treatment occurs if the running variable is greater than the cutoff):

gen pastcut = running > cut
gen runXpast = running * pastcut

reg outcome running pastcut runXpast

which is just a local linear regression (without covariates) and the coefficient on pastcut is interpretable as the impact of the treatment.

While there is a risk a predicted value might fall outside 0 and 1, I think that is generally accepted as ignorable unless you face many unusual values.

On Jan 3, 2012, at 2:52 PM, Cameron McIntosh <cnm100@hotmail.com> wrote:

> I think this deck might be helpful:
> Nichols, A. (July 14, 2011). Causal inference for binary regression. http://www.stata.com/meeting/chicago11/materials/chi11_nichols.pdf
> 
> Cam
> ----------------------------------------
>> Date: Tue, 3 Jan 2012 12:41:32 -0800
>> From: ayman.farahat@yahoo.com
>> Subject: Re: st: St : Regression discontinuity with Dichotomous dependent variable
>> To: statalist@hsphsun2.harvard.edu
>> 
>> HI Nick
>> This is exactly correct. I am not sure about the polynomial.
>> 
>> Also, while it is possible to model a 0/1 as a continuous with OLS, there is the risk that i would get values outside the 0/1 range.
>> Thanks
>> Ayman
>> 
>> 
>> 
>> 
>> ________________________________
>> From: Nick Sanders 
>> To: "statalist@hsphsun2.harvard.edu" 
>> Sent: Tuesday, January 3, 2012 11:19 AM
>> Subject: Re: st: St : Regression discontinuity with Dichotomous dependent variable
>> 
>> Hello Ayman,
>> 
>> If I understand, you have a 0,1 variable as your outcome and a continuous running variable. You can do this with standard OLS and it is the classic RD setup. Perhaps your concern is the polynomial choice in the running variable (independent)?
>> 
>> On Jan 3, 2012, at 1:10 PM, Ayman Farahat  wrote:
>> 
>>> Hello;
>>> 
>>> I am working on evaluating a treatment effect. The treatment assignment is based on a regression model that assigns a continuous score. Subjects that have a score greater than the cutoff are treated while those below are not treated. So it fits the RD design framework.
>>> 
>>> However, the dependent variable is not a continuous response but rather a dichotomous variable; did the subject perform a certain action. I am using Austin Nichol's excellent RD package. However, the package assumes that the dependent variable is continuous and uses a polynomial to fit a local regression.
>>> 
>>> Is there a way to extend RD to include dichotomous dependent variables?
>>> Thanks
>>> Ayman
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