R help - Mar 2011 - Matching package - Match function

Hi.

I am using the Matching package for propensity score matching. For each
treated unit, I want to find all control units whose propensity scores lie
within a certain distance from the treated unit. The sample code is as
follows:
> library(Matching)
> x <- rnorm(100000)
> y <- rnorm(100000)
> z <- rbinom(100000,1,0.002)
> logit.reg <- glm(z~x+y,family=binomial(link='logit'))
> match <-
>
Match(Y=NULL,Tr=z,X=logit.reg$fitted,version='fast',ties=TRUE,M=1,distance.tolerance=1e-5)
According to the function definition
(http://sekhon.berkeley.edu/matching/Match.html):

"distance.tolerance: This is a scalar which is used to determine if
distances between two observations are different from zero. Values less than
distance.tolerance are deemed to be equal to zero. This option can be used
to perform a type of optimal matching"

Thus, for each treated unit I should get all control units whose difference
in propensity scores from the treated unit is less than 1e-5. However, the
actual difference between the treated unit's and the control units'
propensity is distributed as follows:
>
summary(abs(logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control]))
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
7.453e-13 2.959e-07 5.849e-07 5.842e-07 8.741e-07 1.167e-06 

The maximum difference is only 1.167e-6 instead of the 1e-5 I expected.
Similarly, when I set higher tolerances I get:
> match <-
>
Match(Y=NULL,Tr=z,X=logit.reg$fitted,version='fast',ties=TRUE,M=1,distance.tolerance=2e-5)
>
summary(abs(logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control]))
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
7.453e-13 4.133e-07 8.208e-07 8.230e-07 1.232e-06 1.652e-06
> match <-
>
Match(Y=NULL,Tr=z,X=logit.reg$fitted,version='fast',ties=TRUE,M=1,distance.tolerance=3e-5)
>
summary(abs(logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control]))
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
7.453e-13 5.051e-07 1.006e-06 1.008e-06 1.514e-06 2.022e-06
> match <-
>
Match(Y=NULL,Tr=z,X=logit.reg$fitted,version='fast',ties=TRUE,M=1,distance.tolerance=4e-5)
>
summary(abs(logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control]))
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
7.453e-13 5.818e-07 1.162e-06 1.166e-06 1.750e-06 2.365e-06 

So, although there are more control units available with distances greater
than 1.167e-6, for some reason the function doesn't select those and instead
clips it at this value even when the tolerance is set at 1e-5. Similar
issues occur at higher tolerances. I really hope someone can help me resolve
this.

Thanks a lot!


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I have figured out the solution to this. It appears that "distance"
isn't
defined as the difference in propensity scores. Instead, this difference is
then scaled by the standard deviation of the predicted dependent-variable
values of the corresponding logistic regression, and then squared. 

Therefore, instead of checking for:
>
summary(abs(logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control]))
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
7.453e-13 2.959e-07 5.849e-07 5.842e-07 8.741e-07 1.167e-06 

the correct form is:
>
summary(((logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control])/sd(logit.reg$fitted))^2)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
4.078e-18 6.426e-07 2.512e-06 3.337e-06 5.609e-06 1.000e-05 

which then gives the expected maximum value of 1e-5, as set in the
distance.tolerance option.


sunny wrote:
> 
> Hi.
> 
> I am using the Matching package for propensity score matching. For each
> treated unit, I want to find all control units whose propensity scores lie
> within a certain distance from the treated unit. The sample code is as
> follows:
> 
>> library(Matching)
> 
>> x <- rnorm(100000)
>> y <- rnorm(100000)
>> z <- rbinom(100000,1,0.002)
> 
>> logit.reg <- glm(z~x+y,family=binomial(link='logit'))
> 
>> match <-
>>
Match(Y=NULL,Tr=z,X=logit.reg$fitted,version='fast',ties=TRUE,M=1,distance.tolerance=1e-5)
> 
> According to the function definition
> (http://sekhon.berkeley.edu/matching/Match.html):
> 
> "distance.tolerance: This is a scalar which is used to determine if
> distances between two observations are different from zero. Values less
> than distance.tolerance are deemed to be equal to zero. This option can be
> used to perform a type of optimal matching"
> 
> Thus, for each treated unit I should get all control units whose
> difference in propensity scores from the treated unit is less than 1e-5.
> However, the actual difference between the treated unit's and the
control
> units' propensity is distributed as follows:
> 
>>
summary(abs(logit.reg$fitted[match$index.treated]-logit.reg$fitted[match$index.control]))
>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
> 7.453e-13 2.959e-07 5.849e-07 5.842e-07 8.741e-07 1.167e-06 
> 
> 

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