re: Re: st: Propensity Score Matching with Multiple Categorical Variables with Multiple Categories...Dummy Variables?

["Ariel Linden, DrPH" <ariel.linden@gmail.com>]

Austin is absolutely correct (as always). I purposely limited my response to
only the issue of using the "i." prefix within the logit model vs creating
additional dummy variables. In order to round out the discussion points that
Austin raises, including higher order terms for relevant covariates is also
a common recommendation in matching approaches. Balance may be achieved on
the covariate base level but not achieve balance at another order. More and
more, researchers are turning to boosted regression or CART models in order
to estimate the propensity score in order to account for all these issues
without having to manually program the model.

Ariel

Date: Fri, 13 Jul 2012 11:12:40 -0400
From: Austin Nichols <austinnichols@gmail.com>
Subject: Re: st: Propensity Score Matching with Multiple Categorical
Variables with Multiple Categories...Dummy Variables?

Ariel and Pete--
Estimating a logit with dummies is one way to combine across distinct
combinations of the 15 observables to estimate a propensity score. A
fully nonparametric propensity score would include every possible
interaction as well, or simply compute the mean of treatment across
all cells (possibly millions of cells).  If any cells have pscore 0 or
1, and some are almost certain to be degenerate in that way, then you
must combine that cell with another; one way of doing that is using
the marginal across some subset of categories. The logit with no
interactions is one particular method of combining across cells.

sysuse auto
logit foreign i.rep78
predict p if e(sample)
egen m=mean(foreign), by(rep78)
su m p if p<.
* Note that if you do not restrict using if e(sample)
* the estimated p=.818 for rep78=1
* (taken from excl cat rep78=5) when it should be zero.
ta rep78, mi sum(foreign)
ta rep78, mi sum(m)
ta rep78, mi sum(p)

g fakecat=round(mpg,10)
logit foreign i.rep78##i.fakecat
predict p2 if e(sample)
egen m2=mean(foreign), by(rep78 fakecat)
su m2 p2 if p2<.


On Fri, Jul 13, 2012 at 10:19 AM, Ariel Linden, DrPH
<ariel.linden@gmail.com> wrote:
> Hi Pete,
>
> Since estimation of the propensity score is nothing more than a logistic
(or
> probit) regression model, you could leave the categorical variables as-is
> and use the "i." prefix to denote that they are categorical, such as
i.race.
> The regression output will show you that the levels of the categorical
> variable have been dealt with accordingly (including if any of the levels
> are dropped from the model). See for example:
>
> sysuse auto
> logit foreign i.rep78
>
> On the other hand, you could certainly create dummy variables for the
> categorical variable. However, if you have a large number of covariates,
> your dataset will start looking ugly in a hurry. In any case, your results
> will be identical:
>
> tab rep78, gen(rep78_)
> logit foreign rep78_1- rep78_5
>
> I hope this helps
>
> Ariel
>

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