But E "distributes" over addition and subtraction. I remember this being in
Rice, although I do not have my copy with me. Irwin has a proof here on the
last page:
It
is only multiplication where things are weird (E[ab] != E[a]E[b]).
Either way, how do Gary's notes imply that we are supposed to take a draw
from a distribution?
Ben
Ben Goodrich
Graduate Student at Harvard University
Ph.D. Program in Government and Social Policy
-----Original Message-----
From: gov2001-l-bounces(a)lists.fas.harvard.edu [mailto:gov2001-l-
bounces(a)lists.fas.harvard.edu] On Behalf Of Olivia Lau
Sent: Thursday, December 09, 2004 11:51 AM
To: gov2001-l(a)lists.fas.harvard.edu
Subject: Re: [gov2001-l] setx question
The expectation is outside Y(1) - Y(0). So you want the expected value of
the difference, not the difference of the expectations.
----- Original Message -----
From: "Ben Goodrich" <goodrich(a)fas.harvard.edu>
To: <gov2001-l(a)lists.fas.harvard.edu>
Sent: Thursday, December 09, 2004 11:48 AM
Subject: RE: [gov2001-l] setx question
And for
either model, you should be using the predicted values to
calculate the ATE's.
How does this square with the formula for ATE in Gary's notes where
ATE = (1/n)\Sigma E(Y(1) - Y(0))
To me, that implies that we should be looking at the mean over the
difference in expected values rather than the mean over the predicted
values?
Ben
Ben Goodrich
Graduate Student at Harvard University
Ph.D. Program in Government and Social Policy
www.people.fas.harvard.edu/~goodrich/
goodrich(a)fas.harvard.edu
> -----Original Message-----
> From: gov2001-l-bounces(a)lists.fas.harvard.edu [mailto:gov2001-l-
> bounces(a)lists.fas.harvard.edu] On Behalf Of Olivia Lau
> Sent: Thursday, December 09, 2004 11:29 AM
> To: gov2001-l(a)lists.fas.harvard.edu
> Subject: Re: [gov2001-l] setx question
>
> And for either model, you should be using the predicted values to
> calculate
> the ATE's.
>
> ----- Original Message -----
> From: "Olivia Lau" <olau(a)fas.harvard.edu>
> To: <gov2001-l(a)lists.fas.harvard.edu>
> Sent: Thursday, December 09, 2004 11:17 AM
> Subject: Re: [gov2001-l] setx question
>
>
> > that's a great question, Mike.
> >
> > So here's the deal: Usually, the expected values will differ across
> > columns only because the X observations are different. In this case,
> the
> > X observations are all the same (intercept = 1 and treat = 1, for
> > example), so each column looks the same. The ev differ across rows
> > because of the differences in the simulated betas.
> >
> > The predicted values are draws from the distribution defined by the
> > corresponding value in the expected value matrix (and so should be
> > different across rows and columns).
> >
> > ----- Original Message -----
> > From: "Michael Richard Kellermann" <kellerm(a)fas.harvard.edu>
> > To: <gov2001-l(a)lists.fas.harvard.edu>
> > Sent: Thursday, December 09, 2004 11:05 AM
> > Subject: Re: [gov2001-l] setx question
> >
> >
> >>
> >> Here is the reason for my question: when I look at the expected
> >> values
> >> generated by the sim command, using a normal model, they are the
same
> in
> >> the univariate case:
> >>
> >> s.out.0$qi$ev[1:8, 1:8]
> >>
> >> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
> >> [1,] 0.4486 0.4486 0.4486 0.4486 0.4486 0.4486 0.4486 0.4486
> >> [2,] 0.4424 0.4424 0.4424 0.4424 0.4424 0.4424 0.4424 0.4424
> >> [3,] 0.4392 0.4392 0.4392 0.4392 0.4392 0.4392 0.4392 0.4392
> >> [4,] 0.4425 0.4425 0.4425 0.4425 0.4425 0.4425 0.4425 0.4425
> >> [5,] 0.4411 0.4411 0.4411 0.4411 0.4411 0.4411 0.4411 0.4411
> >> [6,] 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485
> >> [7,] 0.4477 0.4477 0.4477 0.4477 0.4477 0.4477 0.4477 0.4477
> >> [8,] 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485
> >>
> >> and then they are different for the predicted values:
> >>
> >> s.out.0$qi$pr[1:8, 1:8]
> >> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
> [,8]
> >> [1,] 0.26540 0.69574 -0.30079 0.7086 0.095671 0.56353 0.5045
> 0.7559
> >> [2,] -0.29949 0.79896 1.81914 -0.2224 0.149480 0.07857 0.9538 -
> 0.7112
> >> [3,] -0.24355 0.54188 0.47502 1.1169 0.675997 0.88817 0.1099 -
> 0.1553
> >> [4,] -0.02701 -0.28023 0.75768 -0.2701 0.296251 0.86762 0.3645
> 0.5838
> >> [5,] 0.27580 0.46741 0.36535 0.4150 1.234477 0.40665 0.5650
> 0.9518
> >> [6,] 0.33215 0.81140 0.39242 0.7009 0.282338 0.97523 0.7354
> 0.1146
> >> [7,] -0.29423 0.09349 0.01257 1.0007 0.721501 0.12567 0.3155
> 0.0861
> >> [8,] 0.24989 0.28098 1.38814 0.6617 -0.007151 -0.19204 0.6433
> 0.5431
> >>
> >> So I guess my question more precisely is, does sim take one set of
> draws
> >> from the sampling distribution of the betas and reuse it for all of
> >> the
> >> sets of starting values?
> >>
> >> Also, for the normal model, should we be using the predicted values
or
> >> the
> >> expected values to calculate the ATE and ATT?
> >>
> >> Cheers,
> >> Mike
> >>
> >> On Thu, 9 Dec 2004, Olivia Lau wrote:
> >>
> >>> There's nothing random about setx(). The randomness comes in
sim().
>> And my
>> understanding of how R handles seeds is that it picks up where it
>> left
>> off.
>> Hence,
>>
>> a <- rnorm(10)
>> b <- rnorm(10)
>> identical(a, b)
>>
>> should be false...
>>
>> ----- Original Message -----
>> From: "Michael Richard Kellermann" <kellerm(a)fas.harvard.edu>
>> To: <gov2001-l(a)lists.fas.harvard.edu>
>> Sent: Thursday, December 09, 2004 10:39 AM
>> Subject: Re: [gov2001-l] setx question
>>
>>
>> >
>> > Does Zelig start with the same random number seed for each vector
>> > of
x
>> > values created by the setx command?
>> >
>> > Cheers,
>> > Mike
>> >
>> > On Thu, 9 Dec 2004, Olivia Lau wrote:
>> >
>> >> If you can't get Zelig to do what you want (right now, before
section
>> >> this
>> >> evening), I suggest that you manhandle the output to get it to
>> >> produce
>> >> what
>> >> you want...just a thought.
>> >>
>> >> ----- Original Message -----
>> >> From: "Andrew Eggers" <aeggers(a)gmail.com>
>> >> To: <gov2001-l(a)lists.fas.harvard.edu>
>> >> Sent: Thursday, December 09, 2004 10:23 AM
>> >> Subject: [gov2001-l] setx question
>> >>
>> >>
>> >> > Can anyone help me understand why my setx function isn't doing
what
>> >> > I
>> >> > thought it would?
>> >> >
>> >> > I'm doing part 2a.
>> >> >
>> >> >> x.out0<- setx(z.out, fn= NULL, phone =0)
>> >> >
>> >> >> x.out0[1:10,]
>> >> > (Intercept) phone
>> >> > 1 1 1
>> >> > 2 1 0
>> >> > 3 1 1
>> >> > 4 1 0
>> >> > 5 1 1
>> >> > 6 1 1
>> >> > 7 1 1
>> >> > 8 1 1
>> >> > 9 1 1
>> >> > 10 1 1
>> >> >
>> >> > I thought this would produce all 0's in the phone column of
x.out0,
>> >> > but clearly it
didn't.
>> >> >
>> >> > Thank you!
>> >> >
>> >> > Andy
>> >> > _______________________________________________
>> >> > gov2001-l mailing list
>> >> > gov2001-l(a)lists.fas.harvard.edu
>> >> >
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
>> >> >
>> >>
>> >> _______________________________________________
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>> >>
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>> > _______________________________________________
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>> >
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>> >
>>
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