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Re: st: Obtaining marginal effects and their standard errors after estimations with interactions


From   Arne Risa Hole <arnehole@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Obtaining marginal effects and their standard errors after estimations with interactions
Date   Mon, 7 Jan 2013 17:14:31 +0000

Thanks Richard, I agree that these manual approaches are useful,
especially from a pedagogical point of view. Having thought about this
some more you could probably do something like this to calculate the
AME:

*continuous/dummy

sysuse auto, clear
set seed 12345
generate dum=uniform()>0.5
table dum
probit foreign turn i.dum i.dum#c.turn, nolog
gen dum_orig = dum
replace dum = 1
margins, dydx(*)
matrix b = r(b)
scalar meff_turn_dum1 = b[1,1]
replace dum = 0
margins, dydx(*)
matrix b = r(b)
scalar meff_turn_dum0 = b[1,1]

di meff_turn_dum1 - meff_turn_dum0

*continuous/continuous

sysuse auto, clear
replace weight=weight/1000
replace length=length/10
probit foreign weight length c.weight#c.length, nolog
gen weight_orig = weight
replace weight = weight+0.0001
margins, dydx(*)
matrix b = r(b)
scalar meff_turn_1 = b[1,2]
replace weight = weight_orig
margins, dydx(*)
matrix b = r(b)
scalar meff_turn_0 = b[1,2]

di (meff_turn_1 - meff_turn_0)/0.0001

Again, I'm not recommending anyone to do the calculations like this. I
think the examples are mainly useful to get a feel for what the
marginal effect of the interaction means: it's just the difference
between two marginal effects computed at different values of the
interacted variable. This is why your approach of graphing the
marginal effects (and/or predictions) is arguably better, as it shows
how the marginal effect changes for a range of values (not just two).

Arne

On 7 January 2013 16:14, Richard Williams <richardwilliams.ndu@gmail.com> wrote:
> At 10:46 AM 1/7/2013, Arne Risa Hole wrote:
>>
>> I don't think it can be extended to AMEs, since the -at()- option of
>> -margins- only takes a single number per variable as far as I know. I
>> imagine you could extend it to three-way interactions etc., but I have
>> not tried this. It's likely to get pretty messy.
>
>
> FYI, slides 27-29 of http://www.nd.edu/~rwilliam/stats/Margins01.pdf show
> how you could compute AMEs for categorical variables if you didn't have
> -margins-. It is a fairly simple example and I'd have to think about whether
> it could be extended to more complicated problems. Cameron and Trivedi show
> how you can manually compute AMEs for continuous variables; see section
> 10.6.10 of http://www.stata.com/bookstore/microeconometrics-stata/index.html
>
> Also, the -at- option does let you specify a range of values for a variable,
> e.g. in my examples i varied the value of age between 20 and 70.
>
> I think the do it yourself approaches have some pedagogical value in that
> they show what margins is doing. They may also be helpful in that they show
> you how much variability there is in effects across cases, as opposed to
> just seeing a single "average"effect.
>
>
>
>> On 7 January 2013 15:26, Richard Williams <richardwilliams.ndu@gmail.com>
>> wrote:
>> > Thanks again. I wonder how easy it would be to extend this to AMEs,
>> > three
>> > way interactions involving squared terms, etc. In other words, would it
>> > be
>> > relatively simple for margins to provide marginal effects for more
>> > complicated models with interaction terms, or would it be quite
>> > difficult?
>> > And if you could do it, how useful would it be?
>> >
>> >
>> > At 10:08 AM 1/7/2013, Arne Risa Hole wrote:
>> >>
>> >> It's possible to get pretty close when both variables are continuous
>> >> as well, using a finite difference approximation. The code below
>> >> approximates "dydlw" in the FAQ.
>> >>
>> >> sysuse auto, clear
>> >> replace weight=weight/1000
>> >> replace length=length/10
>> >> probit foreign weight length c.weight#c.length, nolog
>> >> margins, dydx(*) atmeans at(weight=3.019559)
>> >> matrix b = r(b)
>> >> scalar meff_turn_1 = b[1,2]
>> >> margins, dydx(*) atmeans at(weight=3.019459)
>> >> matrix b = r(b)
>> >> scalar meff_turn_0 = b[1,2]
>> >>
>> >> di (meff_turn_1 - meff_turn_0)/0.0001
>> >>
>> >> I'm not saying that this is a good way of actually performing these
>> >> calculations, but it does help in giving some intuition to what the
>> >> numbers represent (at least I think so).
>> >>
>> >> Arne
>> >>
>> >> On 7 January 2013 13:41, Arne Risa Hole <arnehole@gmail.com> wrote:
>> >> > I don't have much to add to what Richard has already said on this
>> >> > topic but I just wanted to mention one thing: if the interaction is
>> >> > between a continuous variable and a dummy variable, then the second
>> >> > derivative (or "marginal effect of the interaction") is the
>> >> > difference
>> >> > between the marginal effect of the continuous variable when the dummy
>> >> > is "switched on" and when dummy is "switched off". The code below
>> >> > replicates the final result in the FAQ (this uses -margins- so
>> >> > requires Stata 11 or higher).
>> >> >
>> >> > sysuse auto, clear
>> >> > set seed 12345
>> >> > generate dum=uniform()>0.5
>> >> > table dum
>> >> > probit foreign turn i.dum i.dum#c.turn, nolog
>> >> >
>> >> > margins, dydx(*) atmeans at(dum=1)
>> >> > matrix b = r(b)
>> >> > scalar meff_turn_dum1 = b[1,1]
>> >> > margins, dydx(*) atmeans at(dum=0)
>> >> > matrix b = r(b)
>> >> > scalar meff_turn_dum0 = b[1,1]
>> >> >
>> >> > di meff_turn_dum1 - meff_turn_dum0
>> >> >
>> >> > Arne
>> >> >
>> >> > On 6 January 2013 13:11, Ebru Ozturk <ebru_0512@hotmail.com> wrote:
>> >> >> But without getting separate interaction terms, how do we know that
>> >> >> the
>> >> >> moderator affects the relationship between x and y positively or
>> >> >> negatively?
>> >> >>
>> >> >> ----------------------------------------
>> >> >>> Date: Sat, 5 Jan 2013 13:39:53 -0500
>> >> >>> To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu
>> >> >>> From: richardwilliams.ndu@gmail.com
>> >> >>> Subject: RE: st: Obtaining marginal effects and their standard
>> >> >>> errors
>> >> >>> after estimations with interactions
>> >> >>>
>> >> >>> Thanks for the references. FYI, if you have Stata
>> >> >>> 11 or higher, here is how you can easily
>> >> >>> reproduce almost everything that is in the FAQ at
>> >> >>>
>> >> >>>
>> >> >>> http://www.stata.com/support/faqs/statistics/marginal-effects-after-interactions/
>> >> >>> -- the one exception being that you DON'T get
>> >> >>> separate marginal effects for the interaction terms.
>> >> >>>
>> >> >>> sysuse auto, clear
>> >> >>> regress mpg weight c.weight#c.weight
>> >> >>> margins, dydx(*) atmeans
>> >> >>> sysuse auto, clear
>> >> >>> replace weight=weight/1000
>> >> >>> replace length=length/10
>> >> >>> probit foreign weight length c.weight#c.length, nolog
>> >> >>> margins, dydx(*) atmeans
>> >> >>> sysuse auto, clear
>> >> >>> set seed 12345
>> >> >>> generate dum=uniform()>0.5
>> >> >>> table dum
>> >> >>> probit foreign turn i.dum i.dum#c.turn, nolog
>> >> >>> margins, dydx(*) atmeans
>> >> >>>
>> >> >>> With regards to the references, Greene is
>> >> >>> brilliant but I wish he would write in English
>> >> >>> and use Stata examples. I think he is saying that
>> >> >>> the marginal effect of the interaction is not
>> >> >>> useful. The other two articles are also
>> >> >>> expressing concerns or suggesting alternatives. I
>> >> >>> am also not a big fan of using MEMs (marginal
>> >> >>> effects at the means); AMEs (Average Marginal
>> >> >>> Effects) make more sense to me, especially when
>> >> >>> categorical variables are involved.
>> >> >>>
>> >> >>> If the marginal effect of the interaction term is
>> >> >>> useful or even valid, I continue to wonder why
>> >> >>> -margins- does not provide it. And what exactly
>> >> >>> does it mean? The interaction term can't change
>> >> >>> independently of the variables used to compute the interaction.
>> >> >>>
>> >> >>> At 11:53 AM 1/5/2013, André Ferreira Coelho wrote:
>> >> >>> >Dear all,
>> >> >>> >
>> >> >>> >As far as i know there is no consensus on whether margins should
>> >> >>> > be
>> >> >>> >computed for marginal terms.
>> >> >>> >
>> >> >>> >Maybe you are interested in using odds for interactions instead of
>> >> >>> >margins.
>> >> >>> >
>> >> >>> >But you might want to take a look on some literature:
>> >> >>> >
>> >> >>> >http://www.maartenbuis.nl/publications/interactions.pdf
>> >> >>> >
>> >> >>> >http://pages.stern.nyu.edu/~wgreene/Discret
>> >> >>> > eChoice/Readings/Greene-Chapter-23.pdf
>> >> >>> >
>> >> >>> >http://www.stata-journal.com/sjpdf.html?articlenum=st0063
>> >> >>> >
>> >> >>> >Best,
>> >> >>> >
>> >> >>> >Andre
>> >> >>> >
>> >> >>> >
>> >> >>> >
>> >> >>> > > From: ebru_0512@hotmail.com
>> >> >>> > > To: statalist@hsphsun2.harvard.edu
>> >> >>> > > Subject: RE: st: Obtaining marginal effects and their standard
>> >> >>> > > errors
>> >> >>> >after estimations with interactions
>> >> >>> > > Date: Sat, 5 Jan 2013 13:32:47 +0200
>> >> >>> > >
>> >> >>> > > Yes,that's true but I dont think it is wrong to produce a
>> >> >>> > > separate
>> >> >>> >marginal
>> >> >>> >effect. Also this 2004 FAQ is for Stata 10. Maybe that's the
>> >> >>> > reason
>> >> >>> > to
>> >> >>> >still have this information on FAQ page.
>> >> >>> >
>> >> >>> >----------------------------------------
>> >> >>> > > Date: Fri, 4 Jan 2013 15:15:58 -0500
>> >> >>> > > To: statalist@hsphsun2.harvard.edu;
>> >> >>> > > statalist@hsphsun2.harvard.edu
>> >> >>> > > From: richardwilliams.ndu@gmail.com
>> >> >>> > > Subject: RE: st: Obtaining marginal effects and their standard
>> >> >>> > > errors
>> >> >>> >after estimations with interactions
>> >> >>> > >
>> >> >>> > > At 12:24 PM 1/4/2013, Ebru Ozturk wrote:
>> >> >>> > > >It's not that hard, just you need to be careful. Stata 10 is
>> >> >>> > > > the
>> >> >>> > > >only choice for me. I just need an example that inludes a few
>> >> >>> > > > more
>> >> >>> > > >independent and control variables.
>> >> >>> > > >
>> >> >>> > > >Ebru
>> >> >>> > >
>> >> >>> > > I think it is interesting that the -margins- command works
>> >> >>> > > somewhat
>> >> >>> > > differently than the approach presented in the FAQ. In
>> >> >>> > > particular,
>> >> >>> > > margins does not produce a separate marginal effect for the
>> >> >>> > > interaction term while the FAQ approach does. This makes me
>> >> >>> > > wonder
>> >> >>> > > if
>> >> >>> > > (a) the 2004 FAQ is now considered wrong, or (b) both the FAQ
>> >> >>> > > and
>> >> >>> > > margins approaches are considered legitimate but alternative
>> >> >>> > > approaches. Personally, I think what margins does is very
>> >> >>> > > logical,
>> >> >>> > > but nonetheless people keep on asking for marginal effects of
>> >> >>> > > interaction terms.
>> >> >>> > >
>> >> >>> > > >----------------------------------------
>> >> >>> > > > > From: richardwilliams.ndu@gmail.com
>> >> >>> > > > > Date: Fri, 4 Jan 2013 11:56:50 -0500
>> >> >>> > > > > Subject: Re: st: Obtaining marginal effects and their
>> >> >>> > > > > standard
>> >> >>> > > > errors after estimations with interactions
>> >> >>> > > > > To: statalist@hsphsun2.harvard.edu
>> >> >>> > > > >
>> >> >>> > > > > I hate trying to do something like this by hand. Too much
>> >> >>> > > > > room
>> >> >>> > > > > for
>> >> >>> > > > > error. Can't you tell whoever you work for that you can't
>> >> >>> > > > > be
>> >> >>> >expected
>> >> >>> > > > > to work under such primitive inhumane conditions and you
>> >> >>> > > > > need
>> >> >>> > > > > Stata
>> >> >>> > > > > 12?
>> >> >>> > > > >
>> >> >>> > > > > You might check out the user-written -inteff- command and
>> >> >>> > > > > see
>> >> >>> > > > > if it
>> >> >>> > > > > helps. -margeff- is another user-written command that has
>> >> >>> > > > > various
>> >> >>> > > > > advantages over -mfx-.
>> >> >>> > > > >
>> >> >>> > > > > Sent from my iPad
>> >> >>> > > > >
>> >> >>> > > > > On Jan 4, 2013, at 11:33 AM, Ebru Ozturk wrote:
>> >> >>> > > > >
>> >> >>> > > > > > Thank you, I use Stata 10 therefore I asked this
>> >> >>> > > > > > question. I
>> >> >>> > > > just wonder when we have more independent or control
>> >> >>> > > > variables
>> >> >>> > > > how
>> >> >>> > > > do we adjust the given equations on this link:
>> >> >>> > > >
>> >> >>> >http://www.stata.com/support/faqs/statistic
>> >> >>> > s/marginal-effects-after-interactions/
>> >> >>> >[1]
>> >> >>> > > > > >
>> >> >>> > > > > > Kind regards
>> >> >>> > > > > > Ebru
>> >> >>> > > > > >
>> >> >>> > > > > > ----------------------------------------
>> >> >>> > > > > >> Date: Fri, 4 Jan 2013 09:32:25 -0500
>> >> >>> > > > > >> To: statalist@hsphsun2.harvard.edu;
>> >> >>> >statalist@hsphsun2.harvard.edu
>> >> >>> > > > > >> From: richardwilliams.ndu@gmail.com
>> >> >>> > > > > >> Subject: Re: st: Obtaining marginal effects and their
>> >> >>> > > > > >> standard
>> >> >>> > > > errors after estimations with interactions
>> >> >>> > > > > >>
>> >> >>> > > > > >> At 03:17 PM 1/3/2013, Ebru Ozturk wrote:
>> >> >>> > > > > >>
>> >> >>> > > > > >>> Dear All,
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> On Stata FAQs' page, there are some given examples for
>> >> >>> > > > > >>> Probit
>> >> >>> > > > > >>> estimation with interaction effects for Stata 10 titled
>> >> >>> > > > > >>> as
>> >> >>> > > > > >>> "I am
>> >> >>> > > > > >>> using a model with interactions. How can I obtain
>> >> >>> > > > > >>> marginal
>> >> >>> >effects
>> >> >>> > > > > >>> and their standard errors?" and the link is:
>> >> >>> > > > > >>>
>> >> >>> > > >
>> >> >>> >http://www.stata.com/support/faqs/statistic
>> >> >>> > s/marginal-effects-after-interactions/
>> >> >>> >[2]
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> Do you think this way is still applicable to Probit
>> >> >>> > > > > >>> estimation?
>> >> >>> >and
>> >> >>> > > > > >>> Is the below command correct when we have other
>> >> >>> > > > > >>> independent or
>> >> >>> > > > > >>> control variables?
>> >> >>> > > > > >>
>> >> >>> > > > > >> I don't know if you did it right or not, but if you have
>> >> >>> > > > > >> Stata 11
>> >> >>> >or
>> >> >>> > > > > >> higher why not use -margins-, e.g.
>> >> >>> > > > > >>
>> >> >>> > > > > >> sysuse auto, clear
>> >> >>> > > > > >> probit foreign weight length c.weight#c.length, nolog
>> >> >>> > > > > >> margins, dydx(*)
>> >> >>> > > > > >>
>> >> >>> > > > > >>> local xb _b[weight]*`meanwei' + _b[len]*`meanlen' +
>> >> >>> > > > > >>> _b[wl]*`meanwei'*`meanlen' + _b[C1]*C1+_b[C2]*C2 +
>> >> >>> > > > > >>> _b[_cons] //
>> >> >>> >if
>> >> >>> > > > > >>> more variables //
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> /////// example /////////
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> sysuse auto, clear
>> >> >>> > > > > >>> generate wl=weight*length
>> >> >>> > > > > >>> probit foreign weight length wl, nolog
>> >> >>> > > > > >>> quietly summarize weight if e(sample)
>> >> >>> > > > > >>> local meanwei = r(mean)
>> >> >>> > > > > >>> quietly summarize length if e(sample)
>> >> >>> > > > > >>> local meanlen = r(mean)
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> local xb _b[weight]*`meanwei' + _b[len]*`meanlen' +
>> >> >>> > > > > >>> _b[wl]*`meanwei'*`meanlen' + _b[_cons]
>> >> >>> > > > > >>> predictnl dydw = normalden(`xb')*(_b[weight]+
>> >> >>> > > > _b[wl]*`meanlen') in 1, se(sew)
>> >> >>> > > > > >>> list dydw sew in 1
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> predictnl dydl = normalden(`xb')*(_b[len]+
>> >> >>> > > > > >>> _b[wl]*`meanwei')
>> >> >>> > > > in 1, se(sel)
>> >> >>> > > > > >>> list dydl sel in 1
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> predictnl dydlw =normalden(`xb')*(-(`xb'))*(_b[weight]+
>> >> >>> > > > > >>> _b[wl]*`meanlen')*(_b[len]+ _b[wl]*`meanwei') +
>> >> >>> >normalden(`xb')*(
>> >> >>> > > > > >>> _b[wl]) in 1, se(selw)
>> >> >>> > > > > >>> list dydlw selw in 1
>> >> >>> > > > > >>>
>> >> >>> > > > > >>> Ebru
>> >> >>> > > > > >>
>> >> >>>
>> >> >>> -------------------------------------------
>> >> >>> Richard Williams, Notre Dame Dept of Sociology
>> >> >>> OFFICE: (574)631-6668, (574)631-6463
>> >> >>> HOME: (574)289-5227
>> >> >>> EMAIL: Richard.A.Williams.5@ND.Edu
>> >> >>> WWW: http://www.nd.edu/~rwilliam
>> >> >>>
>> >> >>>
>> >> >>> *
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>> >
>> >
>> > -------------------------------------------
>> > Richard Williams, Notre Dame Dept of Sociology
>> > OFFICE: (574)631-6668, (574)631-6463
>> > HOME:   (574)289-5227
>> > EMAIL:  Richard.A.Williams.5@ND.Edu
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>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW:    http://www.nd.edu/~rwilliam
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