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

[Arne Risa Hole <arnehole@gmail.com>]

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/DiscreteChoice/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/statistics/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/statistics/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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