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

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

Thanks for this Richard. Plotting adjusted predictions (or marginal
effects) like in your slides seems like a very good alternative to
reporting a single number.

It would be great if you could share the response from Stata tech
support with the list when you hear from them.

Arne

On 7 January 2013 15:09, Richard Williams <richardwilliams.ndu@gmail.com> wrote:
> Thanks for showing how to do this Arne. FYI I have asked Stata tech support
> why margins does not provide marginal effects for interaction terms. One
> theory I have is that it would be a programming nightmare. The 2004 FAQ is a
> very simple example and it required that you know what the derivatives are.
> My impression (possibly wrong) is that margins doesn't actually know what
> all the formulas for derivatives are. Instead, it takes more of a brute
> force approach -- it plugs in numbers and computes the marginal effects from
> there.
>
> I also continue to be unclear how useful the marginal effect of an
> interaction term is. It may be more useful to plot adjusted predictions for
> men and women and see how they differ across the range of some other
> variable that gender is interacted with. See the last few slides of
>
> http://www.nd.edu/~rwilliam/stats/Margins01.pdf
>
>
>
> At 08:41 AM 1/7/2013, Arne Risa Hole 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/Discrete
>> >> > Choice/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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>
>
> -------------------------------------------
> 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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