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

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

Thanks for the reference Richard, this looks very interesting and useful.

Arne

On 7 January 2013 15:52, Richard Williams <richardwilliams.ndu@gmail.com> wrote:
> Thanks Arne. Yes, the problem with any "average" number (AME or MEM) is that
> it disguises a great deal of individual level variability (and this is true
> whether the model includes interaction terms or not). In my slides I show
> how racial differences in the likelihood of having diabetes are very small
> at young ages (mostly because young people in the sample are very unlikely
> to have diabetes regardless of their race) and much larger at older ages.
> Giving a single marginal effect for race obscures these differences by age.
> You can't plot everything, but I think it is useful to plot at least a few
> key relationships. That is why I like MERs (marginal effects at
> representative values), or else APRs (a term I made up) which stands for
> Adjusted Predictions at Representative Values. The points made in the slides
> were further developed in my SJ paper,
>
> http://www.statajournal.com/article.html?article=st0260
>
>
> At 10:27 AM 1/7/2013, Arne Risa Hole wrote:
>>
>> 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
>> >> >>
>> >> >>
>> >> >> *
>> >> >> * For searches and help try:
>> >> >> * http://www.stata.com/help.cgi?search
>> >> >> * http://www.stata.com/support/faqs/resources/statalist-faq/
>> >> >> * http://www.ats.ucla.edu/stat/stata/
>> >> > *
>> >> > *   For searches and help try:
>> >> > *   http://www.stata.com/help.cgi?search
>> >> > *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> >> > *   http://www.ats.ucla.edu/stat/stata/
>> >>
>> >> *
>> >> *   For searches and help try:
>> >> *   http://www.stata.com/help.cgi?search
>> >> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> >> *   http://www.ats.ucla.edu/stat/stata/
>> >
>> >
>> > -------------------------------------------
>> > 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
>> >
>> >
>> > *
>> > *   For searches and help try:
>> > *   http://www.stata.com/help.cgi?search
>> > *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> > *   http://www.ats.ucla.edu/stat/stata/
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
> -------------------------------------------
> 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
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/