# Re: st: probit with interaction dummies (significance and marginaleffects)

 From Alan Acock To statalist@hsphsun2.harvard.edu Subject Re: st: probit with interaction dummies (significance and marginaleffects) Date Sat, 26 Jul 2008 19:54:10 -0700

```I've not followed all of this discussion, but with continuous variables,
what Tony says makes centering extremely important. Centering education at
12 years in the U.S. Makes the 0 value meaningful. Changing where you center
a variable can dramatically change interactions so the centering should be
conceptually justified. Uncentered continuous variables for which a zero
value is extremely rare, e.g., years of education, age, etc., can produce
bizarre results.

Alan Acock

On 7/25/08 8:19 AM, "Tony Lachenbruch" <Peter.Lachenbruch@oregonstate.edu>
wrote:Tony Lachenbruch

> With logistic regression, interaction is usually interpreted as effect
> modification:  the effect of predictor A is different at different levels of
> predictor B.  With probit regression it is likely to be similar although not
> identical.
>
> It is often useful to write the predicted probabilities:
> For logistic regression you have
> (1) ln(p/(1-p))=B0  when A=B=0
> (2) ln(p/(1-p))=B0+B1 when A=1, B=0
> (3) ln(p/(1-p))=B0+   B2  when A=0, B=1
> (4) ln(p/(1-p))=B0+B1+B2+B3  when A=1, B=1
>
> The differences  (2)-(1)=B1 is the ln(OR) for A at B=0
> (3)-(1)=B2 is the ln(OR) for B at A=0
> If B2=0 the interpretation of the above is how the ln(OR)s behave.  If B2 is
> not 0, then
> (4)-(2)=B2+B3 is how the ln(OR) for A is modified when B=1
> (4)-(3)=B1+B3 is how the ln(OR) for B is modified when A=1
>
> Tony
>
> Peter A. Lachenbruch
> Department of Public Health
> Oregon State University
> Corvallis, OR 97330
> Phone: 541-737-3832
> FAX: 541-737-4001
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Erasmo Giambona
> Sent: Friday, July 25, 2008 3:05 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: probit with interaction dummies (significance and marginal
> effects)
>
> Dear Statalisters,
>
> I have found this thread particulalrly interesting. I have found the
> questions asked by Andrea and especially the answer of Marteen very
> useful. However, despite having read a lot about it over the last
> several days, it is still hard for me to have a good intuition on how
> to intepret interaction terms in logit regressions. I have also found
> that papers in finance (my field) usually miss to provide a clear
> interpretation of interaction terms in logit regressions.
>
> I truly hope some other people might join the thread to provide more insights.
>
> Here is my major source of confusion. Consider the case of interaction
> of two continuos variables (e.g., profit and number of employees) in a
> logit model. The dependent variable is 1 if the firm's ceo is fired
> and zero otherwise. The coefficient estimate on the interaction from
> the logit output is positive (for example, +0.25) and statistically
> significant. I interpret this to mean that the odds that the ceo is
> fired are higher when both profit and number of employees are large
> (small) in absolute term (rather than changes). However, Ali et al.
> (2004) show that the marginal effect for the interaction of two
> continuos variables can be negative even if its coefficient estimate
> is positive. Assuming that the marginal effect is negative (e.g.,
> -0.2) in my example, I would interpret this to mean that the
> likelihood of firing the ceo decreases by 20% on average as the
> interaction term increases by 1%.
>
> Assuming that my way of interpreting coefficient and marginal effect
> of the interaction term in a logit is correct, I would still find it
> hard to reconcile the "seemingly contradictory" evidence of the above
> example.
>
> I hope this can stimulate further discussion on the issue.
>
> Best regards,
> Erasmo
>
> Reference
> Norton, Wang, & Ai. 2004. Computing interaction effects in logit and
> probit models. The Stata Journal 4(2):103116.
>
>
>
>
> On Fri, Jul 18, 2008 at 5:00 AM, Andrea Bennett <mac.stata@gmail.com> wrote:
>> Thank you so much!
>>
>> May I sum up for clarification: When I am using e.g. a probit model with a
>> dependent variable Y and include an interaction term  -female*wage- and I am
>> primarily interested in the interaction effect of a woman with wage then it
>> is save to use the standard regression output to interpret the direction
>> (AND the significance?) from the regression table. E.g. if the
>> beta-estimators are -female- ==0.5, -wage- == 0.34 and -female*wage- ==
>> -0.03 and all being significant then I can say that the wage effect is
>> significantly smaller when being a woman? Does this also hold when one is
>> formulating models like -female*low_education-, -female*mid_education-,
>> -female-high_education-? Or did I misinterpret you line "as long as you
>> interpret the effects in terms of the effect on the latent variable you are
>> ok in simply using the output from -probit-"?
>>
>> When I want to know if (and for which range) the interaction of female and
>> wage has a significant effect on Y I should use -inteff-. When I want to do
>> the same for the interaction of female with the education levels, then there
>> is not yet consensus on how it shall be done. Norton et al. 2004 mention
>> -predictnl- but urge to use it with extra care. Another source would be Rich
>> Williams webpage.
>>
>> Did I completely mess it up (I fear so!) or is it like I described?
>>
>> Andrea
>>
>>
>> On Jul 17, 2008, at 6:13 PM, Maarten buis wrote:
>>
>>> Regarding problem 1, this is just a matter of interpretation, as long
>>> as you interpret the effects in terms of the effect on the latent
>>> variable you are ok in simply using the output from -probit-, if you
>>> want to interpret the results in terms of the probability you should
>>> use -inteff-.
>>>
>>> Problem 2 is much harder to solve. Any solution would in one way or
>>> another try to controll for things that haven't been observed. It
>>> should not come as a surprise that that is hard (read: impossible). So,
>>> the fact that "the solution" hasn't been implemented yet in Stata is
>>> not so much a problem with Stata but with the state of the statistical
>>> science: we know the problem, but we just don't know the answer. Though
>>> Rich Williams discusses one solution on his website.
>>>
>>> -- Maarten
>>>
>>> --- Andrea Bennett <mac.stata@gmail.com> wrote:
>>>>
>>>> Thanks for the link! Still, I wonder if there's really no Stata
>>>> command I could use to "simply" test if the interaction is
>>>> significant and what influence (direction) it has on the dependent
>>>> variable. I'd be just rather surprised if this does not exist
>>>> because it seems to me this is a very common issue in any regression
>>>> design (interaction effects).
>>>
>>> --- Maarten buis wrote:
>>>>>
>>>>> There are two distinct issues when interpreting interaction effects
>>>>> in a probit:
>>>>>
>>>>> 1) a significant positive (negative) interaction in terms of the
>>>>> latent
>>>>> variable does not mean a significant positive (negative)
>>>>> interaction effect in terms of the probability that y = 1.
>>>>>
>>>>> 2) The scale of the latent variable is identified by setting the
>>>>> residual variance at 1. If the residual variance differs between
>>>>> the groups than that means that the scale of the latent variable
>>>>> differs between the groups and when comparing differences in
>>>>> effects across the groups you are basically comparing apples and
>>>>> oranges.
>>>
>>>
>>> -----------------------------------------
>>> Maarten L. Buis
>>> Department of Social Research Methodology
>>> Vrije Universiteit Amsterdam
>>> Boelelaan 1081
>>> 1081 HV Amsterdam
>>> The Netherlands
>>>
>>> Buitenveldertselaan 3 (Metropolitan), room Z434
>>>
>>> +31 20 5986715
>>>
>>> http://home.fsw.vu.nl/m.buis/
>>> -----------------------------------------
>>>
>>>
>>>     __________________________________________________________
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