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# Re: st: interpreting probit coefficient

 From Paul Byatta To statalist@hsphsun2.harvard.edu Subject Re: st: interpreting probit coefficient Date Mon, 24 Jun 2013 18:51:04 +0300

```Hi David,

Thanks a lot. The PDF on -margins- was quite informative.

Paul

On Sun, Jun 23, 2013 at 5:45 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> Hi, Paul.
>
> Others on this list have far more experience with -margins- than I
> have, but you may find the following comments useful.  -margins- has a
> wide range of capabilities.  If you have not read the PDF
> documentation on -margins- recently, please do so.  The examples
> include situations similar to yours.
>
> m7a and m11a are indicator variables, but you have used them in your
> -probit- command as continuous variables, and so -margins- will also
> consider them continuous.  That will prevent -margins- from
> calculating discrete differences for those variables, as you may want
> it to do.  If you had gotten that output by using i.m7a in the
> -probit- command, you could interpret the result as saying that the
> average marginal effect of having more than 1 wife (on the probability
> of domestic disputes) is .021586.  (-margins- calculates the
> derivative or discrete difference at the level of the observation and
> then averages over the sample.)
>
> You should study your data to judge whether they support that sort of
> averaging.  The derivative or discrete difference works on the model,
> holding constant the predictors that do not involve that particular
> variable.  The actual process of fitting a regression model (including
> probit), however, works differently.  As a result, if you were
> interpreting the coefficients in the model, you would need to say that
> a particular coefficient tells how the outcome varies with change in
> that predictor after adjusting for simultaneous linear change in the
> other predictors in the model in the data at hand.  One should not
> usually pretend to be able to hold the other predictors constant.
>
> For the interpretation of me3_yea it is not accurate to talk about the
> effect of 1 additional year of marriage.  The documentation for
> -margins- points out that the derivative is a rate and it applies to
> small (infinitesimal) changes in the variable.
>
> Have you considered whether your model should include interactions?
> If the data do need interactions in the model, -margins- may be even
> more helpful (if used carefully).
>
> David Hoaglin
>
>
> On Sun, Jun 23, 2013 at 4:46 AM, Paul Byatta <paulbyatta@gmail.com> wrote:
>> Hi Stata list
>>
>> I kindly need help with interpreting coefficients from a probit
>> regression. I have a dataset and I want to examine how years of
>> marriage, polygamy, dowry payment predict probability of domestic
>> disputes among married couples in a country.
>>
>> I have run the command below
>>
>>  probit m181_dispute m3_yea m7a m11a, r
>>
>> I followed that with
>>
>>  margin, dy/dx(*)
>>
>> my variable names are
>>
>> m181_dispute = 1 if there was a domestic dispute, 0 if otherwise
>> m3_yea = length of marriage in years
>> m7a =  1 if husband has more than 1 wife, 0 if has 1 wife
>> m11a = 1 if husband has paid dowry, 0 if not
>>
>> After I run the margin command, I get
>>
>>                 dy/dx
>>  m3_yea |   .0050716
>>  m7a |    .021586
>>  m11a |  -.0608191
>> m12a |  -.0176505
>>
>>
>> I understand that, because m3_yea is a continuous variable, it would
>> be accurate to interpret the marigin coefficient on m3_yea as 1
>> additional year of marriage would on average decrease probability of
>> occurrence of domestic disputes by 0.5 percent.
>>
>> I am, however, confused as to how to interpret a margin coefficient on
>> an indicator variable. For instance, I was wondering whether it would
>> be accurate to interpret the margin coefficient on m7a  as the
>> probability of domestic disputes occurrence in marriages with more
>> than 1 wife is on average higher by 2.16 percent than in those with
>> one 1 wife.
>>
>>
>> Thanks
>> Paul
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