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Re: st: interpreting probit coefficient


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: interpreting probit coefficient
Date   Sun, 23 Jun 2013 10:45:59 -0400

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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