Marginal effects - Probit

[Li Mueller]

Hi all,

I did a probit regression (dependent (binary) variable: withdrawal or not) and now want to get the marginal effects to better interpret the model (I am using Stata 13.1).

I used
. mfx compute
but realized that it is slightly old and instead wanted to use
. margins, dydx(*)

Since I got two different results, I was wondering which command is the correct one.
What I want to get is the change in the withdrawal probability given a change in the independent variable.
I also have dummy variables in my regression and am not sure if I need to consider this when calculating the marginal effects.

Any help on the topic is appreciated!

[Clyde Schechter]

I can't comment about -mfx-. It's an old command, and I have never used it. I don't know what its results might mean.

As for -margins, dydx()-, it does treat dichotomous ("dummy") variables differently from continuous ones if you properly designated them in your model.

So, if you did

probit outcome var1 var2 i.var3 var4 // etc.
margins, dydx(*)

then -margins- will know that var3 is represented by a series of one or more indicator variables. For such indicators it will calculate the expected change in outcome probability associated with a discrete one unit increase in the indicator, with all other variables set to their actual values in the data set. If you did not specify the i. (or if you did so but overrode it with the obsolete -xi:- prefix) then -margins- will not know that these are indicator variables and will instead give you its calculation of the first derivative of the outcome probability with respect to var3 (assumed to be continuous), again with all other variables set to their actual values in the data set.

Notes: 1. The all other variable set to their actual values in the data set part can be overridden with at() options if you prefer to specify otherwise.

2. I have assumed that you literally used the -probit- command. If you ran -ivprobit- or -xtprobit-, then -margins- calculates marginal effect on xb by default, not on predicted probability. (But you can get predicted probability by specifying the -predict(pr)- option.

-mfx- was around for a long time, so it is likely that most of its bugs or errors were worked out long ago.

So it is not a question of which one is correct. Both are giving correct answers, but probably are answering different questions. I've outlined above the questions that -margins- answers--and how it depends on what your -probit- command looked like. I don't know what question -mfx- answers. And, of course, only you know which question you actually wanted to ask.

[Richard Williams]

I don't have Stata handy but I think if you added the atmeans option to margins the two would match up pretty well. Any other differences might be due to one command treating a dichotomy as categorical while the other treated it as continuous, but there are ways to fix that too.

[Li Mueller]

Thanks Clyde and Richard for your input!

Richard, I tried to specify the atmeans option, but I don't get the same results.
I specified the "i" for the dummies, like Clyde suggested and tried running the mfx command again and got the following error message: default predict() is unsuitable for marginal-effect calculation.


I now ran a new probit regression (excerpt):

probit withdrawn log_filing_size i.ff_tech_dummy i.vc_dummy

.margins, dydx(*)

My results look the following now (excerpt):


| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
log_filing_size | -.0169683 .0016812 -10.09 0.000 -.0202635 -.0136732
1.ff_tech_dummy | -.012848 .007352 -1.75 0.081 -.0272577 .0015618
1.vc_dummy | -.0412084 .0049348 -8.35 0.000 -.0508804 -.0315363

Is my interpretation right that a one unit change in log_filing_size decreases the withdrawal probability (dependent variable) by 0.0169?

[Clyde Schechter]

First, sorry if my suggestion was confusing. I didn't mean to use factor variable notation for the -mfx- command: it's an older command and doesn't work with factor variable notation. I meant it only as applied to model you would follow with -margins-. I think for -mfx- you have to back to the old-fashioned approach.

You did run that as I had imagined, and your interpretation of the results is pretty much correct. The only thing I would do is qualify that to say that that's the marginal effect of a unit change in log_filing_size on probability of outcome conditional on the distribution of all the model variables being what they are in the data set. With non-linear models like logit or probit you always have to be careful to condition estimates of marginal effect on probability on whatever values were actually used to calculate them.

[Li Mueller]

Perfect, I understand! Thanks so much for your help & effort!

[Richard Williams]

Li, I don't know exactly what you did since you didn't show all your commands and output (please see #12 in the FAQ for instructions on doing so) but here is an example of what I was talking about. But in any event, it is better to use margins anyway.

. webuse nhanes2f, clear

. logit diabetes weight height, nolog

Logistic regression                             Number of obs     =     10,335
                                                LR chi2(2)        =     130.28
                                                Prob > chi2       =     0.0000
Log likelihood = -1933.9288                     Pseudo R2         =     0.0326

------------------------------------------------------------------------------
    diabetes |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   .0301604   .0028288    10.66   0.000     .0246161    .0357048
      height |  -.0473011   .0052236    -9.06   0.000    -.0575391   -.0370631
       _cons |   2.671749   .8062233     3.31   0.001      1.09158    4.251917
------------------------------------------------------------------------------

. mfx

Marginal effects after logit
      y  = Pr(diabetes) (predict)
         =  .04353047
------------------------------------------------------------------------------
variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
---------+--------------------------------------------------------------------
  weight |   .0012557      .00011   11.09   0.000   .001034  .001478   71.9031
  height |  -.0019694      .00021   -9.46   0.000  -.002377 -.001561   167.653
------------------------------------------------------------------------------

. margins, dydx(*) atmeans

Conditional marginal effects                    Number of obs     =     10,335
Model VCE    : OIM

Expression   : Pr(diabetes), predict()
dy/dx w.r.t. : weight height
at           : weight          =    71.90313 (mean)
               height          =     167.653 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   .0012557   .0001132    11.09   0.000     .0010338    .0014777
      height |  -.0019694   .0002081    -9.46   0.000    -.0023774   -.0015615
------------------------------------------------------------------------------

[Li Mueller]

Sorry, Richard! I just tried to use the margins atmeans option again and it worked. You are right!
I know, it's a little off topic, but maybe you can help me regarding robustness checks for a probit model: Is it possible to use the commands rcheck or checkrob for a probit model, too? Or are there any other useful Stata commands for this purpose?