Opposite signs of average marginal effects after probit

[Sergio Ponguane]

Hello everyone

A probit regression generated the following output


Probit regression Number of obs = 984
LR chi2(8) = 244.09
Prob > chi2 = 0.0000
Log likelihood = -559.84938 Pseudo R2 = 0.1790


account Coef. Std. Err. z P>z [95% Conf. Interval]

female
Female .3697763 .0875213 4.22 0.000 .1982378 .5413148
age -.0329384 .0104788 -3.14 0.002 -.0534765 -.0124002

c.age#c.age .0003704 .0001142 3.25 0.001 .0001467 .0005942

educ
secondary -.9238785 .1031009 -8.96 0.000 -1.125953 -.7218045
(dk) 0 (empty)
(rf) 0 (empty)

inc_q
Poorest 20% 1.03113 .14691 7.02 0.000 .7431919 1.319068
Second 20% .7203338 .1374601 5.24 0.000 .450917 .9897505
Middle 20% .5281499 .1324182 3.99 0.000 .2686149 .7876849
Fourth 20% .598695 .1247253 4.80 0.000 .3542378 .8431521
Richest 20% 0 (omitted)

_cons .2244745 .2359353 0.95 0.341 -.2379502 .6868992


after margins , dydx(_all)

I obtain this

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female |
Female | .1209884 .028537 4.24 0.000 .065057 .1769198
age | -.0024337 .0011359 -2.14 0.032 -.00466 -.0002073
|
educ |
secondary | -.3247773 .0347708 -9.34 0.000 -.3929269 -.2566277
(dk) | . (not estimable)
(rf) | . (not estimable)
|
inc_q |
Poorest 20% | 0 (omitted)
Second 20% | -.1029302 .0510511 -2.02 0.044 -.2029885 -.0028719
Middle 20% | -.1702077 .0505627 -3.37 0.001 -.2693088 -.0711065
Fourth 20% | -.1453447 .0489363 -2.97 0.003 -.2412581 -.0494312
Richest 20% | -.3522531 .0481034 -7.32 0.000 -.4465339 -.2579722
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

my concern is the opposite signs obtained on the categorical variable inc_q after margins , dydx(_all)

Can someone help? Is this normal?

[Richard Williams]

Hi Sergio. First, your output would be much easier to read if you used code tags. See the Statalist FAQ if you don't know how to do that.

It might also be helpful to see the actual probit command.

Second, I'm not seeing any contradiction. In the probit, the largest coefficient is for Poorest 20%. Therefore, with that as the reference category, the ME for every other outcome will be less likely than that.

[Sergio Ponguane]

Thanks Richard

I have gone through the Statalist FAQ as suggested and I hope now is readable

Probit regression                                 Number of obs   =        984
                                                  LR chi2(8)      =     244.09
                                                  Prob > chi2     =     0.0000
Log likelihood = -559.84938                       Pseudo R2       =     0.1790

------------------------------------------------------------------------------
     account |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |
     Female  |   .3697763   .0875213     4.22   0.000     .1982378    .5413148
         age |  -.0329384   .0104788    -3.14   0.002    -.0534765   -.0124002
             |
 c.age#c.age |   .0003704   .0001142     3.25   0.001     .0001467    .0005942
             |
        educ |
  secondary  |  -.9238785   .1031009    -8.96   0.000    -1.125953   -.7218045
       (dk)  |          0  (empty)
       (rf)  |          0  (empty)
             |
       inc_q |
Poorest 20%  |    1.03113     .14691     7.02   0.000     .7431919    1.319068
 Second 20%  |   .7203338   .1374601     5.24   0.000      .450917    .9897505
 Middle 20%  |   .5281499   .1324182     3.99   0.000     .2686149    .7876849
 Fourth 20%  |    .598695   .1247253     4.80   0.000     .3542378    .8431521
Richest 20%  |          0  (omitted)
             |
       _cons |   .2244745   .2359353     0.95   0.341    -.2379502    .6868992
------------------------------------------------------------------------------

the probit command is

probit account i.female age c.age#c.age  i.educ ibn.inc_q

after margins , dydx(_all)

I obtained the following margins

Average marginal effects                          Number of obs   =        984
Model VCE    : OIM

Expression   : Pr(account), predict()
dy/dx w.r.t. : 2.female age 2.educ 4.educ 5.educ 1.inc_q 2.inc_q 3.inc_q 4.inc_q 5.inc_q

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |
     Female  |   .1209884    .028537     4.24   0.000      .065057    .1769198
         age |  -.0024337   .0011359    -2.14   0.032      -.00466   -.0002073
             |
        educ |
  secondary  |  -.3247773   .0347708    -9.34   0.000    -.3929269   -.2566277
       (dk)  |          .  (not estimable)
       (rf)  |          .  (not estimable)
             |
       inc_q |
Poorest 20%  |          0  (omitted)
 Second 20%  |  -.1029302   .0510511    -2.02   0.044    -.2029885   -.0028719
 Middle 20%  |  -.1702077   .0505627    -3.37   0.001    -.2693088   -.0711065
 Fourth 20%  |  -.1453447   .0489363    -2.97   0.003    -.2412581   -.0494312
Richest 20%  |  -.3522531   .0481034    -7.32   0.000    -.4465339   -.2579722
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

Now, when you look at the factor levels there are negative signs but the coefficients in the probit output are positives. Is it right?

[Richard Williams]

Thanks Sergio. I think part of the confusion comes from having different reference categories in the probit part and in the margins. I suggest you change the probit part to

i.inc_q

You should then see negative signs in both the probit and the margins.

[Sergio Ponguane]

Many thanks Richard

That was the case. Now I see negative signs in both the probit and the margins