Let me give an example inspired by Richard William's presentation, and the Stata command margins
.
webuse nhanes2f, clear
keep if !missing(diabetes, black, female, age, age2, agegrp)
gen femage = female*age
label variable femage "female * age interaction"
probit diabetes black female age, nolog
Probit regression Number of obs = 10,335
LR chi2(3) = 380.15
Prob > chi2 = 0.0000
Log likelihood = -1808.992 Pseudo R2 = 0.0951
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diabetes | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
black | .3567259 .0638644 5.59 0.000 .231554 .4818978
female | .0859841 .0450391 1.91 0.056 -.0022909 .1742592
age | .0271895 .0016318 16.66 0.000 .0239912 .0303879
_cons | -3.215875 .1015044 -31.68 0.000 -3.41482 -3.01693
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Among other things, the results show that getting older is bad for your health (surprise!) – but just how bad is it?
Adjusted predictions (also known as predictive margins) can make these results more tangible. With adjusted predictions, you specify values for each of the independent variables in the model, and then compute the probability of the event occurring for an individual who has those values. Using the mean values for the other independent variables (female, black) that are in the model, we get:
margins, at(age=(20(10)70)) atmeans
Adjusted predictions Number of obs = 10,335
Model VCE : OIM
Expression : Pr(diabetes), predict()
1._at : black = .1050798 (mean)
female = .5250121 (mean)
age = 20
2._at : black = .1050798 (mean)
female = .5250121 (mean)
age = 30
3._at : black = .1050798 (mean)
female = .5250121 (mean)
age = 40
4._at : black = .1050798 (mean)
female = .5250121 (mean)
age = 50
5._at : black = .1050798 (mean)
female = .5250121 (mean)
age = 60
6._at : black = .1050798 (mean)
female = .5250121 (mean)
age = 70
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| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | .0063084 .0009888 6.38 0.000 .0043703 .0082465
2 | .0113751 .0013794 8.25 0.000 .0086715 .0140786
3 | .0204274 .0017892 11.42 0.000 .0169206 .0239342
4 | .0364184 .0021437 16.99 0.000 .0322167 .04062
5 | .0641081 .0028498 22.50 0.000 .0585226 .0696935
6 | .1104379 .005868 18.82 0.000 .0989369 .121939
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The results show that a 20 year old has less than a 1 percent chance of having diabetes (.0063084), while an otherwise comparable 70 year old has an 11 percent chance (.1104379).