# Marriage is good for your income

For those of you who are into machine learning, here you can find a cool collection of databases to play around with your favorite algorithm. I choose one out of the available 200 and fit a logistic regression model. The idea is to see what kind of properties are common for those who earn above 50K a year. Our data is such that the “y” variable is binary. A value of 1 is given if the individual earns above 50K and 0 if below. We know many things about the individual. Level of education in years, age, is she married, where from, which sector is she working in, how many working hours per week, race, and more. We can fit logistic regression, which is quite standard for a binary dependent variable, and see which variables are important.

Result:

A variable between 0 and 1 means that it has negative influence on the probability to earn above 50K. The higher the coefficient the more positive influence it has. However, most of the coefficients are insignificant:

Estimate Std. Error z value P.val
(Intercept) -8.9309 0.4451 -20.06 0.0000
age 0.0428 0.0021 20.57 0.0000
edyears 0.3427 0.0115 29.85 0.0000
whperw 0.0321 0.0022 14.33 0.0000
not-married -1.0096 0.0550 -18.37 0.0000
Cambodia 0.8904 0.8982 0.99 0.3216
China -1.3751 0.6159 -2.23 0.0256
Columbia -1.4248 0.9515 -1.50 0.1343
Cuba -0.1931 0.5177 -0.37 0.7091
Dominican-Republic -0.3022 0.8232 -0.37 0.7136
England -0.7531 0.4852 -1.55 0.1207
France -0.8418 1.1822 -0.71 0.4764
Germany 0.3424 0.3910 0.88 0.3812
Greece -1.1965 0.6605 -1.81 0.0701
Guatemala -0.9350 1.1504 -0.81 0.4164
Haiti -0.9143 1.1334 -0.81 0.4199
Honduras -0.0409 1.3071 -0.03 0.9750
Hong Kong 1.0995 1.2604 0.87 0.3830
Hungary -12.8463 882.7434 -0.01 0.9884
India -0.7264 0.4826 -1.51 0.1323
Iran 0.1945 0.5350 0.36 0.7161
Ireland 0.2540 0.7516 0.34 0.7353
Italy 1.1770 0.5147 2.29 0.0222
Jamaica 0.6685 0.5289 1.26 0.2063
Japan 0.2082 0.5782 0.36 0.7187
Laos -12.3934 432.8021 -0.03 0.9772
Mexico -0.6878 0.3607 -1.91 0.0566
Nicaragua -12.3164 244.3564 -0.05 0.9598
Guam-USVI-etc -12.5394 421.4650 -0.03 0.9763
Peru -0.3240 1.1425 -0.28 0.7767
Philippines -0.4033 0.4323 -0.93 0.3509
Poland -0.9650 0.6266 -1.54 0.1236
Portugal 0.0386 0.8386 0.05 0.9632
Puerto-Rico -0.0004 0.5131 -0.00 0.9994
Scotland -12.5727 447.6334 -0.03 0.9776
South -1.4788 0.6520 -2.27 0.0233
Taiwan 0.0304 0.5518 0.06 0.9560
Thailand -0.8068 0.9884 -0.82 0.4143
United-States 0.0049 0.1879 0.03 0.9791
Vietnam -1.5021 0.8277 -1.81 0.0696
Yugoslavia 0.0495 1.3221 0.04 0.9702
Federal-gov 1.1812 0.1939 6.09 0.0000
Local-gov 0.7243 0.1714 4.23 0.0000
Never-worked -9.7524 618.4062 -0.02 0.9874
Private 0.7785 0.1491 5.22 0.0000
Self-emp-inc 1.4118 0.1863 7.58 0.0000
Self-emp-not-inc 0.4238 0.1678 2.53 0.0115
State-gov 0.5512 0.1887 2.92 0.0035
Without-pay -10.6696 622.2566 -0.02 0.9863
Asian-Pac-Islander 0.4790 0.3931 1.22 0.2230
Black 0.0179 0.3375 0.05 0.9576
race – Other -0.6295 0.5792 -1.09 0.2771
White 0.4567 0.3230 1.41 0.1573
Male 0.8382 0.0643 13.05 0.0000

So… what is important?

1. We can see that males has better chance to earn more.
2. Nice to see that race is not important, e.g. being black has no significant effect.
3. Government is a good thing.
4. Being self employed is a good thing.
5. Being from Italy is good thing..  😮
6. working hard is a good thing, “whperw” is working hours per week. However, the value of the coefficient is not high, so don’t work too hard.
7. Older is better, again, the coefficient, despite its importance, is not high.
8. Being educated is important. “edyears” is of years of schooling.
9. Being married is important.  :-D, if you are not married there is a significant negative impact on the chance to earn more than 50K per year.

Notes:

We have a serious endogeneity problem here, in more than one place. For example, you probably wait until you have some money saved in order to get marry to begin with. As another example, you probably open your own company only after you earn enough so that you pay less taxes as a company inc.

So, we can interpret these results more as common features shared by the rich group, and less for causality. It can be used for example to slice the market into potential buyers (people with money), according to their characteristics without the need to go into their bank account statement. Thanks for reading, code and references below.

Related:

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1. eshilts says:

Consider plotting the coefficients from greatest to least effect. In ggplot2 you can do this by reordering the levels of the names of your coefficients. See ?reorder.

2. eshilts says:

Hit Post too soon.

Also, you can show that most variables are insignificant by plotting error bars using geom_errorbar(), geom_segment(), etc. I recommend posting your plotting code as well.

3. Fred says:

Cool, an interesting analysis. To follow-up on eshilts’s comment on error bars, this kind of study might be subject to the Texas-Sharpshooter’s fallacy, and there may need to be a multiple comparisons correction for the confidence intervals.

Cheers,
Fred