Yesterday I presented a multiple regression analysis of the influence of educational attainment, occupational standing, sex, age and race on total personal income. Today I will summarize the results of a multivariate logistic regression on the probability of earning an above median income.
Recall I utilized the recent IPUMS dataset (2011). The dependent variable for the logistic regression is “Above_Median_Income”, scored 1 if the individual’s total personal income is above or equal to the sample’s median income ($35,000), otherwise scored a 0. Above_Median_Income is regressed on 3 levels of educational attainment, occupational standing, age, 3 categories of race, sex and the interaction of educational attainment with age squared. The logistic regression output is found in Appendix B. Predictive margins will be utilized to summarize the results.
II. Logistic Regression
A. Predictive Margins – Race – Probability Above Median Income
In the case of logistic regression the predictive margin on the vertical axis captures probability. In the following graph white probability of attaining an income equal to or exceeding $35,000 peaks at approximately 50 years of age (Pr=.62).
”Other races” and “Blacks” exhibit lower probabilities of attaining an above median income at age 50 with Blacks having the lowest probability (Pr=.49).
B. Predictive Margins – Education – Probability Above Median Income
Individuals with a “Bachelor’s degree or more” have an 82% probability of attaining an above median income at age 50. In comparison to people with a ”Bachelor’s degree or more” or “Some college” individuals with a “high school diploma or less education” are substantially disadvantaged in their chances of attaining an above median income.
C. Predictive Margins – Sex – Probability Above Median Income
Males enjoy higher probabilities of enjoying an above median personal income than females. At age 5o males have a 67% chance of attaining an above median personal income. The female probability at the same age is .52.
D. Predictive Margins – Education and Sex – Probability Above Median Income
The probability ranking of achieving an above median total personal income (highest to lowest) is:
- Bachelor’s degree or more, Male
- Bachelor’s degree or more, Female
- Some college, Male
- ‘High school diploma, Male” and ‘Some college, female’ exchange positions at the lower and upper tails of their probability distributions
- High school diploma or less, Female
E. Predictive Margins – Occupational Standing – Probability Above Median Income
It’s not surprising to observe the above relationship of above median income associated with occupational standing (Duncan’s socio-economic index). People in the lowest occupational standing quartile have less than a 5% chance of attaining an above median income at their peak probability!
Appendix B – Logistic Regression Output
Data Source
Steven Ruggles, J. Trent Alexander, Katie Genadek, Ronald Goeken, Matthew B. Schroeder, and Matthew Sobek. Integrated Public Use Microdata Series: Version 5.0 [Machine-readable database]. Minneapolis: University of Minnesota, 2011.