Interpretation of Regression Table

[Yusuf Ziya Eksi]

In the model below we look at whether or not respondents worked more than 40 hours per week (hardwork, 0 ≤ 40 hours per week, 1 > 40 hours per week) in Germany. Working overtime is explained with the variables female (reference male), east (reference West-Germany), the interaction between east and female, age centered at 40 in decades, and the respondent’s pseudo-years of education centered at 11 (=Realschule or middle general secondary education + vocational). We expand this a bit more by looking at part-time (< 40 hours a week), full time (40 hours a week) and more than full-time (> 40 hours per week). Could you please help me to interpret the relative risk ratios especially for the interaction effect?

[Sule Yaylaci]

Hi, Yusuf Ziya.
An RR 1.00 indicates that the risk is comparable between two groups, and a value greater than 1.00 indicates increased risk. Keeping this in mind, in the more_than_full_time model (and in all interaction models for that matter), the main effects of the variable used in interaction show the effect of each variable when the other variable in interaction is at its base level. So, the main effect of female shows the effect of being female from West Germany, and the main effect of East shows the effect of being from the East for Males. So, we can interpret the 'female' variable as the following: The risk of working over time for females from the West relative to full_time is lower than males from the West as compared to the outcome of working full_time. More specifically, the coefficient .61 means that the risk of working over time relative to working full-time is .39% lower for females from the West than males from the West. Now, when we look at the interaction, it shows the difference between females from the West and East, and it appears that females from the East have even a lower likelihood than females from the West to work over time. But for part_time model, females from the West are at a higher risk of working part_time (as compared to the odds of working full_time) than Males from the West(because the coef 4.5 is higher than 1). Yet, this effect is less strong for females in the East (given the negative direction of the interaction term). I usually find it easiest to look at the marginsplot to make more sense of the interactions. To find the marginal effects of variables when they appear in a model that includes them in an interaction term, the following commands can be helpful.

 margins female#East, predict(outcome(more_than_full_time))
marginsplot recast(bar) xdimension(female east)

margins female#East, predict(outcome(full_time))
marginsplot recast(bar) xdimension(female east)

 margins female#East, predict(outcome(part_time))
marginsplot recast(bar) xdimension(female east)

Alternatively, you can also use:

margins female, at (East=0 1) predict(outcome(INSERT WHATEVER OUTCOME YOU ARE INTERESTED IN))

See https://www.stata.com/manuals/cmmargins.pdf for further help with more advanced options.
I hope this helps some.