Interpreting a positive interaction term when the two main effects are negative

[amira elshal]

Hi everybody,

I am running the model below:

Profits = a + b.Woman + c.Corruption + d.(Woman*Corruption) + ... + Error
Woman: Dummy variable=1 for women
Corruption: Continuous variable

When I ran the model (code below), both b and c are negative (as expected) but d is positive and significant. How can d be interpreted?

reg profits c.corruption##i.female_manager i.subsector i.size_firm i.country_dummy i.year_dummy, vce(cluster id)

Thank you in advance.

Best regards,
Amira

[Bruce Weaver]

It is the difference in the simple slopes for male and female managers. The sign will depend on which is subtracted from which. Here's a simplified example using the auto dataset.

clear
sysuse auto
generate wtk = weight/1000
regress mpg c.wtk##i.foreign
* Get simple slopes for domestic and foreign cars
margins foreign, dydx(wtk)
display "Foreign slope - domestic slope = " -10.426-(-5.975)

HTH.

[Carlo Lazzaro]

Amira:
one of the easiest way to have an idea of what is going on, is to add the -allbaselevels- option to your code:

reg profits c.corruption##i.female_manager i.subsector i.size_firm i.country_dummy i.year_dummy, vce(cluster id) allbaselevels

Another approach is to display the coefficients matrix via:

mat liste(b)

Eventually, what you experienced is (with a bit of guess-work, as you did not share what you typed and what Stata gave you back, as per FAQ) due to the fact that you do not center -corruption- around its mean. Hence, how do your results change if you replace -corruption- with -centered_corruption-?

[Richard Williams]

Once you add interaction terms, the meaning and interpretation of main effects changes.

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

[amira elshal]

Many thanks to you all for your prompt responses.

Bruce Weaver: Thank you. So, in my example, if the interaction term is positive and the two main effects are negative, this means that the profits of male-managed firms are more negatively affected by corruption?
Carlo Lazzaro: I added "allbaselevels" as per your suggestion and the signs are the same. So, hopefully I am on the right track. Thank you.
Richard Williams: I will update the interpretation accordingly. Thank you.

[amira elshal]

Here is what I got when I displayed the coefficients separately. ind_instit_final2 reflects the corruption level.

[Bruce Weaver]

Using the output in #6:

. display "Coefficient for female_manag#ind_instit_final2 = " as result 0.152 - (-.004)
Coefficient for female_manag#ind_instit_final2 = .156

Is that the value you see in your table of coefficients?

[amira elshal]

Yes, this is the value I see in my table. Does this mean that the profits of male-managed firms are more negatively affected by corruption?

[Bruce Weaver]

Regarding the linear relationship between corruption and profits, the slope = -0.004 for male-managed companies and 0.152 for female-managed companies. Your output in #6 shows that neither of those simple slopes is significantly different from 0 (assuming alpha = .05). The difference between those (simple) slopes is 0.156. From what you've presented, I can't tell if that difference in slopes is statistically significant or not--you'll have to look at the t-test for the interaction term in your model for that information.

Regarding the terms that you are calling the main effects:

• The coefficient for corruption shows the simple slope for corruption when female_manag = 0 (i.e., the simple slope for males). (In this case, it will be -0.004, the dy/dx value for female_manag = 0 in #6.)
• The coefficient for female_manag shows the F-M difference when corruption = 0.

You haven't said anything about the scaling of your corruption variable, so it's impossible to say whether 0 is a possible value for it or not. See the notes Richard Williams posted in #4 for more details & examples.

HTH.