Graph for regression with inverted U-shape and moderators

[Hanna Marie]

Hello,

I hope to get some help with Stata again.

I would now like to graph the inverted U-shape relationship between q_tot (dependent variable) and rdalliances (independent variable).

My regression still looks like this:

Code:

xtreg q_tot rdalliances rdalliances_2 rdi_w adi_w ln_emp1_w lev_w
​​​​​​​

with 4 control variables (rdi_w, adi_w, ln_emp1_w and lev_w


My questions:

1) Is there a special command to use for a graphic solution in the presence of an inverted U-shape relationship?

2) And what to I have to do, if I want to include a moderator in the graph to show, if the moderator compresses or stretches the main relationship?

Thanks in advance.

Kind regards,
Hanna

[George Ford]

Here's a start.

Re-specify using interactions.

xtreg q_tot c.rdalliances##c.rdalliances rdi_w adi_w ln_empl_w lev_w
margins, over(rdalliances)
margingsplot

Also see

https://stats.oarc.ucla.edu/stata/seminars/interactions-stata/
https://stats.oarc.ucla.edu/stata/faq/how-can-i-use-the-margins-command-to-understand-multiple-interactions-in-regression-and-anova-stata-11/

may youtube videos on it.

[Maarten Buis]

Also see http://maartenbuis.nl/wp/inter_quadr/inter_quadr.html

[Hanna Marie]

Hello George and Maarten,

thanks for your help!

I followed the description of the Paper Maarten posted and got the following graphic. I overwrote my Stata code by accident, that is why I can't post it here, but I did the exact same steps as written in the paper.

Dependent Variable : Total Q (q_tot)
Independent Variable: R&D Alliances (rdalliances)
Moderator: Munificence (munificence)

I do not really understand the graphic as it does not really show the inverted U-shape the U-test (utest) predicted me with its highly significant result.

Could somebody help mw with this issue?

Thanks and kind regards,
Hanna

[Roman Mostazir]

Show the regression commands and the results you have used as you have been requested to in the FAQ section. In the original post #1, your regression equation does not have any moderation (munificence) variable and in the last one #4, you have a moderation variable. Obviously the inverted u relationship you have seen in #1 will be different now after #4 and that should be reflected in your regression results which we cannot see because you have not posted them. You are not helping us by not posting them. Anyway on the problem: Maarten's codes are for earlier versions of Stata before 'margins' was introduced. You can try the codes below (I added the munificence interaction term):

xtreg q_tot c.rdalliances##c.rdalliances##c.munificence rdi_w adi_w ln_emp1_w lev_w

qui su munificence
loc m : di %8.2f r(mean)
loc m1sd : di %8.2f r(mean)+r(sd)
loc m2sd : di %8.2f r(mean)+r(sd)*2
loc m_1sd : di %8.2f r(mean)-r(sd)
loc m_2sd : di %8.2f r(mean)-r(sd)*2

margins, at(rdalliances=(0 (5) 60) munificence=(`m_2sd' `m_1sd' `m' `m1sd' `m2sd' ))

#delimit ;
marginsplot, xdim(rdalliances)  
legend(order(6 "Mean-2SD"  7  "Mean-1SD" 8 "Mean" 9 "Mean+1SD" 10 "Mean+2SD") col(1) pos(3))
;

[Maarten Buis]

Looking at the graph suggests to me that you added rdalliances squared but not rdalliances. That way you forced the maximum/minimum to occur at rdalliances = 0, which is typically not what you want. Something like c.rdalliances#c.rdalliances#c.munificence or c.rdalliances#c.rdalliances##c.munificence. Notice the single # instead of the double ##. What you need is the double ##, so c.rdalliances##c.rdalliances##c.munificence.

There are other problems with your graph, there are 10 lines, while there should be 5. So we really need the code to diagnose what went wrong. I am sorry, but to help you, we need you to do this again and save the do-file.