Plotting correct CIs with coefplot (considering the covariance between two groups )

[Stefan Sliwa]

Dear Statalist forum,

I am trying to plot confidence intervals of a model's interaction effects. However, I noticed that coefplot plots the CIs of the estimated coefficients as if they were independent from each other. Below a working example. Post-estimation tests confirm that the coefficients are not equal. Yet, coefplot draws the CIs in such way that it appears that they overlap. How can I adapt coefplot so that it accounts for the covariance between the two variables? Do I really need to manually extract the coefficient markers and CIs? Thanks a lot!

* I use the community-written package reghdfe
ssc install regdfe

** load sample data
sysuse auto.dta, clear

* Run the reghdfe model with the interaction and test the difference
reghdfe price c.gear##b0.foreign, noabsorb vce(cluster rep78)
test _b[c.gear#0.foreign] = _b[c.gear#1.foreign]
lincom c.gear - c.gear#1.foreign

* Estimate marginal effects for domestic cars (foreign==0)
reghdfe price c.gear##b0.foreign, noabsorb vce(cluster rep78)
margins, dydx(gear) at(foreign==0) noestimcheck level(95) post
estimates store margin_0

* Estimate marginal effects for foreign cars (foreign==1)
reghdfe price c.gear##b0.foreign, noabsorb vce(cluster rep78)
margins, dydx(gear) at(foreign==1) noestimcheck level(95) post
estimates store margin_1

* Plot the results with coefplot
coefplot margin_0 margin_1, xline(0, lc(maroon) lp(dash)) ///
       legend(order(2 "Domestic" 4 "Foreign") holes(1 3))  // CIs are overlapping

[Maarten Buis]

The confidence intervals are correct, but your assumption that overlapping confidence intervals indicate non-significant differences is incorrect. So there is there is nothing you need to do about that graph.