Compare dummy variables in a regression analysis (not to baseline but among each other) ?

noel

New Member
#1
For my regression, I have a variable that has 5 levels (5 different government interventions). Since, I cannot assume the distances between the levels to be the same, I had to split the variable into 4 dummy variables. Now I get statistical information about the direct comparison between each of the dummies and the baseline. However, I don’t get any information on the relationship between the four dummies among each other. I was wondering if there is any way to compare them within the regression (for example compare dummy 2 to dummy 3)

Example:
So if my variable for example had the values {green, blue, red, yellow, black}, then I would make four dummies and let green for example be the baseline. now i know how all the clolours compare to green but how can I also want to know the relationship between blue and red.

Thanks in advance
 
#2
You can compare other categories to one another using the difference in regression coefficients:

Delta_km = Beta_category_k - Beta_category_m.

Using the covariance matrix of the regression coefficients, you can calculate the standard error of Delta_km and see if Delta_km is statistically significant.