I was led to believe that when conducting quantile regression you would expect intercept values to increase as you go up quantiles. However, I have run a quantile regression and the intercepts are as follows:
QUANTILE : INTERCEPT
- 0.2: 11.74 (7.90, 16.24)
- 0.3: 12.85 (8.54, 20.24)
- 0.4: 14.20 (6.29, 21.54)
- 0.5: 13.83 (6.01, 22.06)
- 0.6: 16.29 (8.73, 21.77)
- 0.7: 17.90 (10.67, 23.73)
- 0.8: 21.14 (14.28, 30.52)
All intercept estimates were significant at p<0.001.
I have identified that by removing one of two variables from the equation the intercept values steadily increase. However, through investigating VIF values I can see no suggestion of multicollinearity. There is also no evidence of a bimodal distribution in the dependent variable which I thought may explain the problem.
I was wondering if anyone else had any suggestions of why this may be occurring? And also whether it is a problem, as I would need to explain it in my PhD thesis.