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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.

Thanks

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    $\begingroup$ You’re fitting a series of straight lines or linear surfaces. Each is best for the quantile specified, but a monotonic increase in intercept is not guaranteed any more than parallel lines, planes or hyperplanes. $\endgroup$ – Nick Cox Mar 27 at 10:55

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