Coefficient sign varys over the distribution of the dependent variable


Lets say I am estimating a linear regression with Y as a continuous DV and X as a binary IV. Based on theoretical reasons I am assuming that X has a positive effect on Y in the first quartile of the DV and a negative effect in the other quartiles. If I split the sample this assumption is confirmed.

How am I able to model this relationship without splitting the sample? Quantile regression has produced different results than the splitting of the sample. Are there any other options?

Thank you for your help.


Omega Contributor
Hmm. Let us probe this some more. Can you provide a scattergraph where you have continuous variable on the y-axis and the x-axis is X=1 and X= 0, so kind of like a boxplot without the boxes. Make sure to use a jitter or color gradient on the plots if they are at time directly on top of each other.

I have heard a critique of quantile regression, based on other researchers not having the same sample distribution as you, so their quantiles may not be the same, so generalizing results could be troublesome. Which this critique seems reasonable.