How can I perform regression of Y on different quantiles of X?

[Eric Cheung]

Quantile regression typically examines how the independent variable X affects different quantiles of Y, but I would like to investigate the quantiles of the independent variable X instead. Is there a command to achieve this, and would this approach be valid?

[Joseph Coveney]

Quantile regression typically examines how the independent variable X affects different quantiles of Y, but I would like to investigate the quantiles of the independent variable X instead. Is there a command to achieve this . . .

Are you looking for something like this?

sysuse auto
egen double rpr = rank(price), track
regress mpg c.rpr

(I haven't bothered to convert ranks to quantiles.)

. . . and would this approach be valid?

Inasmuch as there's no distributional requirement for a predictor, I'm not sure what you'd be gaining. Do you expect that it will help with interpretability of the regression coefficient?

[Nick Cox]

I can't follow what is wanted here either. Nevertheless I am reminded of

https://www.stata.com/statalist/arch.../msg00395.html

https://www.statalist.org/forums/for...revised-on-ssc

[Eric Cheung]

Quantile regression typically examines how the independent variable X affects different quantiles of Y, but I would like to investigate the quantiles of the independent variable X instead. Is there a command to achieve this, and would this approach be valid?

For example, suppose I estimate the effect of the proportion of low-ability students in a middle school class (maybe measured by their elementary school performance) on other students. Now, I want to examine whether different quantiles of this proportion have varying effects. For instance, if the proportion oflow-ability students in the sample ranges from 1% to 30%, I would like to see whether the effect differs when the proportion is 10%, what the effect is at 15%, and how it changes at 20%.

[Eric Cheung]

Are you looking for something like this?

sysuse auto
egen double rpr = rank(price), track
regress mpg c.rpr

(I haven't bothered to convert ranks to quantiles.)

Inasmuch as there's no distributional requirement for a predictor, I'm not sure what you'd be gaining. Do you expect that it will help with interpretability of the regression coefficient?

Thanks for reply. For example, suppose I estimate the effect of the proportion of low-ability students in a middle school class (maybe measured by their elementary school performance) on other students. Now, I want to examine whether different quantiles of this proportion have varying effects. For instance, if the proportion oflow-ability students in the sample ranges from 1% to 30%, I would like to see whether the effect differs when the proportion is 10%, what the effect is at 15%, and how it changes at 20%.

[Eric Cheung]

I can't follow what is wanted here either. Nevertheless I am reminded of

https://www.stata.com/statalist/arch.../msg00395.html

https://www.statalist.org/forums/for...revised-on-ssc

Thanks for reply, my purpose is:

For example, suppose I estimate the effect of the proportion of low-ability students in a middle school class (maybe measured by their elementary school performance) on other students. Now, I want to examine whether different quantiles of this proportion have varying effects. For instance, if the proportion oflow-ability students in the sample ranges from 1% to 30%, I would like to see whether the effect differs when the proportion is 10%, what the effect is at 15%, and how it changes at 20%.

[Nick Cox]

So, I suggest that you study the linked threads and decide whether they can help. Perhaps what you want is just some flavour of nonparametric regression. Otherwise this seems to hinge on whether you are imagining smooth dependence -- or wanting to bin the data and fit separate models and then combine them, which seems a very unattractive approach to me.

[Joseph Coveney]

. . . I would like to see whether the effect differs when the proportion is 10%, what the effect is at 15%, and how it changes at 20%.

Maybe try something like the following then.

version 18

clear *

sysuse auto

egen double rpr = rank(price), track
quietly replace rpr = (rpr - 0.5) / _N

regress mpg c.rpr

margins , at(rpr = (0.1 0.15 0.2)) post

// Twentieth versus tenth
lincom _b[3._at] - _b[1._at]

exit

It uses Hazen’s rule; more here if you're interested in alternatives.