Question re the effect of X on the variance of Y

[Spencer Williams]

Hi everyone,

I'm currently using Stata to test the effect of an independent variable X on a dependent variable Y while controlling for a number of other potential explanatory variables. I'm testing both linear and non-linear relationships.

I'm wondering if there is a way for me to specifically examine the effect of X on the variance of Y. The theory that I am testing predicts that an increase in X leads to an increase in the mean of Y, but also that an increase in X leads to an increase in the variance of Y. That is, as X increases, the average value of Y increases, but the spread of Y also increases.

Is there a good way to test (ideally in Stata) for how the variance of Y responds to X?

Thanks for the help!

[Clyde Schechter]

Well, I would approach this by looking at the residuals: y - yhat, where yhat is the predicted value of y from a given model (-help predict- if you aren't familiar with the command). If the model is a proper specification of the mean of y, then the variance of y will be reflected in the variance of the residuals. You can then explore the relationship between X and the residual.

[Nick Cox]

https://www.crcpress.com/Transformat.../9780412014215 is one source looking at variance functions.

[Maarten Buis]

Quantile regression jumps to my mind. With that you can model how the median reacts to changes in x, but also how other percentiles react to changes in x, e.g. the 25th and 75th percentiles, which together define the interquartile range.