Solved – Does it make sense to use residuals as an independent variable

by

I recently ran a regression of the following form:

mod <- lm(log(y) ~ log(x))

To examine how y scales as a function of x. I then examined the top 20 (super-linear scaling with respect to predicted trendline) and bottom 20 residuals (sub-linear scaling with respect to predicted trendline), and noticed that all these observations shared startling regularity in a third variable, z. (all the positive residuals have very large values of z and all the negative residuals have very small values of z.)

I want to be able to demonstrate that this is a meaningful, statistically significant pattern. My intuition was to run

lm(z ~ resid(mod))

but this strikes me as wrong. Is there a way to capture this pattern using residuals, or is this the wrong way of thinking about it altogether?

Re: Heteroskedastic Standard Errors

Here is a QQ plot:

enter image description here

Residuals vs. Fitted Values

enter image description here

The second graph in particular is somewhat alarming. Should I be worried about heteroskedastic standard errors with a huge dataset (300,000 obs), if I'm using robust SEs

Contents hide
1 Best Answer
2 Similar Posts:

Best Answer

Well, you want to understand how the residuals could depend on z. So the model you should look at would be

lm( resid(mod) ~ z )

but maybe first (show us) the corresponding plot. But, maybe what you see is that the spread of the residuals depend on z not its mean (heteroskedasticity). Then try a model like

lm( Id(resid(mod)^2) ~ z )

(or replace the square with absolute value.) If this turns out in the confirmative, maybe try a more complex model, a gamlss which permits simultaneous estimation of mean and variance functions. You could look through for some examples.

Similar Posts:

Rate this post

Leave a Comment