i have three positively-correlated predictors that i'd like to include
in a model. any traditional measure suggests that to include them as
is would introduce a good deal of collinearity. really, these are a
great candidate for either taking the sum of the three, or for PCA,
but hypothetically, let's say i wanted to use a residualization trick
for this three-way interaction.
(they are all on a 15 point scale and I predict they will all have
similar positive betas)
X1 will remain as is.
r.X2 = residuals(lm(X2 ~ X1))
r.X3 = residuals(lm(X3 ~ X1 + r.X2)
then:
outcome ~ X1 + r.X2 + r.X3
this is the solution i vaguely recall seeing in a textbook somewhere
under the name "partialization"
- is this kosher?
- should the form of r.X3 be the naive residuals(lm(X3 ~ X1 + X2)?
- should the form of r.X2 be the less-naive residuals(lm(X2 ~ X1 + X3))?
- kyle
ps: yes, i didn't say anything about language here. but it's a
language study
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