My first reaction was to dismiss what you are saying about

multicollinearity and argue that part of the reason we get the "wrong

sign" sometimes, because we aren't very good at figuring what

the "right sign" should be in cases where we have highly collinear

variables. (We are not good at running regressions in our heads.)

Add in the decreased precision due to multicollinearity and we often

end up with a "wrong sign."

But this got me thinking. Suppose we have the following model.

Y = B0 + B1*X + B2*Z + U1

Suppose that X and Z are highly correlated but the relationship is

nonlinear. Suppose also that Y has a nonlinear relationship with X.

In this case B2 would be picking up some combination of the linear

relationship between Y and Z, plus some of the nonlinear relationship

between Y and X. In some cases, the latter effect could dwarf the

former leading to statistically significant "wrong" sign for B2.

I have never seen any textook mention this possibility (econometrics

texts tend to give very shortshrift to multicollinearity issues), but

I could see this being a pretty pervasive problem. In my own work, I

have been struck by how often putting in two highly multicolinear

variables resulted in one of the two having a statistically

significant estimate in the direction opposite of what I expected.

I tried to a little simulation of this, and it is not very hard to

simulate cases where what I describe above could occur. Strictly

speaking, this is a model mispecification issue exacerbated by

multicolinearity and measurement error, but adding squared terms

won't necessarily fix the problem.

Best wishes,

Dan

--- In APBR_analysis@yahoogroups.com, "jsm_44092" <tpr42345@a...>

wrote:> Strange things can happen when regressions are run with correlated

page

> predictors, including coefficients having the "wrong" sign. (The

> signs really aren't wrong, they just look wrong, as I explain on

> 131 of my book, and signs can be "wrong" even without high

was

> correlations between predictors, as I illustrated in the book.) I

> motivated to write the book by the fact that no textbook author had

done

> discussed some of these important issues.)

>

> Dan, I suspect that problems caused by multicollinearity could

> possibly dwarf the deleterious effects of measurement error in what

> you are doing, but I don't have a feel for that since I haven't

> the work that you have.

I

>

> Some of you seem to be making modeling basketball your life's work.

> am also interested in the subject, although I have limited time to

> think about it.

>

>

> Tom