http://spssx-discussion.165.s1.nabble.com/Inconsistent-Beta-Coefficient-Sign-Between-Multiple-and-Simple-Regression-tp5026243p5027572.html
There are two ways to regard multicollinearity. The strictly-mathematical
approach says "no multicollinearity exists, if it doesn't create a near-zero
as a divisor." Your comments reflect that tradition.
Multicollinearity that messes up the easiest conclusions is indicated, by looser
definition, when there are loadings in the opposite direction from the correlation.
Or when you have any standardized coefficient greater than abs(1).
I always use those guides rather than the VIF but I think your results show
that your use of the VIF isn't sensitive enough.
Your result shows that some difference between variables adds more to
the prediction than taking their sum. (Sometimes, the solution is as easy
as computing the simple DIFF= A- B for two related variables on the same
scale. If you also have scaling problems, taking a ratio may simply the
relations.)
See "suppressor variables". I get 91 hits when I Google Groups for
< suppressor author:ulrich >
--
Rich Ulrich
> Date: Sun, 27 Nov 2011 02:57:27 -0800
> From:
[hidden email]> Subject: Inconsistent Beta Coefficient Sign Between Multiple and Simple Regression
> To:
[hidden email]>
> I am conducting a multiple Linear regression with 3 predictors, all variables
> are continuous and N=51. Before doing linear regression analysis, I did
> first a simple linear regression and found that all the predictors have
> positive correlation with the outcome variable.
> Surprisingly, when I did the multiple linear regression, one of the
> predictors have negative B unstandardized coefficients, with less than -1.0
> coefficient, VIF value less than 10, and these are no indication of
> multicollinearity problem.
>
> Is there anything wrong with the result? Please kindly give any advice how
> to explain this case.
>
> Thank you.
> Joe