Centering to reduce collinearity of x^2?

  • Context: Graduate 
  • Thread starter Thread starter wvguy8258
  • Start date Start date
Click For Summary
SUMMARY

This discussion focuses on the implications of centering independent variables in regression models, specifically regarding the relationship between X and X^2. Centering by subtracting the mean from X before exponentiation is a common method to address collinearity, but it alters the relationship to a U-shape, complicating interpretations of parameter estimates. The user, Seth, notes that while model fit and significance remain unchanged, the parameter estimates differ significantly between centered and non-centered datasets. This highlights the importance of understanding how centering affects the interpretation of regression coefficients.

PREREQUISITES
  • Understanding of regression analysis and its components
  • Familiarity with collinearity and its effects on regression models
  • Knowledge of variable transformation techniques in statistical modeling
  • Experience with statistical software for regression modeling (e.g., R or Python)
NEXT STEPS
  • Explore the concept of centering in regression analysis and its impact on parameter estimates
  • Learn about polynomial regression and the interpretation of U-shaped relationships
  • Research methods for transforming parameter estimates between centered and non-centered models
  • Investigate the use of splines in regression modeling for handling non-linear relationships
USEFUL FOR

Data scientists, statisticians, and researchers involved in regression modeling who seek to understand the effects of variable transformation and collinearity on model interpretation.

wvguy8258
Messages
48
Reaction score
0
Hi,

I would like to exponentiate the values of independent variables in a regression model, possibly using splines. I know that collinearity between X and X^2 is to be expected and the standard remedy is to center by taking X-average(X) prior to exponetiating. This seems odd to me because it will change the shape of the relationship between X and X^2 to one that is U-shaped, not monotonic. For example, if after centering you have

-2
-1
0
1
2

then the formerly lowest value will now be equal to the highest when squared. This seems to disrupt the idea that lower values have a lesser effect, let's say. What am I not getting that makes this make sense to do? Thanks. Seth
 
Physics news on Phys.org
Since X and X^2 are monotonically related, they have a high correlation. When their relationship is U-shaped, they are not, and that's the tradeoff.
 
Hi,

A trade-off implies that it is a bit of a pain in the butt, I suppose. I hadn't played around with this much before posting. I made a small sample data set with and without variable centering. The model fit and significance levels were identical but the parameter estimates were very different for the linear term X and intercept. The noncentered version returned the parameter estimates I used to create the sample data. The centered data set returned the same parameter estimates for the squared term but not the linear term, the intercept was much different as well. I've since learned that the parameter estimates after centering reflect the linear trend when X = 0 (at the mean). Working now on a formula to transform parameter estimates between equation systems so that I understand this a bit more. I can see this should be possible when only X and X^2 are in the right side of the equation. My feeling is that understanding the variables in terms of their untransformed state will not be possible if several variables are transformed and so are all adding to changing the intercept away from what it would if the data were not centered. Anyone know a link that shows the equation I'll be looking for per the last few sentences? Thanks. -seth
 

Similar threads

Undergrad What is the expected value of Cov(x,y)2 in an independent X and Y scenario?
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Interpreting the Association Between y and x while Holding the Group Constant
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Bayesian Priors and relation with ignorance
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How to find which variables w, x, y.... 'most' influence z?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
  • · Replies 4 ·
Replies
4
Views
3K
High School How do I invert this exponential function?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Plotting polar equations and scale invariance
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Can We Construct a Coordinate Chart Where Bell Observers Are At Rest?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Modeling the damping of a physical rigid pendulum
  • · Replies 1 ·
Replies
1
Views
2K
Area between 2 curves, Volume around X and Y, Centroid
  • · Replies 1 ·
Replies
1
Views
2K