I have data with high co-linearity and I am trying to apply the multivariate regression using SPSS .I need to know if there is any method to perform multi linear regression for two variables which had been individually regressed to the target variable using polynomial model of power two. ?
Hi, See the references in the link below. Best, David
https://www.google.com/search?q=collinearity+in+Polynomial+regression&ie=utf-8&oe=utf-8&client=firefox-b-1
Effect size interpretation with polynomials (var^n) can be hard and it can break down due to multicollinearity (Ask for variance inflation factors. Above 10?)
You can:
See if different transformations (Google Tuckeys ladder) can either make the relationship linear, or the polynomials less correlated
If VIF is high, does centering (var - mean) or scaling (z-scores) help?
However, your main problem is using SPSS. In Stata or R you can solve this easily by introducing (SAS, but I dont know it)
-Orthogonal polynomials or
- Restricted cubic splines
They are uncorrelated, so collinearity goes away. Several options for non linear modeling. With the former, effect size is directly interpretable.
Good luck
Don't forget that if you use multivariate polynomials, you should include polynomial terms with cross-products of the variables, to avoid imposing a specific shape to the polynomial surface. Hence, the number of parameters increases very quickly with the number of variables...
For instance, for two variables x1 and x2, the model should include not only x1, x2, x1^2 and x2^2, but also x1 * x2.
This means also that, in R for instance, using poly(x1, 2) + poly(x2, 2) is not enough and does not completely handle colinearity.
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