# How to test for and remedy multicollinearity in optimal scaling/ordinal regression with categorical IVs

I have a data set containing only categorical variables (both nominal and ordinal in nature). The dependent variable is also ordinal (with 4 categories). I was planning to run a categorical regression with optimal scaling instead of ordinal logistic regression aiming at obtaining a single beta coefficient for each independent variable (and also to account for the non-linearity of course). Because an overall comment is desired on whether the dependent variable is affected by a particular independent variable or not.

Now, to me, by theory a few of the variables seem to be related with each other. So, I am interested to check if multicollinearity exists and want to remove it to facilitate the regression. But I don't want to drop any variable because I have quite a few. The polychoric correlation matrix shows the highest pairwise correlation to be 0.69. Except from this and the other one, all others pairwise correlations are quite small.

As the variables are not continuous in my case, so how do I test the presence of multicollinearity in categorical regression and what is the remedy? How do I remove the effect of multicollinearity? I guess standardization will not help as these variables are categorical.

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I changed your title quite a bit, I hope it clarifies rather than obscures your intent. –  Peter Flom Aug 28 '12 at 11:03
It's okay sir, certainly the title is now more generalized and I think whatever the regression type is (using CATREG or Ordinal logistic regression) the test and remedy of multicollinearity should be the same. Am I right sir? –  Blain Waan Aug 28 '12 at 19:05

If you are using R, SPSS or Stata, you can look at the perturb package. It diagnoses collinearity by adding random noise to continuous variables; for categorical variables, some are changed to different categories.

In the documentation for perturb in R, it notes that the model need not be lm, implying that any model (including ones built with optimal scaling or ordinal logistic) could be used.

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I am sure the previous answer must be great. But I just want to add another option that I have tried. It looks quite easy for SPSS users like me. The following two links were very useful for my purpose. The theme amounts to just jamming your data into an ill-fitting linear model and request the collinearity diagnostics. Then look at the tolerance or VIF. If colinearity is present and seems problematic (over-fitting), then you may opt to use good reasoning to eliminate one of the variables or possibly consolidate.

The two useful links are here: (the second link describes how to make dummies in SPSS)

http://www-01.ibm.com/support/docview.wss?uid=swg21476696

http://www-01.ibm.com/support/docview.wss?uid=swg21476169

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