topic Re: MULTICOLLINEARITY, TEST OF SIGNIFICANCE, CONFIDENCE INTERVAL in SAS Studio

MULTICOLLINEARITY, TEST OF SIGNIFICANCE, CONFIDENCE INTERVAL

lizzy100 — Wed, 12 Feb 2020 21:37:25 GMT

Hello,

Please, how can one detect evidence of Multicollinearity through a correlation matrix. How can one remedy the problem of Multicollinearity?

Secondly, how can the test of significance be performed for each coefficient?

Thirdly, based on two confidence intervals gotten through the Multiple Regression equation/ result, how can one know the variable to remove/ variable that is not relevant?

Thanks a lot as I await your feedback.

Regards,

lizzy100

Re: MULTICOLLINEARITY, TEST OF SIGNIFICANCE, CONFIDENCE INTERVAL

PaigeMiller — Thu, 13 Feb 2020 13:44:55 GMT

@lizzy100 wrote:

how can one detect evidence of Multicollinearity through a correlation matrix.

High correlation between two or more x-variables is multi-collinearity.

How can one remedy the problem of Multicollinearity?

Lots of remedies have been proposed. They all have drawbacks, and most of them I don't like. I prefer Partial Least Squares regression (or PROC PLS in SAS) although it has its own drawbacks. But when I consider the drawbacks of all the different methods, PLS is the winner in my opinion.

Secondly, how can the test of significance be performed for each coefficient?

The math works fine, the test of significance appears in the SAS output, but the multi-collinearity causes the variances to be inflated, making it more difficult to obtain significance.

Thirdly, based on two confidence intervals gotten through the Multiple Regression equation/ result, how can one know the variable to remove/ variable that is not relevant?

You can't know statistically which one to remove*. Which is why I prefer Partial Least Squares, where the idea of removing one of the highly correlated variables is absent. You leave all the variables in the model, and have the model compensate for the mutli-collinearity.

* — you might be able to know based upon your subject matter knowledge, for example, if you are a chemist and your knowledge of chemistry tells you that X12 ought to be in the model and not X4, but that's outside the realm of statistics.

Re: MULTICOLLINEARITY, TEST OF SIGNIFICANCE, CONFIDENCE INTERVAL

lizzy100 — Thu, 13 Feb 2020 21:21:43 GMT

Hello PaigeMiller,

Thanks a lot for your response. I really appreciate.

Regards,

Lizzy100

Re: MULTICOLLINEARITY, TEST OF SIGNIFICANCE, CONFIDENCE INTERVAL

Rick_SAS — Mon, 24 Feb 2020 13:53:43 GMT

Although you mention the correlation matrix, it sounds like your main interest is detecting collinearities in a linear regression model. If so, you might want to look into the TOL, VIF, and COLLIN options on the MODEL statement of PROC REG. The COLLIN option produces output that you can use to answer most of your questions. The article "Collinearity in regression: The COLLIN option in PROC REG," shows how to interpret the output.

Re: MULTICOLLINEARITY, TEST OF SIGNIFICANCE, CONFIDENCE INTERVAL

PaigeMiller — Mon, 24 Feb 2020 14:53:09 GMT

Good point, Ric, some types of collinearity may not show up in the correlation matrix.