RE: Condition number

Hi Ayyappa, I think the condition number was first proposed as a statistic to diagnose multicollinearity in multiple linear regression analyses based on an eigenvalue analysis of the X'X matrix. You can probably search the statistical literature and multiple linear regression textbooks to find various rules for the condition number as well as other statistics related to the eigenvalue analysis. For the CN<1000 rule I typically reference the following textbook: Montgomery and Peck (1982). Introduction to Linear Regression Analysis. Wiley, NY (pp. 301-302). The condition number is good at detecting model instability but it is not very good for identifying the source. Inspecting the correlation matrix for extreme pairwise correlations is better suited for identifying the source of the instability when it only involves a couple of parameters. It becomes more challenging to identify the source of the instability (multicollinearity) when the CN>1000 but none of the pairwise correlations are extreme |corr|>0.95. Although when CN>1000 often we will find several pairwise correlations that are moderately high |corr|>0.7 but it may be hard to uncover a pattern or source of the instability without trying alternative models that may eliminate one or more of the parameters associated with these moderate to high correlations. Best, Ken Kenneth G. Kowalski Kowalski PMetrics Consulting, LLC Email: [email protected] Cell: 248-207-5082