A **condition index** (sometimes called a condition number) shows the degree of multicolinearity in a regression design matrix. It is an alternative to other methods like variance inflation factors.

Although there’s no generally agreed on method to identifying multicollinearity in data, condition indices give a relatively straightforward way to find potential issues. The indices are widely available in statistical software. For example, SPSS gives a condition index as part of the SPSS Collinearity Diagnostics table found in output.

Kennedy (2003) describes a condition index is the largest to smallest characteristic root of X’X; it’s a measure of how close X’X is the perfect multicollinearity (called *singularity*). The indices are calculated as “—the square roots of the ratios of the largest eigenvalue to each successive eigenvalue” (IBM Knowledge Center).

## Condition Index Interpretation

Kennedy gives the following rule of thumb for interpreting a condition index; Any index greater than 30 “—indicates strong collinearity.” The IBM knowledge center calls values over 30 a “serious problem” and also suggests values greater than 15 may indicate a problem that warrants a closer look.

## References

IBM Knowledge Center. Collinearity diagnostics. Retrieved July 23, 2019 from: https://www.ibm.com/support/knowledgecenter/en/SSLVMB_23.0.0/spss/tutorials/reg_cars_collin_01.html

Jackson, S. (2006). Statistics Plain and Simple. Cengage Learning.

Kennedy, P. (2003). A Guide to Econometrics. MIT Press.

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