Most regression output tables include a VIF column alongside coefficients, or users can run specific diagnostic commands to generate a variance inflation factor table. A low tolerance value directly corresponds to a high VIF, signaling the same underlying issue from opposite perspectives.
Understanding Auxiliary Regression Variance Inflation Factor Calculation
Analysts must use the VIF as a diagnostic tool rather than a rigid rule, investigating high values to determine if the redundancy is a data artifact or a substantively meaningful overlap that necessitates model restructuring. This context-dependence underscores the need for domain knowledge alongside statistical metrics.
Mathematical Formula and Theoretical Rationale The formal variance inflation factor definition is expressed as 1 / (1 - R²), where R² represents the quality of the collinear relationship. Tolerance is the reciprocal of the VIF, calculated as 1 minus the R-squared from the auxiliary regression.
Auxiliary Regression and the Variance Inflation Factor Formula
Practical Implications for Model Building Applying the variance inflation factor definition requires a balance between theoretical purity and empirical necessity. The VIF is calculated by taking one plus this R-squared value and dividing it by one minus this R-squared value, creating a ratio that scales the original variance.
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