Variance Inflation Factor
Variance Inflation Factors (VIFs) provide a one-number summary description of collinearity for each model term. Given an experiment with multiple factors, the variance inflation factor associated with the ith factor reflects the increase in the variance of the estimated coefficient for that factor compared to if the factors were orthogonal, and is defined as VIFi = 1/1-R2i where R2i is the coefficient of determination of a regression model where the ith factor is treated as a response variable in the model with all of the other factors. VIFi can range from one to infinity. Values equal to one imply orthogonality, while values greater than one indicate a degree of collinearity between the ith factor and one or more other factors. The square root of the VIF indicates how much larger the standard error is (and therefore, how much larger the confidence intervals will be), compared to a factor that is uncorrelated with the other factors. As a rule of thumb, values greater than 5 suggest that collinearity may be unduly influencing coefficient estimates. A variance inflation factor is calculated for each factor in the experiment. A shortcoming of relying solely on as a measure of merit is that it does not provide detailed correlation information between the the factor and other specific factors. For this, we must turn to the correlation coefficient matrix.
