Using tolerance and VIF, how does one know that collinearity is presence in any given situation, especially in model involving more than two explanatory variables?
In a model involving more than two explanatory variables, collinearity can be detected using tolerance and VIF (Variance Inflation Factor) statistics. Collinearity refers to a high correlation or linear relationship between two or more independent variables in a regression model. It can cause unstable coefficient estimates and make it difficult to interpret the individual effects of the variables.
Tolerance is a measure that indicates the proportion of variation in one independent variable that is not explained by the other explanatory variables. It can be calculated by taking the inverse of the correlation coefficient between two variables. A tolerance value close to 1 indicates low collinearity, whereas a value close to 0 indicates high collinearity. Generally, a tolerance value below 0.2 or 0.1 is considered problematic.
VIF is another metric that assesses collinearity by measuring how much the variance of the estimated regression coefficients is increased due to collinearity. It is calculated as the reciprocal of tolerance, with values greater than 1 indicating the presence of collinearity. A VIF value above 5 or 10 is often used as a threshold to identify problematic collinearity.
To determine collinearity in a model involving multiple variables, you can calculate tolerance and VIF for each independent variable. If any variable has a low tolerance or high VIF, it suggests collinearity. A general rule of thumb is to identify variables with VIF values exceeding 5 as potential collinearity concerns.
Additionally, examining the correlation matrix between the independent variables can provide insights into the pairwise relationships. Higher absolute correlation coefficients between variables suggest a higher likelihood of collinearity.
In summary, by calculating tolerance and VIF for each independent variable, and by examining the correlation matrix, one can identify the presence of collinearity in a model involving multiple explanatory variables.