Correlation, variance inflation and multicollinearity in regression model

Since observational data are often used and variables in real life are often correlated, correlations among the variables are common in transportation research. In practice, this problem is often addressed by examining the correlations among the explanatory variables and estimating the variance inflation factors. More importantly, it is a common practice to exclude variables that are highly correlated from the regression model. This study provides some simulated cases to demonstrate that including highly correlated variables, as measured by correlation coefficients and the variance inflation factor in the estimation models, will not necessarily create significant estimation problems, at least in terms of coefficient estimates. Therefore, depending on the purpose of the research, researchers and practitioners should not automatically exclude any variables from their regression models simply because they are highly correlated with other explanatory variables. Some discussions on possible strategies to deal with multicollinearity are also provided.