Modeling Vehicle Crash Frequency When Multicollinearity Exists in Vehicle Crash Data: Ridge Regression versus Ordinary Least Squares Linear Regression

Ridge Regression is an important statistical method in modeling vehicle crash frequency when crash data contains collinear predictors. The term multicollinearity refers to the condition in which two or more predictors are highly correlated with one another. This would make the explanatory variables become very sensitive to small changes in the model. Multicollinearity reduces the precision of the estimated coefficients, which weakens the statistical power of the regression model. Common methods to address multicollinearity include: variable selection and ridge regression. Variable selection simply entails dropping predictors that are highly correlated in the model. But sometimes this is not possible, especially when a variable that contributes to the collinearity might be a main predictor in the model. However, using ridge regression will allow retention of all explanatory variables of interest, even if they are highly collinear, and provide information regarding which coefficients are the most sensitive to multicollinearity. Ridge regression works by adding a degree of bias to the regression estimates that reduce the standard errors and produce estimates that are much more reliable. This paper uses a five-year vehicle crash data extending from 2011 to 2015 on the interstate highway (I-90) in the state of Minnesota, USA. The data has shown multicollinearity between some independent variables. Results show that the Ridge regression is an effective tool to address the existing multicollinearity and produce accurate regression estimates compared with multiple linear regression.