Exploring Piecewise Linear Effects of Crash Contributing Factors with a Novel Poisson–Mixed Multivariate Adaptive Regression Splines Model

Pavement maintenance is vital to ensuring the structural integrity and ride quality of the roadway and in reducing traffic congestion and the number of incidents. Of these, traffic safety represents a major component. Previous research contributed greatly to understanding the effects of pavement management or traffic engineering factors on occurrence and severity of traffic crashes. However, to the authors' knowledge, very few studies have investigated the piecewise linear (nonmonotonic) effects of these factors on crash frequency. It is hypothesized that the influence of some factors may vary over a few regimes, and yet the factors may interact with each other. Analyzing and understanding these kinds of piecewise linear effects and interactions could help transportation agencies identify key crash determinants and proactively apply remedial treatments. Moreover, it will provide a reference for agencies to manage pavement strategically and efficiently from a safety perspective. To achieve that goal, a novel statistical model [Poisson–mixed multi-variate adaptive regression splines (MARS) model] is proposed. This model can identify piecewise linear and multilevel interactive effects as does conventional MARS. The new model can also account for temporal and spatial correlations of crash data. Pavement quality, traffic, roadway geometric, and crash data from 2004 to 2009 on Tennessee state route roadways were used. Results support the hypothesis that the relationship between crash frequency and many explanatory variables is piecewise linear and that some of these variables are significantly interactive. The goodness of fit shows that the Poisson–mixed MARS model notably outperforms the Poisson MARS model. The proposed method could be used as a good alternative in modeling traffic crash data, especially for a wide range of traffic variation.