Linear accident models assume that accident risk increases proportionally with exposure factors like driving distance or time, while nonlinear models recognize that risk relationships are more complex and may change at different exposure levels.
In linear models, doubling your driving distance doubles your accident risk. This simplicity makes them easy to interpret and apply, but they often fail to capture real-world behavior. Nonlinear models account for phenomena like learning effects, fatigue, and adaptation. For instance, novice drivers experience sharply declining accident rates as they gain experience, then the improvement flattens—a nonlinear relationship.
Nonlinear models can take various forms. Some assume diminishing returns, where additional exposure provides less protective benefit over time. Others incorporate threshold effects, where risk remains stable until a critical exposure level is exceeded. Regression to the mean is another nonlinear consideration: if a road segment has an unusually high accident count in one year, it often shows lower counts the next year due to random variation, not intervention effectiveness.
Empirical research suggests nonlinear models generally fit accident data better. However, this comes at a cost: they require more complex mathematics, more data to estimate accurately, and greater care in interpretation. The choice between linear and nonlinear depends on your purpose. Linear models suffice for quick estimates and policy discussions, while nonlinear models are preferable for detailed safety analysis, infrastructure investment decisions, and research into how risk factors actually operate.
Both approaches have limitations—no model perfectly captures accident causation. Practitioners often use multiple models to test whether conclusions are robust across different modeling assumptions.