Selection bias in post-encroachment time conflict severity modeling using a full information maximum likelihood framework

Traffic engagement analysis at signalized intersections using innovative safety measures, such as post-encroachment time, has received significant attention in literature. However, existing studies apply conventional modeling techniques to study post-encroachment engagements and overlook the potential dependence between the occurrence and the severity of engagements, which may introduce selection bias. Ignoring selection bias may lead to inaccurate and biased estimates. This study presents a full-information maximum likelihood model corrects for selection bias by jointly estimating the probability of a vehicle being involved in an engagement and the severity of the engagement. The probability of a trajectory being involved in an engagement was estimated using a binary probit model, and the probability of severity of engagement was estimated using an ordered-probit model with three severity levels: interaction (for engagements with post encroachment time greater than 3 s), minor engagement (for engagements with post encroachment time greater than 2 s and less than or equal to 3 s), and critical engagement (for engagements of post encroachment time less than or equal to 2 s). Using high-resolution trajectory data extracted from 360 h of recordings in Washington State, USA at an urban signalized intersection, this study demonstrates that selection bias can occur at a statistically significant level if low severity engagements are ignored. The degree of selection bias varies can be as high as 35% for behavioral variables such as trajectory speed skewness measures. The second major finding from this study was that a full set of marginal effects (inclusive of direct, indirect and full marginal effects) is necessary to provide comprehensive insight into the effect of behavioral (kinematic), temporal, land use, geometric design and movement type indicators on post encroachment occurrence and severity of engagement probabilities. When selection is accounted for and indirect marginal effects due to selection are factored, it was determined that the marginal effects exerted by behavioral (speed skewness) and design policy variables (lane width and lane count asymmetry) were significant in magnitude at the lowest severity level. These findings suggest a focused design policy that pays attention to traffic operations and control, and approach geometry can play a significant role in moderating errant trajectory behavior by mitigating high severity post encroachment engagement probabilities.