Pavement Marking Demonstration Projects: State of Alaska and State of Tennessee

APPENDIX I. REVIEW OF LOGIT MODEL ANALYSIS

MULTINOMIAL LOGIT MODEL

The multinomial logit model is widely used to estimate accident severity. Shankar and Mannering attempted to address the potential bias that univariate analyses create by presenting a multinomial logit model of motorcycle rider accident severity in single-vehicle collisions.⁽¹²²⁾ They concluded that the multinomial model is a promising approach to evaluating the determinants of motorcycle accident severity.

Savolainen and Mannering researched a similar topic (motorcyclists' injury severities in single- and multi-vehicle crashes) using a multinomial logit model for multi-vehicle crashes.⁽¹²³⁾ They concluded that collision type, roadway characteristics, alcohol consumption, helmet use, and unsafe speeds play significant roles in crash-injury outcomes. The injury severity of male and female drivers in single- and two-vehicle accidents for different types of vehicles were explored by Ulfarsson and Mannering using a multinomial logit model.⁽¹²⁴⁾ The results suggest that there are important behavioral and physiological differences between male and female drivers that must be explored further and addressed in vehicle and roadway design.

Multinomial logit models were used by Khorashadi et al. to explore the differences between urban and rural driver injuries in accidents that involve large trucks.⁽¹²⁵⁾ The results showed that many variables were significant in either the rural or the urban model but not in both because of the different perceptual, cognitive, and response demands placed on drivers in rural versus urban areas.

NESTED LOGIT MODEL

Generalized extreme value (GEV) models constitute a large class of models that exhibit a variety of substitution patterns. The unifying attribute of these models is that the unobserved portions of utility for all alternatives are jointly distributed as GEV. This distribution allows for correlations over alternatives and, as its name implies, is a generalization of the univariate extreme value distribution that is used for standard multinomial logit models. When all correlations are zero, the GEV distribution becomes the product of independent extreme value distributions, and the GEV model becomes standard multinomial logit. The class therefore includes logit but also includes a variety of other models. Hypothesis tests on the correlations within a GEV model can be used to examine whether the correlations are zero, which is equivalent to testing whether standard logit provides an accurate representation of the substitution patterns.

The most widely used member of the GEV family is nested logit. This model has been applied by many researchers in a variety of situations, including energy, transportation, housing, and telecommunications. Its functional form is simple compared to other types of GEV models. Nested logit models allow partial relaxation of the IIA property. Sometimes, different alternatives may share the same unobserved terms. The nested logit model can overcome the restriction of the multinomial logit model that requires the error term for different alternatives, ε_in, to be independent from each other.

Shankar et al. presented a nested logit formulation as a means for determining accident severity on rural highways given that an accident has occurred.⁽¹²⁶⁾ They concluded that a nested logit model, which accounted for shared unobservables between PDO and possible injury accidents, provided the best structural fit for the observed distribution of accident severities.

Chang and Mannering studied the occupancy/injury severity relationship in truck-and non-truck- involved accidents using the nested logit model.⁽¹²⁷⁾ The findings of the study demonstrated that the nested logit model, which was able to take into account vehicle occupancy effects and identify a broad range of factors that influence occupant injury, is a promising methodological approach.

Holdridge et al. analyzed the in-service performance of roadside hardware on the entire urban SR system in Washington State by developing multivariate nested logit models of injury severity in fixed-object crashes.⁽¹²⁸⁾ The models showed the contribution of guardrail leading ends toward fatal injuries and also indicated the importance of protecting vehicles from crashes with rigid poles and tree stumps.

ORDERED LOGIT AND ORDERED PROBIT MODEL

Wang and Abdel-Aty examined left-turn crash injury severity using an ordered logit model.⁽¹²⁹⁾ This study found that neither the total approach volume nor the entire intersection volume affected crashed injury significantly; however, the specific vehicle movements did.

Duncan et al. examined the impact of various factors on injuries to passenger car occupants involved in truck-passenger car rear-end collisions and demonstrated the use of the ordered probit model in the complex highway safety problem.⁽¹³⁰⁾ They concluded that the ordered probit model is flexible because it allows the injury severity probabilities to vary differently across categories.

Klop and Khattak explored the effect of a set of roadway, environmental, and crash variables on bicycle injury severity using the ordered probit model.⁽¹³¹⁾ The model results showed that variables that significantly increase injury severity include straight grades, curved grades, darkness, fog, and speed limit.

Quddus et al. used an ordered probit model to examine factors that affect the injury severity of motorcycle accidents and the severity of damage to the motorcycles and vehicles involved in those crashes.⁽¹³²⁾ They concluded that factors leading to increased probability of vehicle and motorcycle damage included some similar factors and different factors.

Kockelman and Kweon described the use of ordered probit models to examine the risk of different injury levels sustained under all crash types, two-vehicle crashes, and single-vehicle crashes.⁽¹³³⁾ This work suggested that the manner of collision, the number of vehicles involved, driver gender, vehicle type, and driver alcohol use played major roles in terms of crash severity.

Adbel-Aty analyzed driver injury severity at locations of roadway sections, signalized intersections, and toll plazas using the ordered probit model.⁽¹³⁴⁾ This study illustrated the similarities and differences in the factors that affect injury severities at different locations.

O'Donnell and Connor used both an ordered logit model and ordered probit model to predict the severity of motor vehicle accident injuries.⁽¹³⁵⁾ They concluded that occupant age, vehicle speed, seat position, blood alcohol level, and type of collision affect the probabilities of serious injury and death

MIXED LOGIT MODEL

Gkritza and Mannering demonstrated a mixed logit approach that can be used to better understand the use of safety belts in single- and multi-occupant vehicles.⁽¹³⁶⁾ They concluded that the mixed logit model can provide a much fuller understanding of the interaction of the numerous variables that correlate with safety-belt use.

Milton et al. analyzed the injury-severity distributions of accidents on highway segments, and the effect that traffic, highway, and weather characteristics have on these distributions using a mixed logit model.⁽¹³⁷⁾ Their results showed that the mixed logit model has considerable promise as a methodological tool in highway safety programming.

Pai et al. estimated mixed logit models to investigate the contributory factors to motorists' right-of-way violations in different crash types.⁽¹³⁸⁾ It was found that motorcycle right of way was more likely to be violated on non-built-up roads and in diminished light conditions.

Kim et al. applied a mixed logit model to analyze pedestrian injury severity in pedestrian-vehicle crashes to address possible unobserved heterogeneity.⁽¹³⁹⁾ It was found that several factors increased the fatal injury level significantly, including darkness, drunk driving, and speeding. They found that the effect of pedestrian age was normally distributed across observations and that as pedestrians become older, the probability of fatal injury increases substantially.

Eluru et al. developed an ordered mixed logit model to examine pedestrian and bicyclist injury severity in traffic crashes.⁽¹⁴⁰⁾ They concluded that an ordered mixed logit model does not produce inconsistent estimates of the effects of some variables as does an ordered probit model. The analysis suggested that the general pattern and relative magnitude of elasticity effects of injury severity determinants are similar for pedestrians and bicyclists.

SUMMARY

There are several commonly used discrete choice models for predicting crash severity such as the multinomial logit model, the nested logit model, the ordered probit model, and the mixed logit model. These approaches have been applied to crash severity analysis on the relationship between crash severity and its contributing factors. Table 109 shows a summary of commonly used discrete choice models. Advantages and limitations as well as important assumptions of these models are presented.

Table 109. Summary of discrete choice models of crash severity.