Author Instructions for Extended Abstract

Huang, Seraneeprakarn and Shankar

This paper is published in Transportation Research Board 95th Annual Meeting: Conference Proceedings and is referenced as: Huang, S., P. Seraneeprakarn, and V. Shankar. A Hierarchical Mixed Logit Model of Hybrid Involved Crash Severities. Transportation Research Board 95th Annual Meeting: Conference Proceedings.Washington,D.C. USA, 2016.

A Hierarchical Mixed Logit Model of Hybrid Involved Crash Severities Shuaiqi Huang Graduate Student Pennsylvania State University Transportation Econometric Application Laboratory University Park, State College, PA 16801 Tel: 814-321-4458 Email: [email protected] Puttipan Seraneeprakarn Graduate Student Pennsylvania State University Transportation Econometric Application Laboratory University Park, State College, PA 16801 Tel: 814-321-4458 Email: [email protected] Venkataraman Shankar Professor of Civil Engineering Pennsylvania State University 226C Sackett Building University Park, State College, PA 16801 Tel: 814-865-9434 Email: [email protected]


ABSTRACT In this paper we present a mixed logit model of the severity of a crash involving hybrid vehicles. The most severe outcome of the crash is modeled. Crash data from the Washington State Department of Transportation was obtained for the period 2006-2010 and hybrid vehicle identification data was added to the database. Data such as vehicle width, weight, horsepower, turning radius, drivetrain and ground clearance was added. It was found that the factors associated with the most severe outcome of the crash included crash specific variables relating to occupant count, vehicle involvement, collision type, crash site roadway alignment, functional class of roadway, pavement surface condition at the time of the crash, and the maximum occupant age (in multi-occupant crashes). The most severe outcome was based on three injury categories, namely, property damage only, possible injury and injury (inclusive of evident, disabling and fatal.) It was also determined that random effects are plausible in the possible injury severity function. Heterogeneity in means due to vehicle age appeared significant; yet, the standard deviation of the vehicle involvement coefficient in the property damage severity function was not statistically significant. Heteroskedasticity in the random parameter variances was also tested as a function of hybrid vehicle weight and width; the random effect is weakly heteroskedastic. The results are from an analysis of 1,665 crashes; while the heteroskedastic effects and heterogeneity in means appear inconclusive, they suggest that random effects with parameter heteroskedasticity and heterogeneous means cannot be ignored in hybrid crash severity analyses.

Keywords: Hierarchical mixed logit model, heterogeneity in means, heteroskeadastic random parameter

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INTRODUCTION One of the well cited studies on crash severity modeling was conducted in 1988, when Jones and Whitfield applied logistic regression to model the severity risk as a function of anthropometric measures, vehicle mass, age of driver, and restraint system use (1). This model included some vehicle safety features by using ratings from the New Car Assessment Program (NCAP), which was produced by the National Highway Traffic Safety Administration's (NHTSA). The findings showed that there is a significant relationship between vehicle safety features and the risk of serious injury or death in crashes. Since vehicle safety features are inherently tied to vehicle make, model, and vintage, this research is suggestive of the importance of vehicle model information. By doing so, we could capture the influence of both vehicle safety features and vehicle designs on the observed severity of crashes. The field of multivariate crash severity modeling began with bivariate models of injury outcomes [(2);(3)]. A somewhat contrasting view is taken in some studies via the discrete ordered-probability approach, which has been applied by numerous researchers with considerable success [for example, (4); (5); (6)]. The limitation with this approach is it forces the parameters to be the same across severities, although the marginal effect computation can differ in magnitudes. Shankar et al. [(7);(8)] showed in one of the earliest studies that forcing parameters to be the same in severity models can lead to poorer likelihoods due to undue restrictions on the models. These approaches, regardless of the nature of the treatment of the severity outcome, used fixed parameter models. Recent research however has shown that fixed parameter models may result in undue restrictions on parameters, especially when heterogeneity is a significant factor. Heterogeneity in crash severity contexts can arise from a number of sources: environmental effects, interactions between driver and vehicle, and interactions between vehicles. To demonstrate that heterogeneities do play an important role in the estimation and prediction of crash severities, in 2008, the mixed logit model was used to predict highway proportions of crash frequencies by severity (9). This application evaluated crash severity at the unconditional level. The dimension of crash severity at the conditional level involves a multitude of factors specific to the crash. While the Milton et al paper (9) provided a better understanding of the injury-severity distributions of crashes on highway segments, it offered no insight into the heterogeneity of crash specific factors and how the heterogeneity might influence the conditional probability of crash severities. To this end, recent work [(10); (11)] has demonstrated the use of methods that can accomplish two objectives: a) estimate coefficients that are potentially random in the presence of heterogeneity; and b) estimate coefficients that are subject to heteroskedasticity in the parameter distribution. The first objective, namely heterogeneity in the mean of random parameters is dealt with in (10) through the use of geometrics that hierarchically influence the frequency probabilities of crash types on interstates. The second objective, namely heteroskedasticity in parameter distributions is dealt with through the use of crash specific factors that hierarchically influence conditional crash severities. The extant severity literature does not have a single reference that simultaneously addresses the impact of heterogeneity in the mean and heteroskedasticity in parameter distributions. Further the current literature is scant in the specific focus on hybrid vehicle crashes. In this paper, we aim at the following objectives: a) estimating a model of crash severity that simultaneously addresses heterogeneity in the mean and parameter heteroskedasticity; and b) and deriving insights using this method to identify the influence of hybrid vehicle attributes on hybrid crash severity.

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METHODOLOGY The application of the hierarchical mixed logit model is undertaken by considering injury-severity distributions at the crash level. Severity is defined as the resulting injury level of the most severely injured person in the observed crash. To develop the modeling approach, a severity function determining the proportion of injury severities in every observation is defined as 𝑆𝑖𝑛 = 𝛽𝑖 𝑥𝑖𝑛 + 𝜀𝑖𝑛

(1)

where 𝑆𝑖𝑛 is a severity function determining the injury-severity category 𝑖 proportion (property damage only, possible injury, injury) in observation 𝑛; 𝑥𝑖𝑛 is a vector of explanatory variables (geometric, environment, driver and passengers attributes and vehicle information variables); 𝛽𝑖 is a vector of estimable parameters; and 𝜀𝑖𝑛 is error term (9). If 𝜀𝑖𝑛 s are assumed to be generalized extreme value distributed, while allowing for parameter variations across observations (variations in 𝛽), a mixing distribution is introduced giving injury-severity proportions (12;13): 𝐸𝑋𝑃[𝛽𝑖 𝑥𝑖𝑛 ]

𝑃𝑖𝑛 = ∫ ∑

𝐼 𝐸𝑋𝑃[𝛽𝑖 𝑥𝑖𝑛 ]

𝑓(𝛽|𝜑)𝑑𝛽

(2)

Where 𝑓(𝛽|𝜑) is the density function of 𝛽 with 𝜑 referring to a vector of parameters of the density function (mean and variance), and all other terms are as previously defined. Equation 3 is the formulation for the mixed logit model. For model estimation, 𝛽 can now account for observation-specific variations of the effect of 𝑋 on injury-severity proportions, with the density function 𝑓(𝛽|𝜑) used to determine 𝛽. Mixed logit proportions are then a weighted average for different values of β across observations where some elements of the vector 𝛽 may be fixed and some may be randomly distributed. If the parameters are random, the mixed logit weights are determined by the density function 𝑓(𝛽|𝜑). Heterogeneity and heteroscedasticity in the random parameters was modeled according to equation 3 shown below: 𝛽𝑖𝑘 = 𝛽 + 𝛿𝑘 𝑍𝑖 + σ𝑘 exp(𝜔𝑊)𝜐𝑖𝑘

(3)

where 𝑍𝑖 contains hybrid attributes which capture heterogeneity in the mean of the beta parameter; the delta parameter being the coefficient of the heterogeneity; and W containing attributes which capture heteroscedasticity in the parameter variance sigma, with the omega parameter representing the coefficient effect on heteroskedasticity. This structure shown in equation 3 allows for two different vectors of hybrid attributes Z and W to influence the random parameters associated with the most severe outcome. It is plausible that Z and W may contain other attributes such as those relating to occupants, or other potential sources of heterogeneity and heteroscedasticity. EMPIRICAL SETTING Crash data from the Washington State Department of Transportation crash database was used to extract hybrid involved crashes. Data recording from 2006 to 2010 was used. Hybrid occupant severity was recorded as separate observations for evaluation using the hierarchical mixed logit model. Of the 1,665 crashes we analyzed, 1,380 resulted in property damage only as the most severe outcome, 245 resulted in possible injury and 40 resulted in injury. The PDO proportion is 82.883%, while PINJ constitutes 14.72%. The injury proportion is 2.4%.


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We then used vehicle identification numbers (VIN) to extract detailed vehicle specific information, including information on turning diameter, weight, height, width, length, ground clearance, horsepower, make and model and vintage, safety equipment, and torque. In addition, an exhaustive list of hybrids for the years 2001-2010 was compiled – twenty different hybrids were identified from the crash records in this manner. When combined with the crash characteristics and hybrid occupant characteristics, a total of 72 variable categories were developed. TABLE 1 Descriptive statistics of key variables in hybrid vehicle crash dataset Crash Variable Vehicle involvement crash dummy 1 (1 if two vehicles were involved in crash; 0 otherwise) Vehicle involvement crash dummy 2 (1 if three or more vehicles were involved in crash; 0 otherwise) Collision dummy 1 (if collision type involved fixed or other object; 0 otherwise) Collision dummy 2 (1 if collision involved entering at angle movement; 0 otherwise)

PDO(%*)

PINJ(%*)

INJ(%*)

Sum(%**)

946 (83.64)

159 (14.06)

26 (2.30)

1,131 (67.928)

329 (80.44)

74 (18.09)

6 (1.47)

409 (24.565)

61 (75.31)

11 (13.58)

9 (11.11)

81 (4.685)

124 (83.22)

18 (12.08)

7 (4.70)

149 (8.949)

Collision type dummy 3 (1 if collision involved sideswipe; 0 otherwise)

193 (94.51)

8 (3.90)

4 (1.95)

205 (12.312)

Crash location dummy (1 if crash occurred on a curve with grade; 0 otherwise)

105 (80.15)

18 (13.74)

8 (6.11)

131 (7.868)

360 (85.31)

57 (13.51)

5 (1.18)

422 (25.345)

370 (83.71)

65 (14.71)

7 (1.58)

442 (26.547)

324 (82.86)

59 (15.09)

8 (2.05)

391 (23.438)

1,056 (82.89)

186 (14.60)

32 (2.51)

1,274 (76.517)

76 (88.37)

6 (6.98)

4 (4.65)

86 (5.165)

91 (82.73)

11 (10.00)

8 (7.27)

110 (6.07)

Functional class dummy (1 if crash occurred on principal arterial that is not an expressway; 0 otherwise) Pavement condition dummy (1 if crash occurred on wet pavement; 0 otherwise) Newer vehicle age dummy (1 if hybrid vehicle age is 3 years or less; 0 otherwise) Older vehicle age dummy (1 if hybrid vehicle age is more than 3 years; 0 otherwise) Light hybrid single vehicle crash dummy (1 if hybrid involved in single vehicle crash weighs 2,890 lbs or less; 0 otherwise) Narrow hybrid single vehicle crash dummy (1 if hybrid vehicle involved in single vehicle crash is between 66 and 68 inches wide; 0 otherwise) *represents severity percent of total for the variable ** represents variable proportion in the sample

Table 1 provides information about the distribution of crash severity by key variables. This distribution is described in the first three columns. The fourth column represents the total count of crashes associated with the variable. In each column, there is a percentage number in parentheses. The percentage number in the first three columns represents the percent proportion of the severity associated with the variable. The fourth column percentage is associated with the sum measure. This percentage represents the percent of the total sample, the variable represents. As noted in table 1, the majority of the variables are consistent in their association with the severity distributions with PDO occurrence percentages around 82-83%, possible injury percentages around 14%, and injury percentages around 3-4%. Some variables however, noted in bold, were noticeably lower or higher – for example, the fixed object collision dummy had over 11 percent of


crashes resulting in injury, and correspondingly, a lower percent of PDO compared to the sample averages. The sideswipe collision dummy was over-represented in PDO and PINJ collisions compared to the sample average. Similarly, the light hybrid dummy for single vehicle crashes was over-represented in PDO and PINJ severities; while the narrow hybrid single vehicle crash dummy was over-represented in PINJ and INJ severities. MODEL ESTIMATION The estimation of hierarchical mixed logit model had three level of severity, where property damage only, possible injury and injury were the major outcomes. The estimation was conducted by applying the standard maximum likelihood method using simulations of the observation specific likelihoods. To achieve this, we used 100 Halton draws. Halton draws are more efficient and involve much fewer draws to achieve a given rate of convergence (13). Crash Level Most Severe Outcome Mixed Logit Model The estimation was based on drivers and occupants (person) level severity effects, where factors such as age, gender, education, seat belt use, seat position, sobriety and insurance status may be of relevance. According to the results showing in Table 2, we could conclude that all variables’ signs are plausible and the heterogeneity in means model showed improvement over the multinomial logit model, with log-likelihood equal to -834.865 at convergence, compared to -838.918 for the convergent fixed parameter multinomial logit likelihood. Two parameters were evaluated as random effects, namely the constant in the PINJ and the vehicle involvement variable in the PDO functions respectively. A detailed interpretation of each variable was provided below. Variable: Constant specific for PINJ and INJ The constant for the possible injury level was random, while being a fixed parameter for the injury severity. These constants may capture the unobserved heterogeneity in different observations that could include the effect of a multitude of factors involving the driver, occupant, vehicle and the environmental conditions. We note that several of the plausible variables, such as seat belt usage, seat position, sobriety level, vehicle age, were not significant. The absence of these effects could be absorbed by the constant in the PINJ and INJ severity functions. Variable: Vehicle involvement Finding: Increase the likelihood of PDO Variable: Two vehicle involvement dummy Finding: Decreases the likelihood of property damage Variable: Three-plus-vehicle involvement dummy Finding: Decreases the likelihood of property damage The vehicle involvement variables shown above are interpreted cumulatively. The vehicle involvement variable is a continuous effect, while the two vehicle variable is a dummy effect, as is the three-plus variable effect. With the exception of the single-vehicle crash, these variables combined capture the effect of hybrid-non-hybrid vehicle collisions. Only two out of the 1,665 observations involved hybrid-hybrid crashes. Hybrid collisions involve crashes under low speeds in urban, congested conditions due to the predominance of hybrid users in urban areas. In

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multi-vehicle crashes, whether it is two-vehicle or three-plus-vehicle crashes, the exposure to higher severities increases due to the fact that non-hybrid vehicles are involved. Even with the positive coefficient for the vehicle involvement variable, the net effect (inclusive of the dummy effects) is to decrease the likelihood of property damage only severities. The above finding is an important one, since the pure non-hybrid two-vehicle collisions have been reported to result in higher injury likelihoods (8). This raises the question of whether multi-vehicle hybrid collisions show the same pattern of injury likelihoods as pure non-hybrid collisions. This issue is not researched in this study, but remains an area of fruitful research. The second important note is that the vehicle involvement variable could be potentially random. In our study, heterogeneity in the means was significant due to the effect of vehicle age. Vehicle age effects were divided into two ranges (0-3 years as a continuous effect and 4 or older as a continuous effect). An examination of the statistical significance of these effects indicated high significance (t-statistics in excess of 2). The signs of the effects were to increase the heterogeneity in the parameter mean for the vehicle involvement variable. This effect was significant at the 75% confidence level. However, the heteroskedasticity in the variance of the parameter was a lot weaker, indicating an almost fixed parameter effect. The variables used to capture the heteroscedasticity, namely, vehicle weight and width were found to be of very low significance. Regardless, the significance of the heterogeneity parameters indicates that some factors unique to vehicle age are plausibly causing a shift in the parameter mean to differing degrees. The newer vehicle age effect appears to be stronger (coefficient of 0.15) than the older vehicle effect (coefficient of 0.05). Variable: Collision type is fixed object Finding: Decrease the likelihood of PDO and PINJ This variable has a negative sign and a marginal effect that indicates an increased likelihood of injury. The parameters as estimated in the model are separate, with the parameter means showing statistically different values (based on a one-parameter chi-squared test.) The increased likelihood of injury likelihoods due to fixed object collisions is not unexpected due to the fact that fixed objects usually involve median side concrete barriers or roadside objects such as luminaires or utility poles – the relative strength of the marginal effects (with respect to PDO and PINJ) indicate that the decrease in likelihood of PDO is stronger than that in PINJ. Variable: Collision type is entering at angle Finding: Decrease the likelihood of PDO and PINJ This variable has a negative sign and a marginal effect that indicates an increased likelihood of injury. The parameters as estimated in the model are separate, with the parameter means showing statistically different values (based on a one-parameter chi-squared test.)

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TABLE 2 Mixed logit model of crash severity involving hybrid vehicles Variable

Variable

Coeff.

S.E.

T-Stat

Random parameters in severity functions Constant*

Specific to possible injury

-2.994

1.097

-2.73

VEHINV*

Count of vehicle involvement as continuous variable (specific to property damage only)

0.335

0.288

1.16

Non-random parameters in severity functions TW_INV

Vehicle involvement crash dummy 1 (1 if two vehicles were involved in crash; 0 otherwise; specific to property damage only)

-1.609

0.711

-2.103

THPL_INV

Vehicle involvement crash dummy 2 (1 if three or more vehicles were involved in crash; 0 otherwise; specific to property damage only)

-2.536

0.826

-3.237

FCOLTYP6

Collision dummy 1 (if collision type involved fixed or other object; 0 otherwise; specific to property damage only)

-2.632

0.895

3.298

FCOLTYP7

Collision dummy 2 (1 if collision involved entering at angle movement; 0 otherwise; specific to property damage only)

-1.24

1.213

-4.097

CUR_GRA

Crash location dummy (1 if crash occurred on a curve with grade; 0 otherwise; specific to property damage only)

-0.998

0.369

1.533

COLLTYP1

Collision type dummy 3 (1 if collision involved sideswipe; 0 otherwise specific to possible injury)

-2.173

0.417

2.259

FCOLTYP6

Collision dummy 1 (if collision type involved fixed or other object; 0 otherwise; specific to possible injury)

-2.099

0.718

2.526

FCOLTYP7

Collision dummy 2 (1 if collision involved entering at angle movement; 0 otherwise; specific to possible injury)

-1.731

0.714

2.236

CUR_GRA

Crash location dummy (1 if crash occurred on a curve with grade; 0 otherwise; specific to possible injury)

-0.921

0.723

-3.312

OCCHY

Count of occupant in hybrid vehicle, continuous variable (specific to possible injury)

0.222

0.241

1.605

Constant

Specific to injury

-5.163

0.296

1.787

OPATRIAL

Functional class dummy (1 if crash occurred on principal arterial that is not an expressway; 0 otherwise; specific to injury)

-0.858

0.157

2.086

SURFWET

Pavement condition dummy (1 if crash occurred on wet pavement; 0 otherwise; specific to injury)

-0.764

0.181

-2.681

0.019

0.103

2.485

MAXAGE

Age of oldest occupant(s) in the crash, continuous variable (specific to injury) Log-Likelihood at convergence Fixed parameter convergent log-likelihood

-834.865 -838.918

Number of observations 1,665 *Heterogeneity in the mean significant due to vehicle age effects. Vehicle age effects were specified in two ranges (continuous in 0-3 year range; and continuous in 4 and older range). Heteroskedasticity due to vehicle weight and width effects was marginally significant for constant; not significant for vehicle involvement parameter. Vehicle weight and width effects were dummies.


The increased likelihood of injury likelihoods due to fixed object collisions is not unexpected – the relative strength of the marginal effects is reversed compared to the fixed object effect (with respect to PDO and PINJ). It appears that the expected decrease in likelihood of PINJ is stronger than that in PDO when collisions involved entering at angle hybrid crashes. Entering at angle collisions involve broadside collisions in which occupant exposure to injury is increased due to lateral forces. While the presence of side airbags might mitigate some of these effects, the exposure to higher levels of injury of the lower part of the occupant’s body increases the likelihood of injury as a whole. Variable: Collision type is sideswipe. Finding: Decrease the likelihood of PINJ Sideswipe crashes involve contact between two or more vehicles usually due to maneuvers such as improper lane changing, parked vehicles entering the traffic stream at slow speeds, or parking lot collisions where vehicle damage is on the side panels of the involved vehicles. The important point to note is that due to the fact that at least one of the vehicles is hybrid, the speed selection effects and driver self-selection effects factor do not necessarily translate into stronger property damage only likelihoods, compared to sideswipe variable effects in the extant literature (8). Rather, it appears the increase in PDO and INJ likelihoods is similar. This is an area that merits further research, with larger samples. Variable: Junction relationship is that, crash happens on a horizontal curve and on a grade. Finding: Decrease the likelihood of PDO and PINJ. This variable indicates that crashes occurring on horizontal curves and on a grade suffer from the combined alignment effects. Run off the road crashes, especially due to higher speeds on downgrades are typically indicative of higher severity crashes such as injury. The decrease in likelihoods of PDO and PINJ are similar – the potential to represent this effect as a single parameter in the INJ function is high. We have retained the parameters to be separate due to the marginal significance of the one-parameter restriction test chi-squared value. Variable: Hybrid occupant count as a continuous variable Finding: Increase the likelihood of possible INJ This variable captures the effect of occupancy in the hybrid vehicle. This effect could be capturing two factors: a) the higher occupancy effects in hybrids reflecting lower speeds and exposure to lower speeds for a greater number of occupants; and b) the potential for hybrids to offer higher protection for multiple occupants. This area appears to be an interesting avenue for further research, since the finding appears to indicate that escalation of the most severe outcome to injury levels might be mitigated in high-occupant hybrid collisions. Variables: Crash location is on a non-expressway principal arterial Finding: Decrease the likelihood of INJ This variable captures the effect of roadway functional class on the most severe outcome of hybrid involved crashes. The variable in question is the non-expressway principal arterial dummy, which indicates that the baseline variable is all other functional classes, inclusive of interstates,

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expressways, minor and collector arterials. Since hybrid involved crashes primarily occur on urban roadways, it appears the lower speeds in principal arterials (compared to interstates and expressways) due to congestion play a significant role. Further, the higher design levels of principal arterials compared to minor and collector arterials mitigates the likelihood of injuries as the most severe outcome. Variable: Wet pavement dummy Finding: Decrease the likelihood of INJ This variable indicates the effect of wet pavements on hybrid involved crash severities. Wet pavement crashes are indicative of vehicle kinematics due to tire-pavement interactions. Hybrid vehicles due to their battery placement may offer greater tire-pavement interaction at higher speeds, when the interaction effects can be significant. This in turn is expected to mitigate injury likelihoods to a greater extent than one would expect compared to crashes occurring on dry or snow-covered pavements which are the baseline conditions. Variable: Maximum age of occupant crash Finding: Increase the likelihood of injury This variable is a continuous variable which indicates a strong marginal effect on higher likelihoods of injury. This is to be expected in hybrid collisions as well – however, what remains to be researched is the relative strength of this marginal effect in a comprehensive manner. While we evaluate the effect in hybrid involved collisions, a careful comparison of the marginal effects of occupant age in pure non-hybrid collisions is required to determine if hybrids have the potential to mitigate occupant age exposures to injury severities. To assess the marginal effect of key factors, we evaluated them via their direct elasticities in the model (14). In this paper, the elasticity of variable will show the responsiveness of the probability of some crash-severity distributions to changes in variable values. In general, the elasticity is computed as: 𝑃 (𝑖)

𝐸𝑥𝑛𝑛

=

𝜕𝑃𝑛 (𝑖) 𝜕𝑥𝑛

𝑥𝑛

∙𝑃

𝑛 (𝑖)

(4)

where 𝐸 is the elasticity, 𝑥 is the value of the variable being examined, and 𝑃𝑛 (𝑖) is the probability of observation 𝑛 being of severity 𝑖. Applying Equation 5 to the mixed logit formulation (Equation 3) gives: 𝑃 (𝑖)

𝐸𝑥𝑛𝑛

= (1 − ∑𝐽 𝑃𝑛 (𝑗))𝛽𝑖 𝑥𝑛

(5)

where 𝐽 is the set of alternatives that has the variable 𝑥𝑛 in their severity functions (𝑆𝑖𝑛 is in Equation 1).


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TABLE 3 Elasticity effect on probabilities of crash severity Variable Vehicle involvement count

Hybrid occupant count

Age of oldest occupant(s) in the crash

Severity *Property damage only Possible injury Injury Property damage only *Possible injury Injury Property damage only Possible injury *Injury

Value 0.185 -0.889 -1.266 -0.034 0.188 -0.034 -0.028 -0.02 1.023

*Direct elasticity effect of the attribute

We now discuss the elasticity for continuous variables in this model as shown in Table 3. The vehicle involvement count variable had average cross elasticity of -0.889 for possible injury and a direct elasticity of 0.185 for property damage only. This indicates a near-elastic effect on the possible injury outcome. The average value of the vehicle involvement variable was 2.27 in our sample. A 100% increase in this value roughly represents a one-vehicle change in the count. Corresponding to this level of change, the change in possible injury probability can be expected to be a decrease of 88.90% from the current possible injury probability. The injury cross elasticity is very strong, indicating a significantly increase in the expected injury probability (over 126 percent) when vehicle involvement counts increase by one vehicle. The hybrid occupant count elasticities are relatively weaker – with the strongest effect observed in the direct elasticity of possible injury (0.188). In contrast, the effect of the oldest occupant in the crash is substantial with an elastic effect on injury (1.023). For every year increase in the age of the oldest occupant in a hybrid involved crash, the expected increase in injury probability is 1.023%. CONCLUSIONS AND RECOMMENDATIONS This research provides an estimating framework for evaluating crash severity likelihoods conditioned on the occurrence of a crash involving at least one hybrid vehicle. The estimating model is a hierarchical mixed logit. In this model, severity is modeled as a discrete outcome in three mutually exclusive categories namely, PDO, PINJ and INJ. The INJ class consists of evident injury, serious injury and fatality. These classes were combined due to lack of adequate sample size for the individual categories of evident, disabling and fatality respectively. The contribution of this paper is in the identification of hybrid vehicle attributes in terms of their impact on crash severity parameters. Crash severity parameters are modeled as random and fixed parameters in a mixed logit framework. We evaluated two distinct types of effects via the mixed logit – the effect of vehicle age on heterogeneity in the means of random parameters in the model, and the effect of other vehicle attributes such as vehicle weight and width on the heteroscedasticity of the parameters. We find that the heterogeneity effects are statistically strong (confidence level in excess of 95%) while the heteroskedastic effects are very weak. Nevertheless, the findings highlight the importance of hybrid vehicle attributes in the analysis of crash severity. A majority of our dataset consists of hybrid-non-hybrid crashes (only 10 crashes involved hybrid-hybrid crashes.) This suggests the plausibility of heterogeneity and heteroscedasticity due to the vehicle types involved in the crashes. Our initial attempt was to focus on hybrid attributes. In this sense, our finding may be limited to the dataset we collected – a wider dataset consisting of more diverse


hybrid vintage as more years of future crash data is made available may indicate a larger list of potential influencers. Toward this aim of uncovering a larger set of vehicle attributes, the assembly of the dataset as shown in this paper should serve as a useful precedent. We collected a wide variety of hybrid specific information such as vehicle height, width, etc. To the author’s knowledge, this degree of comprehensiveness in the extant literature is absent, which indicates another utility of this paper in terms of original contributions to the field of crash severity research. This analysis has shown the importance of heterogeneous and heteroskedastic influences in the construct of random parameter models of hybrid involved crash severity. The variation in the parameter means due to vehicle vintage underscores the hybrid vehicle technology from a safety standpoint, which in turn can lead to better safety conscious planning of hybrid related design implications. We find that newer hybrids capture heterogeneity in means via a stronger effect than hybrids four years or older. The reference timeline for this finding is a crash dataset for the period 2005-2010. Further research in this area is needed to adequately determine the temporal evolution of hybrid effects with a more diverse vintage of hybrids. As more diversification of hybrids occurs in the market, newer models will be required to expand the heterogeneity vector to include all possible vehicle types. Another area of future research relates to multi-vehicle collision propensities involving hybrid-non-hybrid combinations. As we noted in the discussion of the two-vehicle dummy and multi vehicle effects, a very small percentage consisted of hybrid-hybrid combinations. When one extends this to multi-vehicle collisions, the combinations tend to explode, but nevertheless this is an area that can be explored with a larger and richer sample of hybrid involved collisions as the market continues to adopt more hybrids.

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