Analysis of Existing Data: Prospective Views on Methodological Paradigms (2012)

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33 C h a p t e r 3 This chapter describes each of the data sets analyzed by the Penn State team along with the results of the analyses per- formed on those data. The chapter begins with a discussion of the VTTI data and models followed by a discussion of the data from UMTRI and the models estimated from those data. VttI Driver-Based Data and Models Table 3.1 provides an overview of the data provided by VTTI that were used by the Penn State team. As noted in Chapters 1 and 2, the sample size was much less than the team expected, and in some cases, variables requested were not provided. Events are identified by using a screening technique devel- oped by VTTI (Dingus et al. 2006); the Penn State team received event data and other attributes directly from VTTI. Review of video in and around the vehicle was used by VTTI to develop variables typically recorded on police accident reports (e.g., crash type and assessments of precipitating event, driver distraction, and impairment), but in this case observed on the video. In addition, the driver-related attri- butes typically collected at the time of subject recruitment were subsequently used in models to explore their association with event occurrence. Variables in the data set included measures of demographics, physiological attributes, and often measures of possible crash predisposition, such as indi- ces of driver aggression or life stress. Specific variables derived from the data are defined in Table 3.1. All data were originally collected by VTTI and assembled into a database for Penn State. The basic depen- dent variable was the identification of event by type (i.e., crash, near crash, or critical incident). This dependent vari- able was used individually in event-based models as a cate- gorical outcome or as a count by type in driver-based models. Precipitating event attributes included a designation of vehi- cle loss of control by the driver when driver actions resulted in the vehicle being over the lane or edge line. These variable descriptors were taken from descriptions in police accident reports or NHTSA databases to facilitate subsequent analy- ses. Driver impairment is based on observation of the driver on video, not on any in-vehicle technology. Driver distraction was carefully categorized and included distraction from wireless device use; vehicle-related activities (e.g., adjusting heat and radio); passenger-related activities (e.g., talking and interacting with a passenger); talking to self, singing, and other activities; internal distractions such as day- dreaming or being lost in thought; dining (includes eating or drinking); and a collection of other distractions occurring in small numbers individually. Each of these distraction categories was only coded once for each driver and was dichotomous. Context variables were also observed from the video, including the four variables shown in Table 3.1. Traffic den- sity was estimated in five categories based on the density of traffic observed around the vehicle at the time of the event. Driver attributes included objective variables such as age and gender along with crash predisposition measures. The Dula Dangerous Driving Index (DDDI) was intended to provide a detailed description of the type of dangerous driving partici- pants may engage in, as well as a total danger index (Dula and Ballard 2003). The Life Stress Index was used to describe the level of stress the driver was experiencing caused by issues such as job problems and family difficulties (Dingus et al. 2006). Such issues do not pertain directly to driving, but they are thought to be associated with crash risk. All driver attribute data were collected at the time of subject recruitment. Comparisons with Poisson and Negative Binomial Distributions A preliminary check of model fit was conducted by plotting a dependent variable with an assumed Poisson distribution by using the sample mean, since Poisson distribution can be described by only one parameter, l. An NB distribution is also plotted by using the sample mean and variance, since an Data Description and Modeling Results

34 Accordingly, one may also consider the use of ZIP and ZINB models, which can improve model goodness of fit. Systematic Model Testing A series of count regression models were tested in groups. In general, a Poisson regression, NB regression, and ZIP model were tested with the same set of variables. Early testing using this approach indicated that parameter estimates were not consistent NB distribution needs to be described by two parameters, a and b, which can be substituted by the sample mean and vari- ance. The values of the overdispersion parameter a, shown in Figure 3.1 and Figure 3.2, are 2.55 and 2.15, respectively. The values of a suggest that no matter which dependent vari- able is used, the NB distribution fits better than the Poisson distribution as a result of the violation of the assumption of the mean being equal to variance. Poisson models tend to underpredict zeros, and NB models overpredict zeros a bit. Table 3.1. Summary of VTTI Variables Used in Modeling Variable Type Definition Source Comment Event of interest Crash; near crash; critical incident Observed from video (see text) Crashes include events recorded on police accident reports; others are new information available only from naturalistic studies. Event Attributes Precipitating event • lost control • subject over lane/road edge Event immediately preced- ing crash Video Observed from video in naturalistic studies; categorical dichotomous variable. Driver impairment • suspected drug or alcohol impairment • fatigued/sleepy Suspected alcohol/drug involvement Suspected fatigue/ sleepiness/drowsiness Video Alcohol/drug involvement observed in natural- istic study; required much judgment. Driver distraction • wireless device • vehicle-related • passenger-related • talking, singing, etc. • internal distraction • dining • other Distraction by category Video Distraction is observed in video. Context Road, environment, and traffic conditions at time of event • presence of curve • day/night/dusk • road surface condition • traffic density Presence of a road ele- ment or environmental condition at time of event Video The context within which the event occurred is observed through the use of video; cate- gorical variable, typically dichotomous. Driver Attributes Demographic • gender • age • years driving Self-reported demo- graphic data Self-reported survey Obtained through self-reports as recorded on questionnaires before the initiation of driving in the instrumented vehicle. Psychological (measures of crash predisposition) • Dula Dangerous Driving Index (DDDI) • Life Stress Index • Driving Stress Inventory Measures of personality, life stress and/or risk acceptance at time of initiation into study Self-reported through use of specific tools before driving Specific predisposition used in total; compo- nents of DDDI used to separate negative emotion, aggressive driving, and risky driving. DDDI also used with individual scale adjustment. Estimated exposure Estimated number of miles driven in previous year Self-reported during subject screening Obtained during subject intake surveys.

35 • Set B: Predictors included a series of gender interaction terms for each of the variables used in Set A. The objective was to explore gender differences, which were expected from the literature. Overall consistency of the models improved, but there were still differences in model significance. • Set C: Predictors included Set A plus a series of predisposi- tion variables (DDDI, Life Stress Index, and Driving Stress Inventory) as main effects. Some predisposition variables were significant; main effects proved a poor specification for these data. across the three basic regression types. As a result, several sets of models were constructed, and model fit was assessed for each set; the findings of the models, including model fit criteria, are sum- marized in Table 3.2. The model sets are described as follows: • Set A: Predictors are main effects for objective data (e.g., age, gender, years driving). This is the starting point for most modeling, but it proved inadequate in the present endeavor as the three model types did not yield consistent parameter estimates, levels of significance, or goodness of fit. 0 . 2 . 4 . 6 . 8 Pr op or tio n 0 2 4 6 Crashes and near crashes observed proportion neg binom prob poisson prob mean = .5327; overdispersion = 2.151 Figure 3.2. Observed crashes and near crashes compared with Poisson and NB distributions. 0 . 1 . 2 . 3 . 4 . 5 Pr op or tio n 0 2 4 6 8 10 Events observed proportion neg binom prob poisson prob mean = 2.131; overdispersion = 2.557 Figure 3.1. Observed total number of events compared with Poisson and NB distributions.

36 is gradually getting closer to the actual level of 47%, indicat- ing a generally better fit in this important attribute. One can quickly see that the first four predictors represent variables interacting with gender. Inexperienced males have an elevated number of events expected, while having a college degree reduces the expected number. For females, the num- ber of years driving and the number of previous violations are negatively correlated with the expected number of events, and the scaled AD score is positively associated. All predictors are significant at conventional levels. The team used a com- fortable p = .20 as the cutoff to allow the inclusion of variables of potential interest that may fail conventional tests because of the small sample size. Several variables contribute to the estimation of overdispersion, including miles driven, years of driving experience, and scaled AD score. Additional Discussion of Frequentist Models: Elasticity To provide some insight into the implication of parameter estimation results, elasticities were computed to determine the marginal effects of the independent variables (Shankar et al. 1995). Elasticity provides an estimate of the impact of a • Set D: This set combined Set B with miles driven per year, a combination that provided a dramatic improvement in overall fit. • Set E: Main effects and interactions were included in this parsimonious model. • Set F: This parsimonious model had a parameterized esti- mate for a using a linear model. Four evaluation criteria are listed in Table 3.2: the percent- age of zeros predicted, the value of a, the Pearson dispersion statistic, and the log likelihood. This summary shows how the team systematically evaluated count regression model quality. Several trends are apparent in the data. The log likelihood generally improves with the smallest value (best fit) occur- ring with the NB model enhanced by a parameterized estima- tion for a. This improvement in overall fit is obtained with six predictors for the NB portion and another three for esti- mating a (the model with parameterized a is summarized in Table 3.3). The Pearson statistic shows continued improve- ment and a continues to drop steadily, indicating that over- dispersion is becoming less of a problem. Note also that as the model explains more variability in the data, the value of the a parameter declines. Finally, the percentage of zeros predicted Table 3.2. Overview of Driver-Based Count Regression Models Model Set Predictors Included in Testing N NB Models Note Predicted Zeros (%)a `b( _ ) Pearson Statisticc Log Likelihood A Gender, number years driving, education beyond bachelor’s degree, bachelor’s degree, number of previous violations, number of previous crashes, age of vehicle 83 62.62 1.68 (.39) 1.49 -151.54 All primary predictors are main effects B DRYRF, DRYRM, PGRADM, PGRADF, BSM, BSF, PVIOF, PVIOM, PACCM, PACCF, CYRF, CYRM 83 59.77 1.49 (.35) 1.38 -147.56 Gender difference consider- ation: Break down pri- mary predictors into interaction terms C Gender, years of driving experience, post bachelor’s, bachelor’s degree, previous violations, previous acci- dents, miles driven in last year, scaled DDDI AD score, scaled DDDI NE score, car age, Life Stress Index score 83 54.72 1.21 (.30) 1.29 -142.41 Consider driver’s attitude toward driving, such as DDDI scores, Driving Stress Inventory, and Life Stress Inventory D DRYRF, DRYRM, PGRADM, PGRADF, BSM, BSF, PVIOF, PVIOM, PACCM, PACCF, CYRF, CYRM, miles driven in previous year 83 52.72 1.12 (.28) 1.12 -139.26 Consider miles driven in a year E LOWDRM1, CYRF, BSM, PVIOF, miles driven in previous year, ADADF 83 51.08 1.04 (.26) 0.96 -138.31 Final model, constant a F LOWDRM1, CYRF, BSM, PVIOF, miles driven in previous year, ADADF 83 NA NA NA -132.30 Final model with parameterized a a Observed percentage of zeros is 47%. b a is overdispersion parameter; significantly greater than zero indicates overdispersion. c Pearson chi-square dispersion statistic; sum of model Pearson residuals divided by degrees of freedom.

37 For example, the average event frequency li for driver i increases 0.71% if the driver is male and has less than 10 years of driving experience, compared with males with more than 10 years of driving experience, assuming the error terms are independent of xik and remain unchanged (and the model is correct). The elasticities from the final NB model are shown in Table 3.4. The elasticity gives an indication of the effect of a predictor on the outcome (expected number of events). A quick scan of Table 3.4 shows that males with at least a college degree are substantially safer than their counterparts; males with less than 10 years’ experience have an increase in expected events. A 1% increase in driving mileage results in a 0.14% increase in expected number of events for both males and females per 1,000 miles driven. Mileage driven per year represents driver exposure to events. More exposure results in a higher probability of crashes and thus a higher expected number of events. variable on the expected frequency and is interpreted as the effect of a 1% change in the variable on the expected fre- quency li. The elasticity of frequency li is defined as E x x xx i i ik ik k ikik iλ λ λ β= ∂ × ∂ = ( )12 where E = elasticity, xik = value of kth independent variable for observation i, bk = estimated parameter for kth independent variable, and li = expected frequency for observation i. Note that elasticities are computed for each observation i. It is common to report a single elasticity as the average elasticity over all values of i. The elasticity shown in Equation 12 is only appropriate for continuous variables such as highway lane width, distance from the outside shoulder edge to roadside features, and vertical curve length (Shankar et al. 1995). It is not a valid evaluator for binary categorical indicator variables. A pseudoelasticity can be computed to estimate an approximate elasticity for indicator variables. The pseudoelasticity gives the incremental change in frequency caused by changes in the indicator variables. The pseudoelasticity for indicator variables is computed as E x x x i i ik ik ik i k k k λ β β β λ λ = ∂ ∂ = −( ) −( ) = − e e e e 0 0 1 1 1 eβk ( )13 Table 3.3. NB Driver-Based Model with Parameterized ` , Best Overall Driver-Based Model Variable Coefficient SE Z p-Value 95% CI Males with <10 years driving experience 1.757 0.331 5.310 .000 (1.108, 2.405) Years driving for females -0.324 0.109 -2.980 .003 (-0.537, -0.111) Having a college degree for males -0.610 0.315 -1.930 .053 (-1.228, 0.008) Number of previous violations for females -0.537 0.170 -3.150 .002 (-0.871, -0.203) Miles driven in previous year 0.000 0.000 5.650 .000 (0.000, 0.000) Scaled AD score for females 0.393 0.165 2.390 .017 (0.070, 0.715) Constant -1.907 0.494 -3.860 .000 (-2.875, -0.939) Variables that Parameterize the Dispersion Parameter Coefficient SE Z p-Value 95% CI Scaled AD index (ADAD) 1.241 0.485 2.560 .011 (0.290, 2.191) Years driving experience 0.063 0.034 1.870 .061 (-0.003, 0.130) Miles driven in previous year 0.000 0.000 1.480 .138 (0.000, 0.000) Constant -11.615 4.506 -2.580 .010 (-20.447, -2.784) Note: The model is based on 83 observations. SE = standard error; likelihood ratio (LR). LR chi-squared (6) = 39.42 probability > chi-squared = 0 pseudo R2 = 0.1297 log likelihood = -132.30 Table 3.4. Elasticities from Final NB Model Variable Elasticity Males’ driving experience <10 years 0.71 Interaction between females and age of car -0.36 Males with bachelor’s degree or above -2.11 Females’ past violations -0.74 Mileage divided by 1,000 0.14 Scaled DDDI aggressive driving (AD) score 0.40

38 each individual had in a year, and the explanatory variables include individual socioeconomic characteristics at Level 1 and gender at Level 2. Models were estimated using the open-source software OpenBUGS. The first 1,000 model iterations were dis- carded as burn-in. The next 100,000 iterations were used to obtain summary statistics of the posterior distribution of parameters. Convergence was assessed by visual inspection of the Monte Carlo–Markov chains. The number of iterations was selected such that the Monte Carlo error for each parameter in the model would be less than 10% of the parameter’s SD. In Table 3.5, the variable names appear in the first column followed by the estimated parameter value, or the mean, and its SD in the next two columns, respectively. The hierarchical modeling structure (full Bayes) produces 5% and 95% credi- ble set estimates, instead of the CIs normally produced in fre- quentist estimation. Parameters with 5% to 95% credible set values that do not include zero are generally accepted as sig- nificant. A single asterisk (*) indicates a significant variable, and a double asterisk (**) indicates a variable that is margin- ally significant (i.e., has a credible set of 10% to 90% that does not include zero). Elasticities were also calculated based on the coefficients from the 100,000 iterations and Equations 9 and 10, as shown in Table 3.6. Therefore, the credible sets for all elasticities of predictors are also available. The scaled DDDI for aggressive driving (AD) showed a 0.4% increase in the expected number of events for a 1% change in the index. Recall that this index represented strong positive responses to questions such as: “I verbally insult drivers who annoy me” and “I deliberately use my car/truck to block drivers who tailgate me.” Although ongoing research debates the effects of aggressiveness on the probability of crashes and the design of questionnaires that intend to quantify driver aggressiveness, results show the existence of an association between driver aggressiveness and the number of events. A 1% increase in females’ past violations results in a 0.74% decrease in the expected number of critical events compared with males. This result could be interpreted as a type of learning effect. A 1% increase in the interaction between females and vehi- cle age results in a 0.36% decrease in the expected number of events compared with the interaction between males and vehicle age. This result is difficult to interpret and may be a variable that represents another phenomenon. Despite many attempts to remove this variable, it persisted. Multilevel Driver-Based Modeling The multilevel driver-based model in Table 3.5 has a two-level specification. The response variable is the number of events that Table 3.5. Estimates for Multilevel Driver-Based Model (NB) Variable Mean SD Percentile 2.5% 5% 10% 90% 95% 97.5% Intercept (F)* -13.71 8.26 -29.32 -27.42 -24.44 -3.14 -0.39 2.63 Intercept (M)* -18.97 6.93 -33.17 -30.74 -27.94 -10.29 -7.95 -5.98 Scaled DDDI aggressive driving (AD) (F)** 0.59 0.38 -0.18 -0.06 0.09 1.07 1.20 1.31 Scaled DDDI AD (M) 0.01 0.26 -0.51 -0.42 -0.32 0.34 0.43 0.52 Scaled DDDI risky driving (RD) (F) 0.34 0.32 -0.32 -0.21 -0.08 0.73 0.87 0.98 Scaled DDDI RD (M)** 0.41 0.28 -0.12 -0.04 0.06 0.77 0.88 0.98 Bachelor’s degree or above (F) 0.08 0.87 -1.62 -1.33 -1.02 1.19 1.52 1.83 Bachelor’s degree or above (M)* -1.24 0.65 -2.53 -2.31 -2.06 -0.42 -0.17 0.04 Years of driving experience (F)** -0.05 0.03 -0.11 -0.10 -0.09 -0.01 0.00 0.01 Years of driving experience (M)* -0.06 0.02 -0.11 -0.10 -0.09 -0.03 -0.02 -0.02 Mileage driven in past year (F)* 0.87 0.55 -0.13 0.03 0.18 1.63 1.81 1.99 Mileage driven in past year (M)* 1.77 0.56 0.74 0.89 1.07 2.49 2.73 2.93 Past violations (F)* -0.60 0.29 -1.21 -1.10 -0.98 -0.23 -0.13 -0.05 Past violations (M) 0.06 0.22 -0.38 -0.31 -0.22 0.33 0.41 0.49 sigma2.v* 1.71 0.59 0.85 0.94 1.06 2.49 2.81 3.13 *Significant at 95%, **significant at 90%. Note: M = male; F = female. Dbar (posterior mean of the deviance) = 204.7 Dhat (point estimate of deviance) = 159 DIC (deviance information criterion) = 250.3 pD = 45.62 (pD [effective number of parameters] = Dbar - Dhat)

39 difference is that one can now assess the effect of the variable on men and women separately. Discussion of Outliers As a by-product of running the hierarchical driver-based model using a Poisson lognormal model, the team was able to observe individual drivers’ random effects. Any random effect that has a mean significantly different from zero for a driver identifies that person as an outlier or a substantial deviation from the sampled driver population. This devia- tion can be interpreted as the driver coming from a different population of drivers than the majority of drivers in the data set. The chance that each of the five drivers (2, 4, 15, 16, and 55) listed in Table 3.7 is identified as an outlier is at least 95%. For example, Driver 55 had 28 events at his age of 59 years. Statistical outliers thus may reflect some type of selection bias or model misspecification. Both females’ and males’ total mileage driven in 1 year are inherently significant, supporting the argument that higher exposure increases the likelihood of events. Moreover, both males and females with more driving experience had a reduced expected number of events. Female scaled aggressive driving (AD) scores and male risky driving (RD) scores are marginally significant, implying that a higher female scaled AD score and male scaled RD score increase the expected number of events. This model provides two additional findings. First, males with at least a college degree have fewer events than males without bachelor’s degrees; this effect is not significant for females. Second, females who had more traffic violations in the past had fewer events in a year. The interested reader can compare the parameter values and the elasticities in this hierarchical model (Tables 3.5 and 3.6, respectively) with the NB model in Tables 3.3 and 3.4. There are changes in sign and magnitude, but the greatest Table 3.6. Elasticity Estimates from Multilevel NB Model Variable Mean SD Percentile 2.5% 5% 10% 90% 95% 97.5% E.adad (F)** 1.16 0.80 -0.37 -0.13 0.14 2.17 2.51 2.79 E.adad (M) -0.73 0.86 -2.38 -2.13 -1.82 0.37 0.70 0.96 E.adrd (F)** 1.07 0.83 -0.62 -0.32 0.02 2.12 2.40 2.66 E.adrd (M)** 1.79 1.34 -0.89 -0.42 0.09 3.49 3.98 4.39 E.BSabove (F) -0.83 1.95 -5.65 -3.92 -2.57 0.48 0.60 0.68 E.BSabove (M) -0.97 1.10 -3.73 -3.04 -2.36 0.16 0.33 0.46 E.exp (F)* -0.31 0.18 -0.68 -0.61 -0.54 -0.08 -0.02 0.03 E.exp (M)* -0.79 0.27 -1.34 -1.24 -1.14 -0.46 -0.38 -0.30 E.mil (F)* 2.71 1.47 0.09 0.46 0.89 4.58 5.10 5.76 E.mil (M)* 10.42 3.65 3.98 4.84 5.91 15.21 16.81 18.34 E.pvio (F)* -0.35 0.17 -0.69 -0.63 -0.56 -0.14 -0.09 -0.04 E.pvio (M) 0.10 0.10 -0.11 -0.07 -0.03 0.23 0.26 0.29 Note: E. = elasticity. Table 3.7. Identification of Outliers: Mean and SD of Expected Number of Events for Driver-Based Hierarchical Model Driver ID Mean SD Percentile 2.5% 5% 10% 90% 95% 97.5% Driver 2 1.78 0.92 0.03 0.31 0.63 2.96 3.33 3.66 Driver 4 -1.75 0.82 -3.45 -3.15 -2.81 -0.73 -0.45 -0.21 Driver 15 1.80 0.60 0.64 0.84 1.05 2.57 2.80 3.01 Driver 16 2.01 0.62 0.83 1.02 1.23 2.80 3.05 3.26 Driver 55 2.59 0.61 1.42 1.61 1.83 3.36 3.60 3.81

40 sign and some, such as curve, change in level of significance as well. Using a Chi-square test to compare the two models results in a significant difference being found with the calculated Chi- square equal to 8.82 (resulting level of significance is p = 0.0030). The situation becomes even more dramatic when event attributes are added: ORs double or triple for some predic- tors. The model’s goodness of fit is dramatically improved, as shown by both the log likelihood and pseudo R2 values. Tests between the full model and the model with context and driver attributes again show significant improvement with a Chi- square value of 10.73 and level of significance, p = 0.0011. Why did the team undertake this exercise? The primary rea- son was to point out the difficulty in modeling a data set with almost no prior history. Naturalistic data really are unique, and this experience points out one of the challenges in their analysis. Many other transportation fields provide researchers with a sufficient history to know where to begin and what pitfalls to avoid. In naturalistic analysis researchers are virtually starting from scratch and have to evolve rules from their own experi- ence. This experience is in some ways similar to what was learned in the driver-based models: develop models carefully. In this case, the message is to be sure all three components of the model are present, or ORs and other estimation output are likely to be biased. For the purposes of discussion, one can assume that the fully specified binary logit model shown in Table 3.9 is a reasonable comparison to a hierarchical model, as specified in Chapter 2. Multilevel Event-Based Model Table 3.10 presents a summary of an event-based hierarchical model. The table shows all variables included in the hierar- chy. Parameter values and SEs are included along with ORs (for significant variables only). At Level 1, the event-based data set presents two types of variables: event attributes (occurrences inside the car) and driving environment (occur- rences outside the car). Level 2 models driver attributes, rep- resenting the varying effects of predisposition (DDDI and Life Stress Index values) and years of driving experience. Notice that the two precipitating events are significant (loss of control is marginally significant). Loss of control includes excessive speed and a loss of control with poor road condi- tions. Unfortunately, the team was unable to make further inferences concerning lane versus road edge departures (or left- versus right-side departures) because of limitations in sample size for crashes and near crashes. Both parameters are positive, indicating that these behaviors increase crash and near-crash likelihood compared with that for a critical incident. With the modeling results for a binary logit model (fre- quentist estimated) and a hierarchical model now available, the pattern of parameter significance and magnitude can be discussed. Several interpretations of the distraction variables The conclusion is that there are substantial advantages to using the Bayesian approach, one of which is to identify and quantify individual driver heterogeneity. In this case, the drivers so identified may be considered as sampled from a different population of drivers. Four of the drivers (2, 15, 16, and 55) had higher underlying event risk. Driver 2 was an inexperienced male driver with high annual mileage who had a lower than expected event risk. No generalities can be made from a single observation; however, this result shows that drivers with low expected event risk, as well as high-risk drivers, may be identified by this method. VttI Data: event-Based Models Comparing Different Single-Level Models: Effects of Omitting Predictors In many respects the easiest way to begin to understand the modeling conducted on the 100-car study events is to present a series of straightforward examples. The Penn State team con- ducted initial screening of binary, multinomial, and ordered logit models to assess their ease of interpretation and overall quality of prediction. The binary logit model resulted in the best goodness of fit, as indicated by an Akaike Information Cri- terion (AIC) of 205.32. The AIC values for the multinomial and ordered logit models were 296.62 and 293.11, respectively. The binary logit model is, in many respects, the most straight- forward to interpret. Thus, the focus of the analysis was based on the use of binary logit models. Binary logit models were estimated to develop an under- standing of the effects of omitting variables. One model included only driving environment variables, and the other included a combination of driving environment variables and driver attributes. The third model, with the identical specifica- tion, was a model with the previous two sets of variables and an added set reflecting event attributes. The data used in the analysis are summarized in Table 3.8, and the results of the modeling are summarized in Table 3.9. Additional tests were conducted with other pairs of the three sets of variables, but discussion of these three models is sufficient to identify trends. Table 3.9 shows the parameter mean and SD for each of the three models. Next to these values is the percentage differ- ence with respect to the last, fully specified model. The next column for each model shows the odds ratio (OR) and, in parentheses, the difference in the OR between the full model and the other two. The first model considers context only; this is a familiar model to many road safety analysts because context variables form the primary variables typically included in a safety perfor- mance function, which is fundamental to contemporary road safety management. Notice that by adding driver attributes, the parameters in the first model change substantially: some change

41 • Distraction 5: internal distraction—reading, a moving object in the vehicle, dealing with an insect or pet. • Distraction 6: dining—includes eating or drinking. • Distraction 7: other—smoking, external distraction, per- sonal hygiene, and driving-related inattention to forward roadway were aggregated into this category as a result of sample size constraints. Among the distractions, internal and vehicle- and passenger- related distractions are significant, and talking/singing/ daydreaming is marginally significant. All have positive coef- ficients, indicating that they increase the likelihood of a crash are available. The baseline for this set of variables is no dis- traction. Variables were extracted from video observations of drivers during the events of interest, including • Distraction 1: wireless device—related to locating or oper- ating a wireless device. • Distraction 2: vehicle related—adjusting climate control, radio, audio devices, and other vehicle devices. • Distraction 3: passenger related—attributable to a passen- ger in the subject’s vehicle. • Distraction 4: talking, singing, or daydreaming—self-evident definition. Table 3.8. Variable Definitions for Tests of Event-Based Omitted Variable Bias Group Variable Name Definition Variable Type Mean SD Min Max Dependent variable Event outcome Crash/near crash (1); critical incident (0) Binary 0.25 0.44 0 1 Event attributes Precipitating Factor 1: Loss of control Lose control of vehicle as a result of vehicle failures, poor road conditions, excessive speed (from GES critical event) Binary 0.37 0.23 0 1 Precipitating Factor 2: Subject over lane line/ road edge System detected vehicle over the lane line or roadway edge (from GES critical event) Binary 0.50 0.25 0 1 Driver Impairment 1: Drowsy, sleepy, asleep, and fatigue Driver appears to show these characteris- tics (all are based on GES “driver distracted by” variable) Binary 0.21 0.16 0 1 Distraction 1: Wireless device Distraction related to locating or operating a wireless device Binary 0.10 0.08 0 1 Distraction 2: Vehicle related Adjusting climate control, radio, audio devices, etc. Binary 0.04 0.04 0 1 Distraction 3: Passenger related Distraction attributable to passenger in vehicle Binary 0.06 0.05 0 1 Distraction 4: Talking/ singing/daydreaming Self-evident definition Binary 0.04 0.03 0 1 Distraction 5: Internal distraction Reading, moving object, handling insect or pet Binary 0.06 0.05 0 1 Distraction 6: Dining Includes eating and drinking Binary 0.02 0.02 0 1 Distraction 7: Other Smoking, external distraction, personal hygiene, driving-related inattention to forward roadway Binary 0.11 0.10 0 1 Driving context Alignment Curve (1); tangent (0) Binary 0.31 0.22 0 1 Lighting Dawn/dusk (1); day (0) Binary 0.06 0.06 0 1 Surface condition Dry (1); wet/icy/snowy (0) Binary 0.19 0.15 0 1 Traffic density Not free flow (1); free flow (0) Binary 0.25 0.19 0 1 Driver attributes DDDI AD Index Scale reflecting intent to harm Continuous 11.44 1.41 7 23 DDDI NE Index Scale reflecting negative emotions during driving Continuous 21.19 1.41 11 34 DDDI RD Index Scale reflecting risky driving Continuous 19.28 0.71 12 31 Driver experience Number of years with license Continuous 16.167 7.071 1.5 52 Life Stress Index Scale reflecting stress in one’s life Continuous 180.2 45.3 0 560

42 Table 3.9. Summary of Initial Estimated Binary Logit Event-Based Models Type Variable Context Only Context and Driver Attributes Fully Specified Parameter Coeff Diff (%) OR (% Point Diff) Parameter Coeff Diff (%) OR (% Point Diff) Parameter ORCoeff SD Coeff SD Coeff SD Intercept -1.155 0.231 NA NA 0.903 1.172 NA NA -1.672 1.808 NA Event attributes Precipitating Event 1: Loss of control NA NA 1.135 1.023 3.111 Precipitating Event 2: Subject over lane line/road edge 2.269 0.998 9.670 Driver Impairment 1: Drowsy/ sleepy/asleep/fatigued 1.571 0.618 4.811 Distraction 1: Wireless device 0.780 0.775 2.181 Distraction 2: Vehicle related 2.224 0.940 9.244 Distraction 3: Passenger related 1.794 0.848 6.013 Distraction 4: Talking/singing/ daydreaming 1.996 1.089 7.360 Distraction 5: Internal distraction 3.086 0.985 21.889 Distraction 6: Dining 1.879 1.306 6.547 Distraction 7: Other 1.248 0.740 3.483 Context Alignment 1: Curve 0.644 0.331 -30.89 1.904 (-63.6) 0.475 0.371 -0.06 1.608 (-93.2) 0.932 0.475 2.540 Lighting 1: Dawn/dusk 1.105 0.609 -51.82 3.019 (-688.6) 0.743 0.657 -50.13 2.102 (-780.3) 2.293 0.743 9.905 Surface condition 1: Wet/icy/ snowy 0.078 0.411 -91.53 1.081 (-142.6) -0.171 0.463 -118.61 0.843 (-166.4) 0.919 0.621 2.507 Traffic density 1: Not free flow -1.633 0.554 -25.34 0.196 (8.4) -1.995 0.594 -8.77 0.136 (2.4) -2.187 0.686 0.112 Driver attributes DDDI AD score NA -0.099 0.043 30.39 0.906 (1.9) -0.120 0.050 0.887 DDDI NE score -0.095 0.056 19.19 0.909 (-0.6) -0.089 0.070 0.915 DDDI RD score 0.049 0.075 -33.79 1.050 (0.2) 0.047 0.092 1.048 Driver experience -0.033 0.015 49.33 0.968 (2.6) -0.060 0.020 0.942 Life Stress Index 0.004 0.001 -17.03 1.004 (0) 0.004 0.002 1.004 Fit Statistics Log likelihood -117.802 -103.424 -82.818 Pseudo R2 0.079 0.192 0.349 Note: Coeff = Coefficient; Diff = Differential. *Significant difference between context with driver attributes and context only: chi-square = 8.82, p = .0030. **Significant difference between full specification, single level and context with driver attributes: chi-square = 10.73, p = .0011.

43 the past year. There are 42 events, including such items as per- sonal injury or illness, change in financial state, and change in social activities. Each of these items has a weight; the variable entered in the model is the sum of the weights for each driver for each of the items checked. Based on the structure of the inventory, it measures general stress in someone’s life. The DDDI consists of 28 statements to which the driver is asked to respond on a 5-point Likert scale (never, rarely, sometimes, often, and always). Each of the categories of response is assigned an integer from 1 to 5. Example index statements include but are not limited to the following: “I ver- bally insult drivers who annoy me”; “Passengers in my car/ truck tell me to calm down”; and “I will weave in and out of slower traffic.” The responses to the questions are divided into the three categories of aggressive driving (AD), negative emo- tional (NE) driving, and risky driving (RD) (Dula and Ballard 2003). Each captures a different aspect or component of dan- gerous driving. The AD component is intended to reflect behavior intended to harm other living beings, either physi- cally or emotionally. A positive response to the first example or near crash compared with the likelihood of an incident. Using a wireless device (at least at the time of data collection) is not significant. Driver impairment, including drowsiness, sleepiness, and fatigue, is also significant and positive. Three context variables are significant determinants of event likelihood. Non-free-flow traffic density is negative in sign, indicating that this reduces the likelihood of a run-off-road crash or near crash and increases the likelihood of a critical inci- dent. The presence of a curve and conditions at dawn or dusk both increase run-off-road crash and near-crash likelihood. The variable wet/icy/snowy is marginally significant and positive. Life stress and years of driving experience are significant in differentiating events. A high score on the life stress test increases the likelihood of a crash or near crash compared with the likelihood of an incident, while drivers with more years of (self-reported) driving experience have a reduced likelihood of a crash or near crash compared with the likelihood for a critical incident. Several driver-level variables are significant. The Life Stress Inventory asks drivers to mark each event that occurred during Table 3.10. Multilevel Event-Based Model Type Variable Parameter Percentile ORMean SD 2.5% 97.5% Level 1 Covariates: Event attributes Intercept -1.77 1.88 -5.58 1.86 NA Precipitating Event 1: Loss of control 1.51 1.13 -0.50 3.91 9.08 Precipitating Event 2: Subject over lane line/road edge* 2.83 1.11 0.90 5.21 33.42 Driver Impairment 1: Drowsy/sleepy/asleep/fatigued* 1.29 0.58 0.17 2.46 4.29 Distraction 1: Wireless device 0.25 0.78 -1.31 1.74 NA Distraction 2: Vehicle related* 1.95 0.97 -0.01 3.81 11.1 Distraction 3: Passenger related* 1.51 0.86 -0.16 3.21 6.58 Distraction 4: Talking/singing/daydreaming** 1.67 1.14 -0.64 3.85 9.82 Distraction 5: Internal distraction* 3.13 1.00 1.24 5.18 38.82 Distraction 6: Dining 1.05 1.44 -1.83 3.82 NA Distraction 7: Other 1.12 1.05 -0.97 3.18 NA Level 1 Covariates: Driving environment Alignment 1: Curve* 1.10 0.51 0.11 2.11 3.38 Lighting 1: Dawn/dusk* 2.42 0.79 0.89 3.99 15.12 Surface condition 1: Wet/icy/snowy** 0.82 0.65 -0.43 2.10 2.79 Traffic density 1: Not free flow* -2.38 0.69 -3.83 -1.11 0.12 Level 2 Covariates: Driver attributes DDDI AD Index* -13.67 5.31 -24.35 -3.41 0.87 DDDI NE Index -10.83 7.07 -24.88 2.70 NA DDDI RD Index 6.13 9.21 -11.83 24.39 NA Years of driving experience* -0.06 0.02 -0.11 -0.03 0.94 Life Stress Index* 0.50 0.17 0.18 0.83 1.67 *Significant at 10% level. **Significant at 20% level.

44 sought. Driver Impairment 1 (drowsy, sleepy, fatigued) was substituted as a predictor and a much better fit occurred overall, including reduced SEs for several variables. While the team was pleased by the improved fit, there was concern about the apparent model instability. Such instability may be the result of the small sample size, but it may also reflect endogeneity among the predictors. As a recommendation to future SHRP 2 analysis contractors, the team suggests that care be exercised in surrogate analyses; additional empirical testing in several sites and with other drivers should reveal more about this issue. A Method of Identifying Event Validity in Surrogate Testing Background One of the principal goals and challenges of the SHRP 2 Safety program is to develop procedures to identify crash surrogates. One useful definition was articulated by Hauer and Gårder (1986) in their focused discussion of the traffic conflicts tech- nique as a surrogate measure (quoted above). Additional attri- butes of surrogates as having a time dimension and being responsive to countermeasures in the same way as in an actual crash have been proposed as part of the present research (Shankar et al. 2008). More generally, surrogates can be con- sidered as measures that can be substituted for crashes in a safety analysis: in the data for this project, they are typically vehicle kinematic– and event-related measures that offer some description of vehicle movement and/or position relative to the roadway. In concept, one would like to test and explore these issues in a naturalistic data set of many crashes, near crashes, and critical incidents. With a large naturalistic data set of 100 or more vehicles measured over 2 years or more (as in the S07 project), potentially thousands of observations of each can- didate surrogate (e.g., thousands of measures of individual lateral accelerations at curves) would be available. It may be useful to explore whether the events containing the surrogate measures are similar to crash events. If there were a way to test for similarity, then researchers might be able to obtain a large enough and more valid set of surrogate measurements. So, the goal here is to develop a way to validate surrogates. The Penn State team wants to see if the observations they have do the best job of identifying safety problems. The specific test of validity proposed is to use the event-based model to predict the probability of a crash event. Observations of the surrogate measure (e.g., a vehicle kinematic measurement) would then be screened to include only those involved in events predicted to be crashes by the model. Of course, such an analysis is con- tingent on the model’s correctness. This method is offered as a promising way to improve future surrogate analysis. statement mentioned above represents AD, to the second statement NE, and to the last statement, RD. The value of the predictor variable is the sum of the rating responses to each question in each of the three DDDI components. The model indicates that those who are aggressive or who have negative emotions while driving are more likely to have critical inci- dents (i.e., less likely to have crashes or near crashes). This finding needs to be verified with a larger data set using non- events as the baseline. The point here is that these predisposi- tion measures need to be included in models of this type because they appear to be associated with event outcomes. A few words are in order concerning the use of event-based models to test possible surrogates. Potential surrogates include the precipitating events of subject over lane or road edge and loss of control. These two variables were derived by the VTTI data coders as part of the original 100-car data set. In most event models they were strong indicators of crash or near- crash events in the categorical models; in hierarchical models subject over lane or road edge was the second-strongest predic- tor associated with the prediction of a crash or near-crash event. Although this measure is strongly associated with crash events, it lacks a time dimension, which is one of the desirable surrogate criteria proposed by Shankar and colleagues (2008). In their discussion of the traffic conflicts technique as a surro- gate measure, Hauer and Gårder (1986) commented that “one should be able to make inferences about the safety of an entity on the basis of a short duration ‘conflict count’ instead of hav- ing to wait a long time for a large number of accidents to materialize.” This suggestion could not be applied because the team did not have access to the comparable set of subject behaviors for noncrashes. Were such data available, the hierar- chical model could be formulated to test the association between this measure and crashes. The application of this mea- sure outside of SHRP 2’s instrumented vehicles is as yet uncer- tain, but it is clear that it has some potential as a surrogate. These models have important implications for SHRP 2 pro- gram concerns to identify useful surrogate measures. The cat- egorical models explored in this study appear to be a useful paradigm to explore surrogates when they include event- based data. While kinematic measures or combinations of kinematic and roadway position measures were not directly tested with VTTI data, the Penn State team believes they are possible measures for future testing. The subject over lane or road edge variable contained position-only information and was very strongly associated with crash-related events; the team believes that the inclusion of longitudinal or lateral velocity and lateral position information would enhance this variable’s predictive ability. A limitation of the categorical models deserves mention. Initial event-based models, both bivariate logistic and hierar- chical, used improper speed as an event-based predictor. Successful model fit was obtained, but improvement was

45 crashes. This is the first example of a validated event that can be used as a source of a surrogate observation (e.g., the value coded for the variable exceed road or lane edge); if kinematic measures were available as candidate surrogates, the lateral vehicle position or the longitudinal or lateral speed when the event took place could be used. Events I19 and I195 are incidents, but they are predicted to be crashes. Thus they may be considered statistically close to crash events even though crashes were avoided. A surrogate may be selected from these events with additional validity as well. What is of interest is that researchers now have a statisti- cal method to identify and quantify these promising events. While the figure is a bit cluttered, several promising inci- dents occurring on curves are readily identifiable (e.g., I32, I31, and I205). Events NC624, NC198, and C13 are among several events correctly predicted as crashes or near crashes. Figure 3.3 provides an aggregate perspective, as it contains only the context variable of presence of curve. All six vari- ables listed above can be used to create more specific, well- defined contexts to determine how many valid events are identified in each context. One particular advantage of naturalistic data such as the VTTI data is the ability it offers the researcher to use the nar- rative to compare the etiology of incidents and crashes in each context. The narrative, derived from analysis of video after the event is identified by kinematic screening criteria, can be used to verify if the etiology of the incident in a context was actually similar to that of crashes in the same context. Such verification can be thought of as additional validation for the event in question. Proposed Method The proposed method takes advantage of the event-based models developed from the VTTI data analysis for road departure crashes. One of the important factors derived from the event-based models was the presence of context variables as important predictors of crashes or near crashes. These variables included the presence of a horizontal curve, dawn or dusk, road surface conditions, traffic conditions (free-flow or non-free-flow), and presence of driver distraction at the time of the event. Other combinations of context variables could be used, but these are of particular interest because they were among the most significant predictors in the event- based models. The basis of the method is to work with the predicted outcomes from the model that differentiates the two event groups. Output from the hierarchical models was chosen because the team believed that such output is more valid from a strictly statistical standpoint. Figure 3.3 summarizes all the observations. Events are denoted with a number after a letter code as follows: I for incident, NC for near crash, and C for crash. The left half of the figure shows results for events taking place on tangent sections (curve = 0), and the right half for events occurring on horizontal curves. The y axis rep- resents the predicted probability for each event. Any event with a predicted probability above 0.5 is considered to have been predicted to have that outcome. For example, crashes C130 and C133 occur on tangent sections and are predicted as crashes with a probability close to 76%. Incidents I19 and I195 also occur on tangent sections but are predicted as NC1 C2I3 I45 I6 I12 I14 I16I17 NC18 I19 I20 I21 NC22 I2325 26I27 I 9 3 I33 I34 C35 I36 I37 38423467I 0134 I56 8606 I64 786773 757 NC788081 I82 87 8 992 I94I 5 C96 C98 NC99 I 00 01 102 1 56 8 NC109 1 012 I114 781 45 C126 I127 C130 NC131 C133 I134 36 8 C139 23 145 47 C148 0 I151 3 C155 156 NC157 158 60 6466 168 C169 I 7172 C173 C174 I 75 6I 7 1 8 981 838 NC185 86 7 I18890 9129 I195 NC197 NC199201 203 NC213 2223 I226 227 I7 NC8 NC9 I10 NC11 C13 I15 NC24 NC28 I31 I32 I39 I40 I45I48I529 I61 I62 656I7 I83 I85 C86I89 93 C97 C103104 NC107 113 NC115 I116 I119 NC120 NC122 123 NC129 I 2 NC137 I140 NC141 I144 NC146 149 NC152 59I 61 NC162 63 C165 7I189 194 NC196 NC198 200 2 2 I205 I206 I208 20 210 I212 NC214 I215 219 I 21 225 0 . 5 1 0 .5 1 0 .5 1 0 1 Pr (cr as h)_ by m ult ile ve l m od el Bin Graphs by curve Figure 3.3. Predicted events for tangent (left) and curve (right) sections.

46 tives written by data coders at VTTI during data assembly. All three events involved a driver falling asleep and nearly running off the road. Other scenarios and contexts yielded different numbers of crashes, near crashes, and critical incidents. There is now a structured statistical method that offers promise in using naturalistic data to identify events that are similar to crashes; once identified as such, measures strongly correlated with the event outcome can be tested as surrogates. ExamplE 2 Figure 3.5 illustrates another context in which the nature of the relationships is less clear. This context includes the following Applications to More Specific Contexts ExamplE 1 Figure 3.4 shows the predicted probabilities for three event cases that occurred during a crash scenario with the following condi- tions: tangent road section, dawn or dusk lighting conditions, free-flow traffic, dry road, and vehicle over road edge. For this context, critical incident I195 was predicted with high probabil- ity as a crash. Although the model was structured to differentiate crashes and near crashes from critical incidents, a by-product of the model estimation is the identification of events that are predicted to be similar to crashes or near crashes. These three events were validated as being similar by comparing the narra- Figure 3.4. Example 1: Using predicted probabilities to identify crash surrogate events. Figure 3.5. Example 2: Using predicted probabilities to identify crash surrogate events.

47 looks away from the road to obtain the object. The vehicle drifts to the right and nearly hits a boat loaded on a trailer that is parked on the right side of the road. Case 2 (Figure 3.7) involves the following context: straight alignment, dawn or dusk, free-flow traffic, dry surface, fatigued driver, no loss of control, and vehicle over edge of road. The following narratives compare I195 to NC199 and NC201 (these three events belong to the same male, age 59 years): • I195: Subject falls asleep behind the wheel and drifts toward the right edge of the road. He suddenly wakes up and jerks the wheel to the left to get back in his lane. • NC199: Subject driver falls asleep while driving, and the vehicle runs off the road to the right. • NC201: Subject driver falls asleep while driving, and the vehicle runs off the road to the right. Case 3 (Figure 3.8) involves the following context: curve, daylight, free-flow traffic, dry surface, no fatigue, no loss of control, and vehicle over edge of road. The narratives below compare I15 to C97, NC120, NC198, and NC9: • I15: Subject is distracted and drifts over the left side of her lane. She has to steer right to avoid hitting the median. • C97: Subject driver pulls over to park along the right side of the road and hits the curb as he is parking. • NC120: Subject driver is looking at a piece of paper as he drives under an overpass. The road curves to the left and the vehicle veers left and nearly hits the left median. attributes: horizontal roadway curve, daylight, free-flow traffic conditions, dry surface, no loss of control, and vehicle off road edge. Incident I15 was identified as a promising event, and crash C97 and near crashes NC120, NC198, and NC9 were correctly predicted. There are a host of incidents that were cor- rectly predicted but were likely to be poor events for the pur- poses because they were not similar to crashes. Several crashes and near crashes were also predicted in the range of 0.0 to 0.4 (not well described by the model). This case illustrates that dif- ferent contexts have differing numbers of events, and the abil- ity to predict varies substantially. Other Promising Events Identified and Their Corresponding Narratives The following six cases evaluate I19, I195, I15, I31, I205, and I32 as potential useful events. Case 1 (Figure 3.6) involves the following context: straight alignment, daylight, free-flow traffic, dry surface, no driver impairment, no loss of control, and vehicle over edge of road. The following three narratives compare I19 to C174 and NC99: • I19: Subject driver is reading, and, as a result, she loses control of the car. She has to steer to the left in order to avoid any kind of conflict (internal distraction). • C174: Subject driver is holding a cup in her right hand and turning right at an intersection. She cuts the corner and hits the curb on the right side. • NC99: Subject driver is reaching for what appears to be a cell phone charger. She takes both hands off the wheel and Figure 3.6. Predicted crash probabilities for Case 1. I190 I182 I147 3 I95 I 08 I27 I88 I101 I172 9 2 I136 I60 I19 I227 88 I34226 I64 NC18 NC1 NC22 NC145 NC109 NC185 NC99 81 26 C96 C174 C80 0 . 2 . 4 . 6 . 8 1 Pr (cr as h)_ by m ult ile ve l m od el 0 1 1: Crash/Near Crash; 0: Critical Incident

48 These examples are sufficient to illustrate the method. The team hopes that if a valid model is developed, the screen- ing of valid events will help in the identification of the sur- rogate measured within those contexts, eliminating the need to go back to narratives for additional assurance. Automat- ing the process through the use of an event-based model promises potential time savings and accurate surrogate identification. • NC198: Subject driver is looking at or for an unknown object near the passenger seat. The road curves to the right and the vehicle goes off the right edge of the road. • NC9: Subject driver is talking to a passenger in the adjacent seat while driving on a single-lane road. The road forks at an interchange, and the subject driver moves from the lane on the right to the lane on the left, nearly hitting the median in between the two. Figure 3.7. Predicted crash probabilities for Case 2. I195 NC199201 0 . 2 . 4 . 6 . 8 1 Pr (cr as h)_ by m ult ile ve l m od el 0 1 1: Crash/Near Crash; 0: Critical Incident Figure 3.8. Predicted crash probabilities for Case 3. I116 I144 I210 I208 I161I85I61 I62 225 10 I15 I119 NC8 NC162 NC198 NC115 NC146 NC129 NC9 NC120 NC214 104C103 C97 0 . 2 . 4 . 6 . 8 1 Pr (cr as h)_ by m ult ile ve l m od el 0 1 1: Crash/Near Crash; 0: Critical Incident

49 UMtrI Data: Kinematic Models Table 3.11 is a glossary of interaction term variable acronyms used in UMTRI kinematic models. They include explicit rec- ognition of positive (e.g., PlanoffPpi as positive lane offset interacting with positive pitch) and negative (e.g., Nlaspro, which is negative lateral speed interacting with positive roll) measures so the team could better understand the vehicle’s movement when alerts were triggered. This table is included to help the reader track the detailed discussion of the models that follows. The text generally follows the summary of model structure described for UMTRI data in Chapter 2. Single-Regime Models The first single-regime models developed relationships between speed (both longitudinal and lateral) and main effect kinematic variables. Different combinations of predictor variables were tested, particularly exploring the inclusion and exclusion of steer angle and roadway classification. It was determined dur- ing the course of this initial step in the modeling process that lateral speed proved to be a poor potential surrogate: models showed poor fit, and parameter estimates had little to no effect on the dependent variable (see Table 3.12 as an example). The model in Table 3.13, however, has a respectable good- ness of fit and reasonable parameter estimates. All parameters are significant. It is hard to distinguish the validity of coeffi- cient signs (positive versus negative) because they may be partly based on curve direction. Using directional lateral speed and lane offset (Table 3.13) instead of the general forms improves their significance and interpretation. Overall model fit significantly improves as well, even with steering angle removed. Roadway classification has a substantial effect on longitudinal speed (see Table 3.14), and all road classes are sig- nificant except for Road Class 6 (ramps). Kinematic variables were formed into interacting variables to determine further how they affect longitudinal speed, since it seemed plausible that changes in different vehicle kinematics are correlated (e.g., yaw and roll are correlated, since yaw occurs when the wheels are turned, thus causing the car to undergo slight roll). An example of strong correla- tion between yaw and steering angle can be seen in Table 3.15 (entries of high correlation are in bold). The strong correlation between steer and yaw is expected. When a vehicle enters a horizontal roadway curve, the driver is required to turn the wheels to maintain position on the roadway, thus changing the steering angle from zero. When a vehicle undergoes a turn, it experiences rotation about its ver- tical axis (perpendicular to the roadway surface), also known as yaw. Thus, a change in steering angle will result in a change in yaw in the same direction. Because this relationship exists, models can be developed without having to include all Table 3.11. Glossary for Kinematic Interaction Terms Kinematic Interaction Terms PlanoffPlas Positive lane offset, positive lateral speed NlanoffNlas Negative lane offset, negative lateral speed PlanoffNlas Positive lane offset, negative lateral speed NlanoffPlas Negative lane offset, positive lateral speed PlanoffPy Positive lane offset, positive yaw rate PlanoffNy Positive lane offset, negative yaw rate NlanoffPy Negative lane offset, positive yaw rate NlanoffNy Negative lane offset, negative yaw rate PlanoffPpi Positive lane offset, positive pitch rate PlanoffNpi Positive lane offset, negative pitch rate NlanoffPpi Negative lane offset, positive pitch rate NlanoffNpi Negative lane offset, negative pitch rate PlanoffPro Positive lane offset, positive roll angle PlanoffNro Positive lane offset, negative roll angle NlanoffPro Negative lane offset, positive roll angle NlanoffNro Negative lane offset, negative roll angle PlasPy Positive lateral speed, positive yaw rate PlasNy Positive lateral speed, negative yaw rate NlasNy Negative lateral speed, negative yaw rate NlasPy Negative lateral speed, positive yaw rate PlasPpi Positive lateral speed, positive pitch rate NlasPpi Negative lateral speed, positive pitch rate NlasNpi Negative lateral speed, negative pitch rate PlasNpi Positive lateral speed, negative pitch rate PlasPro Positive lateral speed, positive roll angle NlasPro Negative lateral speed, positive roll angle NlasNro Negative lateral speed, negative roll angle PlasNro Positive lateral speed, negative roll angle PyPro Positive yaw rate, positive roll angle PyNro Positive yaw rate, negative roll angle NyNro Negative yaw rate, negative roll angle NyPro Negative yaw rate, positive roll angle PyPpi Positive yaw rate, positive pitch rate PyNpi Positive yaw rate, negative pitch rate NyNpi Negative yaw rate, negative pitch rate NyPpi Negative yaw rate, positive pitch rate ProPpi Positive roll angle, positive pitch rate ProNpi Positive roll angle, negative pitch rate NroNpi Negative roll angle, negative pitch rate NroPpi Negative roll angle, positive pitch rate

50 Table 3.12. Lateral Speed Model, Linear Regression Variable Name Coefficient Std. Err. t-statistic p-value Speed 0.0025 0.0000 52.2700 0.0000 Yaw rate 0.0059 0.0004 13.7600 0.0000 Pitch rate 0.0007 0.0003 2.3800 0.0170 Roll angle 0.0020 0.0002 13.2900 0.0000 Steer angle -0.0014 0.0001 -17.2400 0.0000 Lane offset 0.0690 0.0004 155.0500 0.0000 Constant -0.0632 0.0013 -49.0100 0.0000 Number of obs = 1,391,799; Prob > F = 0.0000; R-squared = 0.019; Adj R-squared = 0.019. Table 3.13. Model 1: Longitudinal Speed, Single Regime, Directional Kinematics (Except Lateral Speed and Lane Offset), Linear Regression Variable Name Coefficient t-statistic p-value Lateral speed 0.4487 9.56 0.0000 Lane offset 0.1497 5.27 0.0000 Positive pitch -0.7406 -29.11 0.0000 Negative pitch -0.5802 -24.91 0.0000 Positive roll 1.2721 115.08 0.0000 Negative roll 1.6482 145.07 0.0000 Positive yaw -0.9798 -34.00 0.0000 Negative yaw -0.3201 -14.12 0.0000 PSteer -0.3897 -74.92 0.0000 NSteer -0.4188 -116.02 0.0000 Constant 47.4985 1327.18 0.0000 Number of obs = 336,548; Prob > F = 0.0000; R-squared = 0.3182; Adj R-squared = 0.3182. Table 3.14. Model 2: Longitudinal Speed, Single Regime, and Directional Kinematics (All) with Roadway Classification, Linear Regression Variable Name Coefficient t-statistic p-value Positive lateral speed 0.7148 9.68 0.0000 Negative lateral speed 0.8419 14.56 0.0000 Positive lane offset -1.9080 -38.64 0.0000 Negative lane offset -1.6185 -39.95 0.0000 Positive pitch -0.5164 -23.87 0.0000 Negative pitch -0.3892 -19.66 0.0000 Positive roll 1.1603 125.88 0.0000 Negative roll 1.5100 167.13 0.0000 Positive yaw -2.5338 -260.63 0.0000 Negative yaw -2.0422 -204.29 0.0000 Road class: Limited access 12.0936 11.42 0.0000 Road class: Major surface -7.4495 -7.04 0.0000 Road class: Minor surface -4.1978 -3.97 0.0000 Road class: Local road -7.3286 -6.92 0.0000 Road class: Ramp 1.2477 1.18 0.2380 Constant 48.4004 45.76 0.0000 Number of obs = 336,547; Prob > F = 0.0000; R-squared = 0.5079; Adj R-squared = 0.5079. Table 3.15. Correlation Between Steer and Yaw Positive Yaw Negative Yaw Positive Steer Angle Negative Steer Angle Positive yaw 1 Negative yaw -0.27 1 Positive steer angle 0.9777 -0.25 1 Negative steer angle -0.2656 0.9381 -0.2469 1.0000 kinematic variables. When analyzing model results, it can be assumed that longitudinal speed would be affected similarly by yaw rate and steering angle. Tables 3.16, Table 3.17a, and Table 3.17b summarize the best models established for the pure linear, single-regime models. Both models include the variables measurement duration (a measure of time; measurement duration = 0 at the beginning of observation, and measurement duration = 5 at the time when the alert is triggered), dark or light, RDCW disabled or enabled, and roadway classification. Both models also have several kine- matic variables as interaction terms. Model (a) does not include interaction terms for lane offset, instead using only main effects. Table 3.16 shows the goodness-of-fit results from the two mod- els. The parameter estimates are shown in Table 3.17a and b. Yaw and lane offset have the biggest effect on longitudinal speed in the single-regime model without interaction terms. Because the test vehicles had rigid bodies, roll would have less effect than yaw on longitudinal speed changes for kinematic models. Yaw will have the same (mathematical) relationship to speed and steering angle regardless of vehicle body rigidity. Roadway classification plays an important role in affecting longitudinal speed because of the difference in design speeds between roadways of different classifications. The interaction terms with the greatest effect on longitudinal speed are those

51 combining lane offset and yaw, lane offset and pitch, lateral speed and yaw, and lateral speed and roll; the latter two sets of terms (i.e., lateral speed and yaw and lateral speed and roll) can be directly related in fundamental kinematics. Both mod- els in Tables 3.17a and b had good fit and generally significant parameters. The use of roadway classification improved the goodness of fit of the single-regime models, showing that roadway classification may play an integral role in determining other relationships between vehicle kinematics and longitudinal speed. The goodness of fit for the non-interaction-term models was substantially better with roadway classification included (both interaction term models included roadway classification). Two-Regime Models The eight models summarized in Tables 3.18 through 3.26 show the initial approach to the second step in the flow chart in Figure 2.10—that is, pure linear, two regimes. These models include additional predictors, dark and roadway classification. The kinematic variables are separated into positive and negative based on directionality of measurement. Tables 3.22 through 3.25 include a variable called measurement duration. The first regime is defined as occurring when measurement duration is between 0 and 5 s: this is the time before the alert is triggered Table 3.16. Goodness of Fit, Kinematic Models (a) Lane Offset Main Effects Source SS df MS Model 28965404.1 34 851923.7 Residual 32225550.1 336513 95.76317 Total 61190954.2 336547 181.8199 Number of observations = 336,548 F(34,336513) = 8655.86 probability > F = 0 R2 = 0.4734 adjusted R2 = 0.4733 root MSE = 9.7859 (b) Lane Offset Interactions Source SS df MS Model 29386711.1 48 612223.2 Residual 31804243 336499 94.51512 Total 61190954.2 336547 181.8199 Number of observations = 336,548 F(48,336499) = 59,56.3 probability > F = 0 R2 = 0.4802 adjusted R2 = 0.4802 root MSE = 9.7219 Table 3.17a. Model 3: Longitudinal Speed, Single Regime, Interaction Kinematic Variables, Except Lane Offset Model Variable Name Coefficient t p > t Constant 62.1109 1048.44 0 Measurement duration -0.2674 -62.97 0 Dark 0.798 18.28 0 RDCW system disabled 0.9835 25.56 0 Road class: Unknown -11.7686 -18.52 0 Road class: Major surface -20.1951 -321.36 0 Road class: Minor surface -16.9241 -262.02 0 Road class: Local -20.1031 -283 0 Road class: Ramp -11.0104 -189.6 0 PlasPy -1.9049 -25.47 0 PlasNy -2.01 -28.7 0 NlasNy -1.2461 -24.79 0 NlasPy -1.566 -36.64 0 PlasPpi -1.6472 -17.32 0 NlasPpi -0.6317 -8.73 0 NlasNpi -0.7383 -9.88 0 PlasNpi -1.4035 -13.01 0 PlasPro 2.0415 35.49 0 NlasPro 1.1364 29.88 0 NlasNro 1.5697 43.32 0 PlasNro 1.819 29.73 0 PyPro -0.5621 -6.07 0 PyNro -0.0686 -144.55 0 NyNro -0.6218 -3.13 0.002 NyPro -0.055 -72.34 0 PyPpi -0.3765 -20.98 0 PyNpi -0.3984 -18.47 0 NyNpi -0.3637 -13.64 0 NyPpi -0.3645 -19.75 0 NroNpi 0.3786 20.99 0 NroPpi 0.3412 22.99 0 ProPpi 0.2945 21 0 ProNpi 0.3131 17.17 0 PlaneOff -2.2706 -45.14 0 NlaneOff -1.8736 -47.31 0

52 (recall that each observation of an alert or pseudoalert begins 5 s before the alert and continues until 5 s after the alert is extin- guished). The second regime is the magnitude of the defined measurement duration beyond 5 s. This is the duration of time after the alert is triggered until 5 s after the alert turns off—that is, it is the end of observation for each specific alert. In Table 3.18, the fit of Model 4 is good, as indicated by an adjusted R2 value of 0.47. Roadway classification has a negative effect on speed, since freeway is the baseline class (RC0 is insig- nificant due to a small sample size). Directional lane offset vari- ables should be combined, as drivers would be assumed to decrease longitudinal speed in order to increase ease of reposi- tioning their vehicles laterally regardless of offset direction. Roll parameters have positive signs (although lower coefficient absolute values than most other kinematics) because they imply larger values of longitudinal speed (higher speed relates to Table 3.17b. Model 3: Longitudinal Speed, Single Regime, Interaction Kinematic Variables, All; Linear Regression Variable Name Coefficient t p > t Variable Name Coefficient t p > t Constant 61.2216 1081.46 0 PyPpi -0.187 -12.27 0 Measurement duration -0.279 -65.24 0 PyNpi -0.2215 -12.09 0 Dark 0.758 17.43 0 NyNpi -0.265 -11.03 0 RDCW system disabled 0.886 23.22 0 NyPpi -0.2412 -13.41 0 Road class: Unknown -11.1077 -18.09 0 NroNpi 0.2509 16.03 0 Road class: Major surface -19.878 -320.61 0 NroPpi 0.2096 15.93 0 Road class: Minor surface -16.6159 -259.31 0 ProPpi 0.231 16.34 0 Road class: Local -19.7223 -278.23 0 ProNpi 0.2524 14.81 0 Road class: Ramp -10.9782 -191.14 0 PlanoffPlas -0.1476 -0.79 0.427 PlasPy -1.4205 -20.6 0 NlanoffNlas -0.5811 -14 0 PlasNy -1.6799 -25.34 0 PlanoffNlas -1.7864 -9.79 0 NlasNy -0.7116 -13.26 0 NlanoffPlas -0.7072 -4.66 0 NlasPy -1.0807 -23.28 0 PlanoffPy -1.175 -31.41 0 PlasPpi -0.7441 -7.97 0 PlanoffNy -0.9226 -21.19 0 NlasPpi 0.3035 3.87 0 NlanoffPy -0.6296 -20.97 0 NlasNpi 0.1211 1.55 0.121 NlanoffNy -0.758 -23.68 0 PlasNpi -0.595 -5.83 0 PlanoffPpi -1.4029 -25.31 0 PlasPro 1.6342 28.72 0 PlanoffNpi -1.1881 -21.54 0 NlasPro 0.6117 14.65 0 NlanoffPpi -0.9522 -20.17 0 NlasNro 1.0995 27.07 0 NlanoffNpi -0.8805 -19.84 0 PlasNro 1.2776 21.95 0 PlanoffPro 0.5273 14.49 0 PyPro -0.5421 -5.94 0 PlanoffNro 1.0945 33.86 0 PyNro -0.0678 -119.14 0 NlanoffPro 0.6313 25.37 0 NyNro -0.6098 -3.35 0.001 NlanoffNro 0.5448 19.64 0 NyPro -0.0478 -54.34 0 greater lateral force, which is translated to the vehicle body through roll). Yaw would tend to decrease longitudinal speed as a result of additional friction between the tires and the roadway when yaw does not equal zero. Lateral speed is associated with increases in longitudinal speed, since vehicles with higher speeds tend to have more difficulty maintaining lane position. R2 in Model 5 (Table 3.19) is about the same as in Model 4, indicating good model fit. The effects of the kinematic vari- ables on longitudinal speed are similar to but slightly stronger than those in Model 4 (the signs are the same, but the absolute values are generally higher). The alert system being on may have caused drivers to react differently approaching curves, even before alerts were triggered. As in previous models, road- way classification tends to decrease longitudinal speed, given the baseline roadway classification of freeway. RC0 was dropped due to the absence of observations in this regime.

53 Table 3.18. Model 4: Longitudinal Speed, Two- Regime, Week 1, 5 s Before Alert, Linear Regression Variable Name Coefficient t-statistic p-value Dark 1.2521 10.04 0.0000 Positive yaw -3.1605 -85.18 0.0000 Negative yaw -1.6041 -36.75 0.0000 Positive roll 0.6950 19.74 0.0000 Negative roll 1.7320 54.31 0.0000 Positive pitch -0.6966 -10.04 0.0000 Negative pitch -0.5804 -8.70 0.0000 Positive lane offset -1.7872 -11.22 0.0000 Negative lane offset -1.8011 -13.66 0.0000 Positive lateral speed 1.8389 8.24 0.0000 Negative lateral speed 0.7882 4.40 0.0000 Road class: Unknown 2.8306 0.83 0.4060 Road class: Major surface -18.7711 -117.72 0.0000 Road class: Minor surface -16.1927 -99.69 0.0000 Road class: Local -17.5117 -79.02 0.0000 Road class: Ramp -9.1532 -63.32 0.0000 Constant 62.0448 443.54 0.0000 Number of obs = 34,700; Prob > F = 0.0000; R-squared = 0.4026; Adj R-squared = 0.4024. Table 3.19. Model 5: Longitudinal Speed, Two-Regime, Weeks 2 to 4, 5 s Before Alert, Linear Regression Variable Name Coefficient t-statistic p-value Dark 0.8362 10.98 0.0000 Positive yaw -2.256558 -112.88 0.0000 Negative yaw -2.245391 -85.35 0.0000 Positive roll 1.1166 52.02 0.0000 Negative roll 1.0615 56.77 0.0000 Positive pitch -0.6801366 -16.42 0.0000 Negative pitch -0.5676225 -14.23 0.0000 Positive lane offset -2.385719 -24.56 0.0000 Negative lane offset -2.647468 -32.4 0.0000 Positive lateral speed 2.1194 13.77 0.0000 Negative lateral speed 1.7488 14.48 0.0000 Road class: Unknown (dropped) NA NA Road class: Major surface -17.74598 -176.17 0.0000 Road class: Minor surface -15.44258 -148.85 0.0000 Road class: Local -19.32087 -163.8 0.0000 Road class: Ramp -9.120569 -98.1 0.0000 Constant 61.4877 664.57 0.0000 Number of obs = 95,550; Prob > F = 0.0000; R-squared = 0.4719; Adj R-squared = 0.4718. Table 3.20. Model 6: Longitudinal Speed, Two-Regime, Week 1, After Alert Triggered, Linear Regression Variable Name Coefficient t-statistic p-value Dark 0.4697 4.85 0.0000 Positive yaw -2.742213 -129.57 0.0000 Negative yaw -2.213393 -85.57 0.0000 Positive roll 1.4140 61.70 0.0000 Negative roll 1.8732 94.54 0.0000 Positive pitch -0.43522 -8.4 0.0000 Negative pitch -0.2240527 -4.97 0.0000 Positive lane offset -1.900215 -16.88 0.0000 Negative lane offset -0.7797679 -8.55 0.0000 Positive lateral speed 0.2729 1.71 0.0880 Negative lateral speed 0.0749 0.60 0.5490 Road class: Unknown (dropped) NA NA Road class: Major surface -20.70069 -140.53 0.0000 Road class: Minor surface -17.37473 -123.56 0.0000 Road class: Local -17.57807 -96.2 0.0000 Road class: Ramp -11.50564 -97.97 0.0000 Constant 59.3494 462.94 0.0000 Number of obs = 55,916; Prob > F = 0.0000; R-squared = 0.545; Adj R-squared = 0.5448. Table 3.21. Model 7: Longitudinal Speed, Two-Regime, Weeks 2 to 4, After Alert Triggered, Linear Regression Variable Name Coefficient t-statistic p-value Dark 1.0133 17.67 0.0000 Positive yaw -2.463306 -180.99 0.0000 Negative yaw -1.949263 -160.11 0.0000 Positive roll 1.2893 108.46 0.0000 Negative roll 1.6317 128.17 0.0000 Positive pitch -0.3776544 -12.21 0.0000 Negative pitch -0.2904763 -10.49 0.0000 Positive lane offset -1.93061 -27.09 0.0000 Negative lane offset -1.431001 -24.74 0.0000 Positive lateral speed -0.1336889 -1.25 0.2100 Negative lateral speed 0.8682 10.43 0.0000 Road class: Unknown -12.0463 -11.28 0.0000 Road class: Major surface -20.07718 -220.41 0.0000 Road class: Minor surface -16.29487 -179.14 0.0000 Road class: Local -19.30426 -203.35 0.0000 Road class: Ramp -11.32301 -146.28 0.0000 Constant 58.1756 706.91 0.0000 Number of obs = 150,382; Prob > F = 0.0000; R-squared = 0.5184; Adj R-squared = 0.5184.

54 Table 3.22. Model 8: Longitudinal Speed, Two- Regime, Week 1, 5 s Before Alert, Add Measurement Duration, Linear Regression Variable Name Coefficient t-statistic p-value Dark 1.2525 10.04 0.0000 Positive yaw -3.164436 -85.22 0.0000 Negative yaw -1.609261 -36.83 0.0000 Positive roll 0.6985 19.82 0.0000 Negative roll 1.7355 54.38 0.0000 Positive pitch -0.6952267 -10.02 0.0000 Negative pitch -0.5789266 -8.67 0.0000 Positive lane offset -1.772985 -11.12 0.0000 Negative lane offset -1.785805 -13.53 0.0000 Positive lateral speed 1.8408 8.25 0.0000 Negative lateral speed 0.7782 4.35 0.0000 Road class: Unknown 2.6442 0.78 0.4380 Road class: Major surface -18.76191 -117.64 0.0000 Road class: Minor surface -16.18095 -99.58 0.0000 Road class: Local -17.49641 -78.93 0.0000 Road class: Ramp -9.127808 -63 0.0000 Measurement duration -0.0925925 -2.57 0.0100 Constant 62.2482 387.28 0.0000 Number of obs = 34,700; Prob > F = 0.0000; R-squared = 0.4727; Adj R-squared = 0.4725. Table 3.23. Model 9: Longitudinal Speed, Two- Regime, Weeks 2 to 4, 5 s Before Alert, Add Measurement Duration, Linear Regression Variable Name Coefficient t-statistic p-value Dark 0.8362 10.98 0.0000 Positive yaw -2.256553 -112.72 0.0000 Negative yaw -2.245389 -85.35 0.0000 Positive roll 1.1166 52.00 0.0000 Negative roll 1.0614 56.68 0.0000 Positive pitch -0.68014 -16.41 0.0000 Negative pitch -0.5676268 -14.23 0.0000 Positive lane offset -2.385723 -24.56 0.0000 Negative lane offset -2.64747 -32.4 0.0000 Positive lateral speed 2.1194 13.76 0.0000 Negative lateral speed 1.7488 14.48 0.0000 Road class: Unknown (dropped) NA NA Road class: Major surface -17.74599 -176.11 0.0000 Road class: Minor surface -15.4426 -148.78 0.0000 Road class: Local -19.32089 -163.68 0.0000 Road class: Ramp -9.120596 -97.91 0.0000 Measurement duration 0.0001 0.00 0.9960 Constant 61.4875 591.98 0.0000 Number of obs = 95,550; Prob > F = 0.0000; R-squared = 0.4719; Adj R-squared = 0.4718. In Table 3.20, Model 6 has an improved R2 (0.54) com- pared with the previous models. The coefficient for the con- stant is slightly lower than in Models 4 and 5, implying that longitudinal speed through the curve would be lower after an alert was triggered. Lateral speed is insignificant, regard- less of direction. The signs for virtually all kinematic vari- ables are the same as in Models 4 and 5, but the general effect of the variables decreases. This may be the result of anticipated drops in speed while traversing curves. Road- way classification has a generally lesser effect, but only marginally less. In Table 3.21, R2 is 0.518 for Model 7, very close to that in the previous model. Positive lateral speed becomes insignifi- cant and changes sign. The effects of yaw and roll on longi- tudinal speed become stronger, while the effect of most other kinematic variables decreases. Roadway classification increases in general significance while having more overall effect (greater absolute value of coefficients). The Model 7 constant is slightly lower than in Model 6, as drivers would be expected to decrease their speed more quickly than in the system-disabled period. In Table 3.22, the R2 value for Model 8 is 0.47, similar to the same model without the measurement duration variable. Measurement duration is marginally significant and contrib- utes little to the model’s goodness of fit. All signs for kine- matic variables are the same as in the models without measurement duration, and the coefficients are similar. The constant is higher than for all other two-regime models, as drivers would be expected to enter curves at higher speeds, relying on the alert system to warn them when deceleration is necessary. In Table 3.23, R2, variable signs, coefficients, and signifi- cances for Model 9 are similar to the model without measure- ment duration. Measurement duration has virtually no effect on longitudinal speed. Its t-statistic is not actually zero, since the p-value is not exactly one. STATA, the software package used to run these models, will display a zero for a t-statistic if it is close enough to zero based on the number of decimal places with zeros. The actual t-statistic is coefficient dard errorstan = 0 0001049 0 021808 . . 4 0 0048= . In Table 3.24, the R2 in Model 10 is slightly higher than in the comparable model without measurement duration (Model 6). As in Model 9, coefficient values are similar and the constant is slightly higher; measurement duration is sig- nificant and has a negative effect on longitudinal speed. In Table 3.25, the R2 for Model 11 is 0.526, slightly higher than in the model without measurement duration. Positive

55 Adding measurement duration affected the models slightly, but there were no drastic changes in coefficients and goodness of fit. Lateral speed had little effect on longitudinal speed for any two-regime model. When measurement duration was added to the models, the R2 value increased slightly for most models. The effect of specific kinematic factors tended to be relatively constant across the models. Because the baseline classification was freeway, all roadway classification variables had negative coefficients. Measurement duration played a more important role in the after-alert-was-triggered models; the effect of time on change in longitudinal speed should be more noticeable after an alert is triggered (drivers would be expected to decrease speed more significantly after an alert is triggered to decrease the degree of danger). lateral speed is the only insignificant variable. All variables in this model have the same signs and similar effects as in the model without measurement duration. Table 3.26 shows the summary of deceleration results from the two-regime models. There is clear evidence of driver adaptation to the CSW technology. During the first week (pseudoalerts), drivers approached curves during the first 5 s of measurement at a deceleration rate of 0.093 mph/0.1 s. After activation of the system (Weeks 2 to 4), this same 5-s time period had virtually no deceleration (-0.0001 mph/0.1 s). Changes were also observed in deceleration after an alert was triggered (compared with deceleration during the pseudo- alert). In this case, drivers decelerated at a rate of 0.231 mph/0.1 s compared with 0.29 mph/0.1 s. Taken in combin- ation, this driver adaptation indicates that when the CSW is engaged, drivers approach the curve at a constant speed and then decelerate relatively rapidly compared with a decelerat- ing entry and less rapid deceleration without the technology. One interpretation is that the drivers are relying on the sys- tem to warn them of an unsafe curve entry rather than approaching curves more cautiously. It is recognized that the origins of these parameters are models that include all drivers, a form of aggregate analysis. The next steps were to construct similar models for individual drivers or smaller groups of drivers. Table 3.24. Model 10: Longitudinal Speed, Two- Regime, Week 1, After Alert, Add Measurement Duration, Linear Regression Variable Name Coefficient t-statistic p-value Dark 0.3240 3.35 0.0010 Positive yaw -2.7082 -128.32 0.0000 Negative yaw -2.1695 -84.09 0.0000 Positive roll 1.4102 61.84 0.0000 Negative roll 1.9022 96.31 0.0000 Positive pitch -0.4412 -8.56 0.0000 Negative pitch -0.2392 -5.33 0.0000 Positive lane offset -1.9257 -17.19 0.0000 Negative lane offset -0.5608 -6.15 0.0000 Positive lateral speed 0.1085 0.68 0.4950 Negative lateral speed -0.0466 -0.37 0.7080 Road class: Unknown (dropped) NA NA Road class: Major surface -20.8376 -142.07 0.0000 Road class: Minor surface -17.5749 -125.40 0.0000 Road class: Local -17.7594 -97.61 0.0000 Road class: Ramp -11.5181 -98.58 0.0000 Measurement duration -0.2314 -23.88 0.0000 Constant 61.3664 401.15 0.0000 Number of obs = 55,916; Prob > F = 0.0000; R-squared = 0.5496; Adj R-squared = 0.5494. Table 3.25. Model 11: Longitudinal Speed, Two- Regime, Weeks 2 to 4, After Alert, Add Measurement Duration, Linear Regression Variable Name Coefficient t-statistic p-value Dark 0.9294 16.32 0.0000 Positive yaw -2.3985 -176.70 0.0000 Negative yaw -1.9214 -158.84 0.0000 Positive roll 1.3072 110.74 0.0000 Negative roll 1.6316 129.14 0.0000 Positive pitch -0.3959 -12.90 0.0000 Negative pitch -0.3001 -10.93 0.0000 Positive lane offset -1.9495 -27.57 0.0000 Negative lane offset -1.4182 -24.71 0.0000 Positive lateral speed -0.1298 -1.23 0.2200 Negative lateral speed 0.7935 9.61 0.0000 Road class: Unknown -10.8223 -10.21 0.0000 Road class: Major surface -20.1622 -222.99 0.0000 Road class: Minor surface -16.4879 -182.46 0.0000 Road class: Local -19.2835 -204.68 0.0000 Road class: Ramp -11.2679 -146.66 0.0000 Measurement duration -0.2897 -48.01 0.0000 Constant 60.6840 625.89 0.0000 Number of obs = 150,382; Prob > F = 0.0000; R-squared = 0.5257; Adj R-squared = 0.5256. Table 3.26. Summary of Deceleration Results for Two-Regime Models mph/0.1 s Week 1 Week 2–4 5 s before alert (0 ≤ measurement duration ≤ 5) 0.0926 -0.0001 After alert triggered 0.2314 0.2897

56 Cohort-Based approach The cohort design can be used to formulate an exposure- based model relating potential risk factors to several possible outcomes. The cohort design is well-suited to account for measures of exposure such as time at risk or distance traveled under specific driving conditions. Survival analysis, count regression, and logistic regression are suitable statistical meth- ods to analyze data from a cohort design. The Penn State team estimated several models with both CSW and LDW alerts as predictors. Only CSW alert findings are reported because they are principally the same as the LDW alert findings and CSW alerts are, as discussed above, more correlated with roadway departure events. The count regression models for CSW alerts highlight the effect of roadway-related context. The team estimated and compared two models: one for limited access roads (UMTRI Functional Class 1) and the other for nonlimited access roads (UMTRI Functional Class 3). Logistic regression modeling highlights the importance of driver variables and the effect that driver variables have on model fit, parameter signifi- cance, magnitude, and sign. Interestingly, the results are rather different from those for the event-based models devel- oped with the VTTI data. Count Regression The initial analysis involved the use of negative binomial (NB) count regressions to show how both context and driver-related variables affect the likelihood of alert occurrence. In the first set of sample models, the data were segmented by roadway func- tional classification. In the second set of sample models, multi- Three-Regime Models The two-regime model assumes that one model can be used to characterize driver longitudinal speed for alert durations as long as 15 to 20 s. There are relatively few of these long-duration events, but they may need a different model, and they may also influence the estimation of the models of short-to-moderate duration. In addition, few of the observations 20 s from the alert trigger were accurately estimated in the two-regime model. Figure 3.9 summarizes model fit to the data for the best two-regime model. Thus, the next step was to create a model with three regimes. All models included the measurement duration variable. As in the two-regime models, there was a division at measurement duration of 5 s and, in addition, a second division at measure- ment duration of 20 s. The estimation results for the three- regime model are shown in Tables 3.27 through 3.29. One noticeable feature of the models in Tables 3.28 and 3.29 is the substantial change in the estimated value for mea- surement duration: drivers with the system accelerate more aggressively after 20 s than drivers without the system. This difference may reflect a greater confidence in system users that they have, in fact, exited the curve, but it nevertheless demonstrates driver adaptation. A Chow test was performed to determine if there were significant changes in parameters as a whole for the time periods 5 s before the alert and the time after the alert was triggered. Table 3.30 shows that each pair of models differed on the basis that the parameter coefficients were sufficiently different. This test confirms that driver behavior changes with the system activated compared with the system not activated. Figure 3.9. Longitudinal speed versus measurement duration (solid line is mean of data points).

57 Table 3.27. Model 12: Longitudinal Speed, Three-Regime, 5 s Before Alert, Linear Regression Model 12a Week 1 Model 12b Weeks 2–4 Variable Name Coefficient t-statistic p-value Variable Name Coefficient t-statistic p-value Dark 1.2517 9.11 0.0000 Dark 0.8362 10.60 0.0000 Positive yaw -3.1645 -53.23 0.0000 Positive yaw -2.2566 -80.07 0.0000 Negative yaw -1.6091 -21.79 0.0000 Negative yaw -2.2454 -41.04 0.0000 Positive roll 0.6983 13.46 0.0000 Positive roll 1.1166 30.34 0.0000 Negative roll 1.7354 37.36 0.0000 Negative roll 1.0614 44.56 0.0000 Positive pitch -0.6950 -10.68 0.0000 Positive pitch -0.6801 -17.40 0.0000 Negative pitch -0.5788 -9.32 0.0000 Negative pitch -0.5676 -15.12 0.0000 Positive lane offset -1.7731 -12.07 0.0000 Positive lane offset -2.3857 -23.22 0.0000 Negative lane offset -1.7836 -14.11 0.0000 Negative lane offset -2.6475 -32.64 0.0000 Positive lateral speed 1.8396 7.84 0.0000 Positive lateral speed 2.1194 13.21 0.0000 Negative lateral speed 0.7765 4.90 0.0000 Negative lateral speed 1.7488 14.84 0.0000 Road class: Major surface -18.7643 -119.89 0.0000 Road class: Major surface -17.7460 -178.11 0.0000 Road class: Minor surface -16.1835 -94.49 0.0000 Road class: Minor surface -15.4426 -136.77 0.0000 Road class: Local -17.4991 -85.12 0.0000 Road class: Local -19.3209 -159.24 0.0000 Road class: Ramp -9.1299 -58.20 0.0000 Road class: Ramp -9.1206 -91.98 0.0000 Measurement duration -0.0932 -2.58 0.0100 Measurement duration 0.0001 0.00 0.9960 Constant 62.2522 376.14 0.0000 Constant 61.4875 561.09 0.0000 Number of obs = 34,700; Prob > F = 0.0000; R-squared = 0.4727; Adj R-squared = 0.4725. Number of obs = 95,500; Prob > F = 0.0000; R-squared = 0.4719; Adj R-squared = 0.4718. Table 3.28. Model 13: Longitudinal Speed, Three-Regime, Alert Triggered to 20 s, Linear Regression Model 13a Week 1 Model 13b Weeks 2–4 Variable Name Coefficient t-statistic p-value Variable Name Coefficient t-statistic p-value Dark 0.3660 3.37 0.0010 Dark 1.0610 17.61 0.0000 Positive yaw -2.7340 -96.83 0.0000 Positive yaw -2.3950 -137.45 0.0000 Negative yaw -2.1470 -62.77 0.0000 Negative yaw -1.8980 -98.45 0.0000 Positive roll 1.4360 49.50 0.0000 Positive roll 1.3430 82.35 0.0000 Negative roll 1.9510 75.38 0.0000 Negative roll 1.6760 108.50 0.0000 Positive pitch -0.4370 -8.75 0.0000 Positive pitch -0.4380 -15.07 0.0000 Negative pitch -0.2220 -5.00 0.0000 Negative pitch -0.3330 -12.58 0.0000 Positive lane offset -1.9350 -17.25 0.0000 Positive lane offset -1.9080 -27.28 0.0000 Negative lane offset -0.7630 -8.84 0.0000 Negative lane offset -1.4710 -26.92 0.0000 Positive lateral speed 0.3260 2.08 0.0370 Positive lateral speed -0.1220 -1.21 0.2260 Negative lateral speed 0.1840 1.69 0.0910 Negative lateral speed 0.6800 8.70 0.0000 Road class: Major surface -20.8720 -130.05 0.0000 Road class: Major surface -20.0790 -210.70 0.0000 Road class: Minor surface -17.5940 -116.31 0.0000 Road class: Minor surface -16.5850 -172.11 0.0000 Road class: Local -17.7790 -94.20 0.0000 Road class: Local -19.3090 -189.80 0.0000 Road class: Ramp -11.6630 -81.92 0.0000 Road class: Ramp -11.4410 -132.71 0.0000 Measurement duration -0.4190 -28.81 0.0000 Measurement duration -0.5480 -63.66 0.0000 Constant 62.8520 340.11 0.0000 Constant 62.7250 562.56 0.0000 Number of obs = 537,880; Prob > F = 0.0000; R-squared = 0.5539; Adj R-squared = 0.5539. Number of obs = 145,707; Prob > F = 0.0000; R-squared = 0.5347; Adj R-squared = 0.5347.

58 level specification was applied to cluster driver attributes at a second, separate level. Note that road class was used, but addi- tional dimensions beyond road class could have been specified, Table 3.30. Chow Test for Comparison of Parameter Estimates Models 12a and 12b Models 13a and 13b SSR pooled 12252145.2 16207567.5 SSR Model 1 3218375.28 4537057.93 SSR Model 2 8950406.52 11583691.7 k 17 17 n1 34700 53788 n2 95550 145707 Numerator 4903.729412 5106.933529 Denominator 94.07076341 81.24429421 F 52.4856042 63.04938272 Degree N 17 17 Degree D 130250 199495 Result F > 1.96 F > 1.96 p = 0 p = 0 Table 3.29. Model 14: Longitudinal Speed, Three-Regime, 20+ s, Linear Regression Model 14a Week 1 Model 14b Weeks 2–4 Variable Name Coefficient t-statistic p-value Variable Name Coefficient t-statistic p-value Dark -3.6790 -11.22 0.0000 Dark -1.1040 -2.75 0.0060 Positive yaw -1.7680 -17.69 0.0000 Positive yaw -1.4590 -19.13 0.0000 Negative yaw 0.4560 1.32 0.1860 Negative yaw -1.1830 -9.32 0.0000 Positive roll 0.3010 1.34 0.1800 Positive roll 1.1090 11.53 0.0000 Negative roll 1.5030 13.46 0.0000 Negative roll 0.8630 10.68 0.0000 Positive pitch 0.0380 0.15 0.8780 Positive pitch 0.3610 2.50 0.0120 Negative pitch -0.2570 -1.42 0.1570 Negative pitch 0.5820 5.07 0.0000 Positive lane offset -2.7010 -5.51 0.0000 Positive lane offset -2.6160 -9.16 0.0000 Negative lane offset 0.3910 1.14 0.2550 Negative lane offset -2.3950 -9.48 0.0000 Positive lateral speed -7.2000 -6.73 0.0000 Positive lateral speed -3.9790 -6.81 0.0000 Negative lateral speed -3.6780 -4.45 0.0000 Negative lateral speed 1.6290 2.57 0.0100 Road class: Major surface -12.6560 -14.53 0.0000 Road class: Major surface -28.0880 -16.84 0.0000 Road class: Minor surface -12.1850 -17.31 0.0000 Road class: Minor surface -4.7560 -5.97 0.0000 Road class: Local -8.0200 -8.73 0.0000 Road class: Local -14.6600 -18.70 0.0000 Road class: Ramp -14.8210 -21.85 0.0000 Road class: Ramp -9.6080 -13.95 0.0000 Measurement duration 0.3190 6.32 0.0000 Measurement duration 0.7820 22.95 0.0000 Constant 48.7330 31.49 0.0000 Constant 34.3720 27.52 0.0000 Number of obs = 2,158; Prob > F = 0.0000; R-squared = 0.5554; Adj R-squared = 0.5554. Number of obs = 4,766; Prob > F = 0.0000; R-squared = 0.5171; Adj R-squared = 0.5171. such as day/night or wet/dry conditions. The cohort may be defined quite flexibly, using any variable that is an attribute of the road, environment, and/or driver (and is, of course, con- tinuously measured as part of the naturalistic data). Single-Level Models The single-level models segment the data by functional class and alert type. Initial context-related predictors include ramp presence (for nonlimited access roads only), urban/rural set- tings, day/night, dry/wet conditions (based on the use of windshield wipers), and RDCW system disabled/enabled state. Driver predictors included gender, education, years of driving experience, last year’s mileage driven, use of glasses or contacts, and whether or not the driver is a smoker. Two-way interaction terms were tested for both context and driver attributes. Note that the structure of the model bears a strong similarity to the event-based models estimated using VTTI data. The VTTI models were able to capture only those attri- butes immediately surrounding the event. The cohort for- mulation includes many of the same variables, but the cohort models include exposure measured on the same scale as con- text, which is important in obtaining a broader view of the effect of context throughout the driver’s travel.

59 frequency based on the fact that the wet variable has a negative coefficient. Overdispersion results show that the NB regression is a better choice than the Poisson regression. These results are summarized in Table 3.32. Once again a chi-square test of the model compared to a constant term should that the model was significant with a significance probability less than 0.001. Initially, the team expected to see a positive correlation between speed and CSW alert counts. However, the result showed that such a correlation does not always occur. Check- ing scatter plots of speed against CSW count, it was observed that some speeds were below 18 mph, which is the minimum speed required to trigger CSW alerts. This observation illus- trates the need to carefully define homogeneous when using naturalistic data with a cohort data structure. There is tre- mendous power in the method, but only if recognized in the collection of the original data set. The count regression approach with cohort structure can be used to explore crash surrogate measures and their utility in safety analyses. One extension of the models in Tables 3.30 and 3.31 is the inclusion of potential crash surrogates as pre- dictor variables. A count of the frequency of a surrogate occurrence can be used as a predictor, and its association and significance can be tested against the dependent measure. Table 3.31 summarizes the model results for limited access segments. Factors increasing the number of alerts on limited access segments include exposure in the form of distance, dry daytime conditions, urban settings, being male, high mileage in the previous year if the driver is a female, and being a male with a bachelor’s degree or above; all other predictors decrease alert frequency. Six of the predictors in this model are insig- nificant. Higher driving experience generally drives down CSW occurrence, and wet conditions would likely decrease alert frequency as drivers tend to decrease travel speeds in wet weather. The use of the NB model over the Poisson model was warranted based on alpha and its likelihood ratio test. A chi- square test of the model compared to only a constant term yielded a test statistic value of 47.89 with a corresponding sig- nificance probability less than 0.001. The following factors increase CSW alert frequency on Functional Class 3 roads: distance as a form of exposure, day- time conditions, urban roadways (both ramps and nonramps), rural ramps (insignificant), males with more mileage driven in the last year (although gender–mileage interactions are insig- nificant), and males with a bachelor’s degree or above (although the gender–education interaction term is generally insignifi- cant, at least marginally). Dry conditions also increase alert Table 3.31. CSW NB Regression, Functional Class 1: Limited Access, Distance as Exposure CSW Coefficient SE z p > z 95% CI Miles driven 0.027 0.006 4.700 <0.001 (0.016, 0.039) RDCW disabled -0.362 0.236 -1.540 0.125 (-0.825, 0.100) Nighttime baseline NA NA NA NA Daytime wet -0.402 0.376 -1.070 0.284 (-1.139, 0.334) Daytime dry 1.131 0.366 3.090 0.002 (0.413, 1.849) Urban 1.296 0.389 3.330 0.001 (0.534, 2.058) Male 0.777 0.717 1.080 0.279 (-0.629, 2.183) Female last year’s mileage (per 1,000 mi) 0.080 0.033 2.400 0.017 (0.0145, 0.145) Male last year’s mileage (per 1,000 mi) -0.014 0.023 -0.600 0.550 (-0.059, 0.035) Male driving experience (years) -0.031 0.011 -2.830 0.005 (-0.052, -0.009) Female driving experience (years) -0.043 0.012 -3.650 <0.001 (-0.066, -0.020) Female with bachelor’s degree or above -0.532 0.399 -1.330 0.183 (-1.314, 0.251) Male with bachelor’s degree or above 0.325 0.315 1.030 0.301 (-0.291, 0.942) Constant -2.807 0.613 -4.580 <0.001 (-4.009, -1.606) Alpha 1.220 0.348 NA NA (0.697, 2.133) Number of observations = 405 log likelihood = -275.43729 LR chi-squared (12) = 98.54 pseudo R2 = 0.1517 LR test of alpha = 0 chi-bar squared (01) = 47.89

60 paired with and tested against relevant surrogates (such as lateral accelerations) to obtain more targeted evaluations. The cohort formulation would allow the validity of surrogates to be tested using safety performance functions. This concept could be explored as part of the SHRP 2 S08 projects. Multilevel Models Since the output from models including either distance or time as exposure were consistent using the single-level struc- ture, the team only considered models including distance as a form of exposure as analysis examples for further multilevel formulation. The goal of this model development is to dem- onstrate the application of hierarchical models to cohort- structured data. Figure 3.10 summarizes the application of the multilevel approach to CSW alerts on limited access roads (Functional Class 1). The first equation in Figure 3.10 says that the num- ber of CSW alerts obeys the NB distribution. The predictors used here are those used in the best single-level models. The second equation says that the expected number of CSW alerts (log p) is a function of miles driven (miles), RDCW disabled This would show an association between a surrogate and an event of interest such as crashes. Another way to explore surrogate measures is to use them as dependent variables. The variable is entered as a count on a segment similar to the way crashes would be entered for an identification of sites with promise (see Aguero-Valverde and Jovanis 2008 for a recent example of the standard sites with promise formulation). Bivariate Poisson–log normal or similar formulations within a Bayes hierarchical structure (Aguero-Valverde and Jovanis 2010) can be used with crash and surrogate frequency as the dependent variables. Using a common specification, the researcher could explore differ- ences in the significance of predictors. Of even greater utility would be the development of safety performance functions for both crashes and surrogate measures. One could then compare the sites with promise developed for the two safety performance functions. A test of the validity of a surrogate would be its ability to identify the same sites with promise. The ability to validate a surrogate in this way is of particular importance in that one application of surrogates is to identify risky locations without waiting for years of crash data. Specific crash types such as roadway departure could be Table 3.32. CSW NB Regression, Functional Class 3: Nonlimited Access, Distance As Exposure CSW Coefficient SE z p > z 95% CI Miles driven 0.087 0.016 5.440 <0.001 (0.055, 0.118) RDCW disabled -0.762 0.133 -5.730 <0.001 (-1.023, -0.502) Day 1.054 0.150 7.030 <0.001 (0.760, 1.348) Wet -1.535 0.175 -8.780 <0.001 (-1.878, -1.193) Rural nonramp baseline NA NA NA NA Urban ramp 2.184 0.270 8.090 <0.001 (1.655, 2.714) Rural ramp 0.493 0.377 1.310 0.191 (-0.246, 1.231) Urban nonramp 1.068 0.254 4.200 <0.001 (0.569, 1.566) Male -0.542 0.417 -1.300 0.194 (-1.359, 0.275) Female last year’s mileage -0.001 0.017 -0.060 0.950 (-0.034, 0.032) Male last year’s mileage 0.015 0.011 1.330 0.183 (-0.007, 0.037) Male driving experience (years) -0.016 0.006 -2.790 0.005 (-0.027, -0.005) Female driving experience (years) -0.023 0.006 -4.090 <0.001 (-0.035, -0.012) Female with bachelor’s degree or above -0.178 0.207 -0.860 0.390 (-0.583, 0.228) Male with bachelor’s degree or above 0.285 0.163 1.750 0.080 (-0.034, 0.605) Constant -1.702 0.411 -4.140 <0.001 (-2.508, -0.895) Alpha 0.987 0.143 NA NA (0.742, 1.312) Number of observations = 900 log likelihood = -832.47787 LR chi-squared (14) = 320.99 pseudo R2 = 0.1616 LR test of alpha = 0 chi-bar squared (01) = 199.53

61 bachelor’s degree or above, last year’s miles driven, and years of driving experience, are shown after the second equation. Specifically, it is a random intercept and random slope model formulation (i.e., both the intercept and the slope vary ran- domly across the subjects). Thus, the third equation says that the mean constant term for all drivers is -2.891 (SE is 0.856), and their variance is 0.977 (with SE of 0.327; these values are shown in the covariance matrix for all random effects after the second-level predictors). The SE for the coefficient (0.856) is used to construct the CI for the estimated param- eter. The variance for the random intercepts (0.977) indicates how the intercepts vary across individual subjects. In other words, the individual subject intercept varies about this mean (-2.891) with a variance estimated as 0.977 (SE is 0.327). Similarly, the fourth equation says that the mean gender effect is 1.283 with SE of 1.054, suggesting that males tend to have higher numbers of CSW alerts. The individual subject slopes do not vary about this mean on Functional Class 1 because the value for the variance of gender (u61) is 0.000. Concerning multilevel model random effect covariance, it can be assumed either that the second-level predictors are independent of each other or that they are correlated to each other. While a more generalized setup can be used to specify a correlated covariance matrix, the team had to assume inde- pendence (hence values under the diagonal were restricted to being zeros) because of computational difficulties. Along the diagonal, the variance for the random constant term is 0.977, which is much greater than that for other random effects, implying that individual drivers provide the main source of status (rdcwdisabled), the interaction between daylight and the use of windshield wipers (wetday), the interaction between daylight and no use of windshield wipers (dryday), the interaction between night and the use of windshield wipers (wetnight), gender (1 if male), females with bachelor’s degrees or above (Fbsabove), males with bachelor’s degrees or above (Mbsabove), the interaction between females and last year’s miles driven in thousands (Fmiles), the interaction between males and last year’s miles driven in thousands (Mmiles), the interaction between females and years of driving experience (Fexp), the interaction between males and years of driving experience (Mexp), and urban/rural settings. The link function used here is logarithm. The unit of the first level is the context combination (cohort). The coefficients of the predictors in the first level are shown in the second equation (with SEs in parentheses). The variable miles (miles traveled in the homogeneous trip segment) indicates the exposure measured directly. Greater exposure results in a higher expected number of alerts trig- gered. The negative sign of rdcwdisabled implies that the number of CSW alerts triggered during Weeks 2 to 4 is greater than in Week 1, resulting from higher exposure (3 weeks with system enabled versus 1 week with system disabled). The baseline for the group of interacting variables (wiper use and day/night) is the interaction between night and the absence of wiper usage; wet reduces the expected number of alerts triggered in both daytime and nighttime conditions. The unit of the second level is the individual driver. The coefficients for the second-level predictors, such as gender, Figure 3.10. Multilevel NB model: Functional Class 1, limited access, CSW.

62 structure. Thus, these models were structured as event-based models using homogeneous trip segment data. There are 331,641 homogeneous trip segments for all drivers in the data set. Each of the 2,605 CSW and 10,452 LDW alerts were matched to the segments on which they occurred. These logit models can be used to form the basis of a case–control study, which matches cases and controls (noncases) within the lim- its of certain confounding factors (e.g., posted speed limit and average annual daily traffic). Compared with the baseline functional class, all other func- tional classes except Functional Class 3 (limited access, which was insignificant) increase a driver’s odds of having a CSW alert. Ramps substantially increase alert odds, while daytime conditions slightly increase the odds. Urban settings, wet condi- tions (based on windshield wiper use), driving with the RDCW system disabled, higher minimum segment speeds, and longer segment distances decrease CSW odds, although urban settings and windshield wiper use are insignificant. Higher maximum segment speed and higher numbers of brake applications on a segment slightly increase CSW alert odds, although brake appli- cations are insignificant. The pseudo R2 indicates a moderately reasonable fit for this model (see Table 3.33). variation. This finding illustrates that the multilevel approach applied to cohort-based event data can potentially identify driver-related factors that would be difficult or impossible to detect using other typical approaches (such as those applied to the VTTI data). All predictors have the same sign and similar magnitudes as the single-level model for expected numbers of CSW alerts trig- gered and can be interpreted similarly; however, the SEs in the single-level models were underestimated. The following factors increase CSW alert frequency on Functional Class 1 roads: exposure in the form of distance, dry daytime conditions, urban settings, being male, higher previous mileage as a female, and being a male with a bachelor’s degree or above; all other predic- tors decrease alert frequency. The variables of being male, being of either gender with a bachelor’s degree or above, and higher previous mileage as a male in this model are insignificant. Logistic Regression Models The UMTRI data were also applied to logit models, using a single-level structure, to compare alert events with nonalerts, which can only be done using a homogenous trip segment Table 3.33. Single-Level Cohort-Based Logit Model, CSW CSW Coefficient OR SE for OR z p > z 95% CI for OR Functional Class 1: Limited access baseline 1.00 NA NA NA NA Functional Class 2: Limited access 0.42 1.528 0.203 3.190 0.001 (1.178, 1.983) Functional Class 3: Limited access 0.57 1.760 0.804 1.240 0.216 (0.719, 4.309) Functional Class 1: Nonlimited access 1.11 3.024 0.362 9.250 <0.001 (2.392, 3.823) Functional Class 2: Nonlimited access 1.60 4.935 0.487 16.160 <0.001 (4.066, 5.988) Functional Class 3: Nonlimited access 1.00 2.712 0.251 10.780 <0.001 (2.262, 3.251) Functional Class 4: Nonlimited access 0.99 2.694 0.251 10.650 <0.001 (2.245, 3.233) Functional Class 5: Nonlimited access 1.56 4.772 0.498 14.980 <0.001 (3.890, 5.855) Ramp 2.22 9.180 0.517 39.350 <0.001 (8.220, 10.251) Daytime 0.21 1.239 0.063 4.200 <0.001 (1.121, 1.370) Urban -0.13 0.882 0.062 -1.790 0.074 (0.769, 1.012) Windshield wiper use (on/off) -0.06 0.940 0.023 -2.530 0.011 (0.896, 0.986) RDCW disabled -0.16 0.855 0.040 -3.320 0.001 (0.780, 0.938) Maximum segment speed 0.19 1.205 0.004 50.080 <0.001 (1.196, 1.214) Minimum segment speed -0.11 0.894 0.002 -44.880 <0.001 (0.890, 0.898) No. of brake applications on segment 0.00 1.003 0.003 1.000 0.317 (0.997, 1.008) Segment distance (mi) -0.03 0.973 0.005 -5.460 <0.001 (0.964, 0.983) Number of observations = 331,641 log likelihood = -10922.3 LR chi-squared (16) = 8595.98 probability > chi-squared = 0.001 pseudo R2 = 0.2824

63 maximum and minimum speed are similar to their effects in the first CSW logit model, but the OR for brake applications is slightly higher (but is still insignificant). Segment distance increases alert odds but is insignificant. Gender interactions with education, experience, and mileage driven in the previ- ous year mostly have odds ratios (ORs) close to 1.0, meaning they do not have much of an effect on CSW alert odds. Gender–education interactions are significant, as are males interacted with last year’s mileage (all other driver attributes are at least marginally significant). The pseudo R2 is similar to that for the first CSW logit model, indicating decent model fit. Table 3.34 shows a model that incorporates driver attri- butes as predictors. As in the first CSW logit model, all func- tional classes increase CSW alert odds compared with the baseline, but the two limited access functional classes are insignificant. Compared with rural nonramp locations, urban nonramps decrease alert odds but are insignificant. All ramp locations increase CSW alert odds and are significant (this is expected since most CSW alerts occurred on ramps). Daytime conditions slightly increase odds, while wet conditions slightly decrease odds. Driving with the alert system disabled decreases the odds of a CSW alert but is insignificant. The effects of Table 3.34. Single-Level Cohort-Based Logit Model, CSW with Driver Attributes Variable Coefficient OR SE for OR z p > z 95% CI for OR Functional Class 1: Limited access baseline 1.00 NA NA NA NA Functional Class 2: Limited access 0.26 1.295 0.204 1.640 0.100 (0.951, 1.764) Functional Class 3: Limited access 0.27 1.305 0.766 0.450 0.650 (0.413, 4.122) Functional Class 1: Nonlimited access 1.02 2.770 0.369 7.650 <0.001 (2.134, 3.596) Functional Class 2: Nonlimited access 1.64 5.174 0.565 15.040 <0.001 (4.176, 6.410) Functional Class 3: Nonlimited access 1.07 2.926 0.298 10.520 <0.001 (2.395, 3.573) Functional Class 4: Nonlimited access 1.02 2.776 0.283 10.000 <0.001 (2.272, 3.390) Functional Class 5: Nonlimited access 1.70 5.458 0.627 14.770 <0.001 (4.357, 6.836) Rural nonramp baseline 1.00 NA NA NA NA Urban nonramp -0.05 0.953 0.081 -0.570 0.572 (0.807, 1.126) Urban ramp 2.13 8.410 0.775 23.100 <0.001 (7.020, 10.075) Rural ramp 2.28 9.797 1.657 13.490 <0.001 (7.033, 13.648) Daytime 0.28 1.321 0.078 4.730 <0.001 (1.177, 1.482) Wet conditions -0.31 0.737 0.062 -3.620 <0.001 (0.625, 0.870) RDCW disabled -0.15 0.863 0.044 -2.860 0.004 (0.780, 0.955) Maximum segment speed 0.19 1.205 0.005 44.550 <0.001 (1.195, 1.215) Minimum segment speed -0.11 0.893 0.003 -40.160 <0.001 (0.888, 0.898) No. of brake applications on segment 0.01 1.006 0.004 1.700 0.089 (0.999, 1.013) Segment distance (mi) 0.13 1.137 0.069 2.100 0.036 (1.008, 1.281) Female with bachelor’s or above -0.32 0.727 0.064 -3.620 <0.001 (0.612, 0.864) Male with bachelor’s or above -0.01 0.994 0.002 -3.260 0.001 (0.990, 0.997) Male years of driving experience -0.01 0.989 0.002 -5.580 <0.001 (0.985, 0.993) Female years of driving experience 0.0004 1.0004 0.0057 0.730 0.466 (1.000, 1.000014) Female last year’s mileage driven 0.99 1.000 0.0034 2.930 0.003 (1.000, 1.000) Male last year’s mileage driven -0.02 0.978 0.006 -3.370 0.001 (0.965, 0.991) Number of observations = 279,166 log likelihood = -9231.2975 pseudo R2 = 0.2889 LR chi-squared (23) = 7501.19