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Social and Behavioral Sciences

Procedia - Social and Behavioral Sciences 53 (2012) 881 - 890

SIIV - 5th International Congress - Sustainability of Road Infrastructures

A logistic model for Powered Two-Wheelers crash in Italy Salvatore Cafisoa'*, Grazia La Cavaa, Giuseppina Pappalardoa

aDepartment of Civil and Environmental Engineering, School of Engineering, University of Catania, Viale Andrea Doria, 95125 Catania, _Italy_

Abstract

Italy shows the European primacy in number of powered two-wheelers fatalities (PTW), which accounts for 30% of the total, compared to the 17% of the EU average. PTWs are the most vulnerable of powered transport modes because of their lack of safety devices and the absence of a protecting chassis for drivers and passengers. Drawing on ISTAT database, a logistic regression was carried out, in order to identify factors affecting crash severity. The analysis of the results partially confirmed previous international studies and added new knowledge about the causes of injury severity in PTW crashes in Italy.

© 2012TheAuthors.PublishedbyElsevierLtd.Selection and/or peer-review under responsibility of SIIV2012 Scientific Committee

Keyword: road safety, motorcycle, moped, crash severity, logistic regression.

1. Introduction

In 2009 there are currently an estimated of 35 million PTWs, from small 50cc mopeds to powerful motorcycles, circulating in the EU 27 countries, 28.7% of which are located in Italy. These represent about 14% of the entire European private vehicle fleet (cars and PTWs only), but they account for around 19% of the fatalities (34% in Italy) [1]. This sad primacy of Italy in the number of PTW crashes and fatalities are typical of other euro-Mediterranean countries (Spain, France, Italy, Greece, Malta) and reflect the large use of powered two - wheeled vehicles in these countries due, above all, to the good climate conditions.

Worldwide the high vulnerability of PTW users produces a disproportion between the participation to traffic and the level of fatal PTW crashes. Indeed, PTWs are the most vulnerable of powered transport mode because of their lack of safety devices and the absence of a protecting chassis for drivers and passengers, which means that PTW riders are more likely to suffer fatalities than car occupant when involved in similar accidents [2].

Many researches on motorcycle accidents are conducted using an univariate approach, and focused on some risk factors, such as helmet use or riders' age, and then tried to determine their relationship with injury severity.

* Corresponding author. Tel.: + 39 095 738 2213; fax: + 39 095 738 7913. E-mail address: dcafiso@dica.unict.it

ELSEVIER

1877-0428 © 2012 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of SIIV2012 Scientific Committee doi:10.1016/j.sbspro.2012.09.937

The causes leading to the injury severity levels are always complicated by presence of multiple factors, including rider's characteristics (e.g., gender, age and use of restraint systems), environmental factors (e.g., weather and light conditions, urban/rural surrounding), roadway designs (e.g., horizontal and vertical alignment, segment or intersection) and other factors (e.g., collision types, collision partner). Isolating some factors for analysis and treating others as fixed does not allow one to obtain a complete understanding of the underlying causes of injury severity in motorcycle accidents.

In literature there are several studies for motorcycle severity analysis by using multivariate approaches [3] [4] [5] [6] [7]. These studies has identified many risk factors for severe PTW crashes, and also showed multinomial logit formulation as a promising approach to evaluate the determinants of injury severity in PTW accidents.

Chang [4] analyzed 2000 single - vehicle crash data to compare fatality risk factors between non -motorcycle drivers and motorcyclists. On average, motorcyclists had approximately a three times higher fatality risk than non - motorcyclists after adjusting for the driving mileage. Two respective logistic regression models for two categories of drivers indicated that some common features, such a being male, a higher age, and crashes occurring between the hours of 22 and 06 revealed a greater likelihood of fatality.

Ucar and Tathdil [6] examined motorcycle accidents occurring in 2002 in Turkey. As a result, it was determined that drivers who prefer to travel on a two-directed road, in an urban area, during the daytime have a better chance of survival in motorcycle accidents.

The crash injury severity analysis presented in the paper of Savolainen and Mannering [8] about motorcyclists' injury severities in single- and multi-vehicle crashes revealed several problem areas leading to more severe injuries: poor visibility (horizontal curvature, vertical curvature, darkness); unsafe speed (citations for speeding); alcohol use; not wearing a helmet; right-angle and head-on collisions; and collisions with fixed objects. There were some findings that motorcyclists may be managing risks. Crashes were found to be less severe under wet pavement conditions, near intersections, and when a passenger was on the motorcycle. This may indicate that riders may be riding in a more cautious manner under such situations—resulting in less severe crashes once they occur.

By developing a probabilistic model that contains several important variable relating to environmental factors, roadway conditions, vehicle characteristics and rider attributes, Shankar and Mannering [9] provide suggestive results by use of variable such as helmet sobriety interaction and helmet - fixed object interaction. Their study suggests that helmeted - riding may be an effective means of reducing injury severity in some types of collisions, however, the benefit of helmet use may be offset in fixed - object collisions where the risk of fatality was found to increase.

The study of Indriastuti et Sulistio [7] is aimed to develop a probability model of motorcycle accident in urban area, with the case study of Malang City, using logistic regression method the influencing factors on motorcycle accident were identified. The explanatory variables that significantly influenced the probability of a motorcycle rider get in an accident are gender, number of motorcycle owned, travel purpose, distance and riding knowledge.

MAIDS (Motorcycle Accidents In Depth Study) database [10] was used to calibrate logistics models in order to identify factors that may be good predictors of the PTW rider fatality. As the result of this analysis, the following major findings were observed:

• the risk of a PTW rider fatality increases with age. PTW riders over 41 years of age appear to be at greater risk. PTW riders between 18 and 21 years appear to have lesser risk of being involved in a fatality when compared to 26 to 41 year old PTW riders;

• there is a significant increase in the risk of a PTW rider fatality when the accident takes place on a major arterial roadway;

• accidents that take place at a site other than an intersection appear to have a greater risk of PTW rider fatality;

• when other factors are taken into consideration, no vehicle factors were found to be statistically significant predictors of a PTW rider fatality;

• PTW rider speeding was not found to be a good predictor of a PTW rider fatality, but for every 10 km/h

increase in crash speed, the odds of a PTW rider fatality increase by 1.31.

No similar studies, based on a rigorous methodological approach, were found in the recent literature referring to the Italian case study. This lack of information is particularly serious considering that Italy represents a "leading" country in terms of number of PTW users and consequently of PTW crashes and road fatalities.

In this study logistic regression is used to examine the influence of multiple factors related to road geometry, environmental condition, collision characteristics, driver attributes and type of PTW, on road crashes involving PTW in Italy. The variables included in the models and the detailed analysis of the results partially confirmed previous international studies and added new knowledge about the causes of injury severity in PTW crashes in Italy.

2. Data treatment

In Italy, the source of data for statistics on road crashes is provided by ISTAT (National Institute of Statistics). Any injury and/or fatal accident should be reported by the police authorities using a standardized Model (CTT.INC ISTAT) [11]. The different levels of severity are:

• Killed: any person who was killed outright or who died within 30 days as a result of the accident;

• Injured: any person, who was not killed, but sustained one or more serious or slight injures as a result of the

accident.

Data used in this study were extracted from the ISTAT dataset counting 78,419 crashes occurred in 2008 in which at least a moped (power of 50 cc) and/or a motorcycle (power over 50 cc) was involved [12]. Since the goal of the study was to identify the factors that might affect the severity of a PTW crash (i.e. whether it was a fatal or non - fatal accident for the PTW driver), the dependent variable "CRASH SEVERITY" (CR) was defined and treated as a binary variable, assuming the value:

CR=1 if crash results in the PTW driver fatality;

CR=0 in any other case (i.e. PTW drive injury, PTW passenger fatality/injury, opposing vehicle driver or passenger fatality or injury).

From the dataset 8 variables were selected basing on the relevance of the parameter and on the completeness of the information (some variables are not full fillet in the data set): time of day, road type, road geometry, collision type, PTW type, partner collision, age of driver, crash circumstances.

Because some variables have several codes in the crash report (e.g. crash circumstances is coded with 107 different values, driver age is an integer value ranging from 14 to 89) a first aggregation was carried out to simplify the information. Other variables were treated to define derived information (e.g. the date and hour of the crash were used to define the light condition: daylight/night time). Each categorical variable is described by several levels describing a sub-set of design variables. A model reporting many design variables can give a more detailed analysis of the phenomenon, but the more variables the model includes, the more difficult the model calibration and interpretation becomes. To define a criterion of selection, the hypothesis testing technique for proportions was used to decide whether the number of levels for a design variable could be reduced due to the significant probability that the proportion of level i (pi) could be equal to zero. Available data were compared using the chi square test of independence [13] in order to evaluate the null hypothesis: proportion=0.

The chi-square statistic is defined as:

J2^!^^ (1)

where:

Oi is the observed frequency;

Ei is the expected frequency. If the pi is significantly different from zero and falls in the rejection region at the 5% significance level, the null hypothesis is rejected (P-value > 0.05). Table 1 summarizes the hypothesis testing results for all the design variables defined after the first selection. Basing on the test results, some levels were deleted. For example the variable "crash location" was reduced from four levels to three levels after the test showed that the proportion of "other" (location) was not statistically significant at the 5% level. Considering, also, the uncertainty of the condition other locations, this level was not considered removing from the data set all the cases classified with "other" in the variable "Location". In other cases, new levels were created merging previous levels in order to realize one statically significant (i.e. single accident merges falling from vehicle, run off and sudden braking).

3. Crash modeling

3.1. Logistic Regression model and interpretation

Since the response variable, CRASH SEVERITY, is a binary variable and the independent variables are categorical, the logistic regression is a suitable technique to be used because it is developed to predict a binary dependent variable as a function of predictor variables both numerical and categorical. Logistic regression is widely used in road safety studies were the dependent variable is binary, because it provide useful results:

• to predict a dependent variable on the basis of continuous and/or categorical independents and to determine the percent of variance in the dependent variable explained by the independents;

• to rank the relative importance of independents;

• to assess interaction effects;

• to understand the impact of covariate control variable.

For a binary response variable [14] the linear logistic regression model, expressed in terms of the logit transformation of the ith individual's response probability, pi (e.g., probability of severe injury), is a linear function of the vector of explanatory variables:

logit(p0 = log = p0 + plXl + - + PjXj + ••• + pnxn (2)

Pj: regression coefficients; j=1,..., n for n predictor variables xj.

The negative sign before the linear combination of predictors produces a positive relationship between the sign of the coefficient and the direction of effect on risk. In other words, a positive coefficient represents an increase in risk and a negative coefficient represents a decrease in risk.

The logit is the natural logarithm of the odds or the likelihood ratio that the dependent variable is 1 (fatal crash) as opposed to 0 (no fatal crash). When an independent variable xi increases by one unit, with all other factors remaining constant, the odds increase by a factor exp(pi) which is called the odds ratio (OR), ranging from 0 to positive infinity. It indicates the relative amount by which the odds of the outcome (fatal) increase (OR>1) or decrease (0<0R<1) when the value of the corresponding independent variables increases by one unit.

3.2. Model Development and Results

To assess the goodness of fit for binary response models, Hosmer and Lemeshow [15] proposed a statistic test. The test assesses whether or not the observed event rates match expected event rates in "n" subgroups of the model population. The Hosmer-Lemeshow test specifically identifies n=10 subgroups sorting the observations in increasing order of their estimated event probability ng (the deciles of fitted risk values).

Table 1. Summary of variables and statistical significance

VARIABLE CLASSIFICATIONS REF. VARIABLE Code number proportion P-value

ROAD TYPE Rural road Urban road R 9344 0.119 0.119

Urban road U 69075 0.881 1.000

LIGHT CONDITION Day time Night Day 61245 0.781 1.000

Night time Night 17174 0.219 0.219

ROAD GEOMETRY Curve Intersection C 5640 0.072 0.083

Straight road ST 39916 0.509 1.000

Intersection J 31988 0.408 0.491

Other* OT 875 0.011 0.011*

COLLISION TYPE Falling from vehicle* Single accident FV 1407 0.018 0.020*

Run off RO 2879 0.037 0.134

Front/side collision FS 56211 0.717 1.000

Front collision* F 181 0.002 0.002*

Sideswipe collision S 7433 0.095 0.283

Obstacle collision O 2290 0.029 0.098

Pedestrian accident* PA 1696 0.022 0.042*

Sudden braking SB 2078 0.026 0.068

Rear - end accident RE 4244 0.054 0.188

PTW TYPE Moped Motorcycle M 26723 0.341 0.341

Motorcycle MC 51696 0.659 1.000

PARTNER COLLISION Bus* Car B 558 0.007 0.010*

Car CAR 53275 0.679 1.000

Truck GV 4340 0.055 0.158

Moped* M 1190 0.015 0.038*

Motorcycle MC 2279 0.029 0.105

No partner NP 12751 0.163 0.321

Pedestrian P 1696 0.022 0.076

Bicycle B 1297 0.017 0.055

Others* OTH 1033 0.013 0.023*

AGE OF DRIVER (years) 14<Age<18 25<Age<44 <18 12219 0.156 0.203

18<Age<24 18-24 14627 0.187 0.555

25<Age<44 25-44 34870 0.445 1.000

45<Age<60 45-60 13026 0.166 0.369

>60* >60 3677 0.047 0.047*

CRASH CIRCUMSTANCES Falling from vehicle Passing FA 2355 0.030 0.089

Safety distance SD 4188 0.053 0.216

Regular driving RE 30736 0.392 1.000

Speed SP 4977 0.063 0.279

Braking* SB C 348 0.004 0.004*

Inattention I 8069 0.103 0.608

Manoeuvring MA 2703 0.035 0.115

No circumstances** NC 7613 0.097 0.505

Yield fault YF 5017 0.064 0.343

Pedestrian yield fault* PYF 1014 0.013 0.017*

Slipping SL 5083 0.065 0.408

Passing PAS 3277 0.042 0.162

Other circumstances** OC 2498 0.032 0.121

* Statistically insignificant at 5% level - ** Undefined factor

Based on these assumption, the Hosmer-Lemeshow test statistic is given by:

tj _ vn i°g~Eg) /-¡i

H-^Ng-n g.(l-ng) (3)

Og = observed events for the gth risk group

Eg= expected events for the gth risk group

Ng= observations for the gth risk group

ng= predicted risk for the gth risk group.

When there is no replication in any of the subpopulations, the H statistic asymptotically follows a %2 distribution with n-2 degrees of freedom. Large values of H (and small p-values) indicate a lack of fit of the model. As goodness of fit for the model a P-value greater than or equal to 0.10 was assumed to assess that there is no reason to reject the adequacy of the fitted model at the 90% or higher confidence level. The Wald statistic is a test which is commonly used to test the significance of individual logistic regression coefficients for each independent variable (that is, to test the null hypothesis in logistic regression that a particular logit coefficient is zero, H0: pj =0). The Wald statistic W is the square of the ratio of the estimated value of the logistic coefficient pj with its standard error SE(pi) and it follows a standard normal distribution under the null hypothesis that pj =0

W = i-Thf (4)

ISEiPOl V '

It was observed that the Wald test often fail to reject the null hypothesis when the coefficient is significant. Therefore, the likelihood ratio test should be used in suspicious cases. The likelihood ratio can be expressed as:

G=-2 ln [(likelihood without variable)/(likelihood with variable)] (5)

Under the null hypothesis of pi =0, G follows a %2 distribution with one degree of freedom.

The backward selection process of logistic regression was adopted in the model calibration in order to eliminate, step by step, those variables that could result not significant (i.e. P-value of Wald test higher than 0.1) and continue with testing interaction effects with only significant variables.

Since some independent variables x! have several levels, a sub-set of dichotomous variables (dummy variables) has to be derived to represent the data in a logistic regression. It is important to understand the coding strategy in order to conduct hypothesis testing on the variables as well as to interpret their estimates. When the independent variables are characterized by a series of dichotomous variables, one of the variable is used as reference in the estimation (Table 2).

The reference variable is not represented in the model since it is defined by all 0 value in the sub-set of the design variables.

Table 2 shows the results from fitting all the explanatory variables because the backward process has not removed any variables (P-values of all the independent variables less than 0.1).

Moreover, Hosmer-Lemeshow test shows that there is no reason to reject the adequacy of the fitted model at the 90% confidence level. Finally, a graphical assessment of the fit to the logistic model developed in this study also shows that the model appears to fit the data reasonably. Figure 1 shows the plot of Pearson residuals, in which no trend can be detected.

The PTW model including all the available data for rural and urban areas showed the discriminating influence to PTW driver fatality of rural area with respect to urban area (odds ratio of 4.85). Therefore, to reach a more in deep analysis of the phenomenon, two different logit models were calibrated considering separately PTW crashes in rural and urban area.

For both the models, the P-values of all the dependent variables resulted less than 0.1, therefore the backward process has not removed any variables from the model. Hosmer-Lemeshow test shows that there is no reason to reject the adequacy of the fitted models at the 90% confidence level.

The functions g(x) for rural and urban dataset are expressed by the form of (2) with coefficients bj reported in Table 2.

From the model coefficients and odds ratio (Table 2), the following results regarding probability of a PTW crash with fatal consequences can be highlighted common to both areas:

• high speed is an important factor affecting the probability of a fatal consequences.

• crashes in daylight time are less severe than in night time;

• crashes on bending curves have higher probability of fatal consequences than accident at intersection tangents;

• single crashes have a higher probability of fatal consequences than any other collision type or partner;

• crashes involving motorcycle are more severe than crashes involving moped;

• the PTW drivers in the age classes of 25-44 years have the highest probability of fatality respect the other classes with the only exception of old drivers (age over 60).

Fig. 1. Plot of Pearson residuals

Table 2. Wald Statistics, P-value and Odds ratio for the model variables

RURAL MODEL URBAN MODEL

Test of Hesmer - Lemeshow l2= 6.478 Sig = 0.594 /2= 6.943 Sig = 0.543

VARIABLE(ID) REF. VAR. Pi Wald P-value OR Pi Wald P-value OR

Constant (0) -2.1 0.000 0.122 -3.694 0.000 0.025

TYPE OF ROAD

R (1) U

LIGHT CONDITION

Day (2) Night -0.653 0.000 0.520 -0.817 0.000 0.419

ROAD GEOMETRY 0.026 0.006

C (3) J 0.383 0.012 1.467 0.538 0.002 1.712

ST (4) 0.077 0.560 1.080 0.144 0.150 1.155

COLLISION TYPE 0.000 0.000

FS (5) -0.181 0.395 0.835 -0.616 0.010 0.540

S (6) -1.713 0.000 0.180 -1.434 0.000 0.238

O (7) -0.384 0.293 0.681 -0.036 0.906 0.965

RE (8) -0.798 0.008 0.450 -0.753 0.024 0.471

PTW TYPE

M (9) MC -0.393 0.016 0.675 -0.541 0.000 0.582

COLLISION PARTNER 0.000 0.000

GV (10) CAR 0.796 0.000 2.217 1.279 0.000 3.593

NP (11) 0.702 0.005 2.018 0.192 0.270 1.211

PTW (12) 0.685 0.002 1.984 -0.280 0.281 0.756

AGE OF DRIVER 0.000 0.000

<18(13) 25-44 -0.817 0.002 0.442 -0.327 0.049 0.721

18-24 (14) -0.483 0.005 0.617 -0.166 0.179 0.847

45-60(15) 0.028 0.829 1.029 -0.046 0.719 0.955

>60(16) 0.583 0.006 1.792 0.716 0.000 2.046

CIRCUMSTANCES 0.000

FA (17) PAS -1.509 0.002 0.221 -0.985 0.035 0.374

SD (18) -0.211 0.505 0.810 -0.491 0.180 0.612

RE (19) -0.108 0.668 0.897 -0.038 0.885 0.962

SP (20) 0.575 0.030 1.778 1.365 0.000 3.918

IN (21) -0.08 0.779 0.923 0.232 0.411 1.262

MA (22) -0.049 0.886 0.952 0.405 0.211 1.499

YF (23) -0.454 0.254 0.635 0.293 0.341 1.341

SL (24) -0.909 0.013 0.403 0.437 0.208 1.547

Analyzing the different road surrounding environment and traffic condition, some differences of rural

respecting to urban area can also be highlighted (Figure 2):

• generally collisions with a car is less severe with respect to any other partner (Good Vehicle or PTW) with the exception of collision between PTWs in rural area

• high speed remains the first contributing factors among all the variables in the class "crash typology", but passing is a high risk maneuver only in rural roads;

• inattention, Yield fault, slipping and maneuverings in the traffic are high risk circumstances above all in urban area.

Fig. 2. Comparison of the odds ratio among the different models

4. Conclusion

Italy shows the European primacy in the number of Powered Two-Wheelers fatalities in road crashes which accounts for 30% of the total compared to the 17% of the EU average. For this reason a strong effort has to be devoted for a better understanding of the phenomenon in order to carry out effective safety policies for PTW users. In this study logistic regression is used to examine the influence of multiple factors related to road geometry, environmental condition, collision characteristics, driver attributes and type of PTW, on road crashes involving PTW in Italy. Considering the different probability of fatal consequences for PTW crashes on rural roads with respect to PTW crashes on urban streets, two different logistic models (urban, rural) were calibrated selecting the independent variable to be considered and included in the model. The Wald test and the Hosmer and Lemeshow test were performed to assess the significance of the independent variables and the goodness of fit of the models. The analysis of these models provided specific information about the contribution of the different factors to the conditional probability that PTW crash has a fatal consequences for the driver. The detailed analysis of estimated coefficients and odds ratio is reported in the paper. Some conclusions and general consideration are summarized in the following. Common factors affect the probability of a fatal crash both in

rural and urban area, others have different impact to the severity of a collision. Driving at high speed results as the first circumstance of a fatal crashes if compared with other driver responsibilities or driving conditions. High speed can be considered the influencing factors to explain also other results carried out from the model:

• rural compared to urban area has a high odds ratio;

• single crashes and hit obstacles which have a higher probability of fatal consequences than the other crash typologies can be associated with free flow high speed driving;

• crashes involving motorcycle are more severe for the PTW driver than crashes involving moped which are constrained at a speed limited less than 50 km/h.

Driver's roadway perception and visibility and loss of vehicle control can be related to high severity of crash in night time and on bending curves. The high vulnerability of the PTW drivers is highlighted by the fact that among multiple vehicle collisions the more severe consequences occur when the partner of collision is a gross vehicle followed by collision with another PTW when compared with collision with a passenger car.

Analyzing the different traffic conditions between rural and urban areas, some differences of rural respecting to urban area have been highlighted by the study: passing is a high risk maneuver in rural roads and inattention, yield fault and maneuvering in the traffic are high risk circumstances above all in urban area.

Acknowledgements

The authors wish to thank Italian Automobile Club (ACI) for the support in the data acquisition and elaboration.

References

[1] European Union Road Federation (2011). "ERF 2011 European Road Statistics", http://www.erf.be/images/stories/Statistics/2011/ERF-2011-STATS.pdf (Accessed March 15, 2012)

[2] Albalate, D., Fernandez-Villadangos, L. (2010). "Motorcycle injury severity in Barcelona: the role of vehicle type and congestion", Traffic Injury Prevention, Vol. 11, pp. 623-631.

[3] Quddus, M., Noland, R., Chin, H. (2002). "An analysis of motorcycle injury and vehicle damage severity using ordered probit models", Journal of Safety Research, Vol. 33, pp. 445-462.

[4] Chang, L. (2005). "Empirical analysis of the effectiveness of mandated motorcycle helmet use in Taiwan", Journal of the Eastern Society for Transportation Studies, Vol. 6, pp. 3629-3644.

[5] Symmons, M., Mulvihill, C., Haworth, N. (2007). "Motorcycle crash involvement as a function of self assessed ryder style and rider attitudes". Proceedings of Australasian Road Safety Research, Policing and Education Conference, Melbourne, Australia.

[6] Ucar, O., Tathdil, H. (2005). "Application of three discrete choice models to motorcycle accidents and a comparison of the results", Hacettepe Journal of Mathematics and Statistics, Vol. 34, pp. 55-66.

[7] Indriastuti, A.K., Sulistio, H. (2010). "Influencing factors on motorcycle accident in urban area of Malang, Indonesia", International Journal of Academic Research, Vol. 2. No. 5.

[8] Savolainen, P., Mannering, F. (2007). "Probabilistic models of motorcyclists injury severities in single and multi-vehicle crashes", Accident Analysis and Prevention, Vol. 39, pp. 955-963.

[9] Shankar, V., Mannering, F. (1996). "An exploratory multinomial logit analysis of single-vehicle motorcycle accident severity", Journal of Safety Research, Vol. 27, No. 3, pp. 183-194.

[10] Smith, T.A. (2009). "Multivariate Analysis of MAIDS Fatal Accidents", DRI-TR-08-11 Technical Report, ACEM-Dynamic Research, Inc.

[11] ISTAT, (2008). "Statistics on Highway Accidents", Italy.

[12] Cafiso, S., La Cava, G., Pappalardo, G. (2012). "A comparative analysis of powered two wheelers crash severity in urban areas", presented at 5th SIIV International Congress, Rome, Italy, 29-31 October 2012.

[13] Chung, C.A. (2003). "Simulating modeling handbook", CRC Press.

[14] Kononena, D.W., Flannaganb, C.A.C., Wangc, S.C. (2011). "Identification and validation of a logistic regression model for predicting serious injuries associated with motor vehicle crashes", Accident Analysis and Prevention, Vol. 43, pp. 112-122.

[15] Hosmer, D. W., Lemeshow, S. (2000). "Applied Logistic Regression", John Wiley & Sons.