3.1. Modal choice study

In the first case study, we will analyze the transport behavior of transport users by estimating an unordered multimodal logit model on a sample of urban transport users from the city of Sousse (Tunisia). This study will allow us to analyze the transport demand and to identify several information about the direct and indirect elasticities of transport demand in relation to the different attributes of the modes envisaged (transport price, travel time, waiting time, etc.) and to calculate the psychological value of transport time.

The behavior of individual choice in the transport market is considered as a selection process between several modes of transport available (car, bus, metro, two-wheeled vehicle, etc.). The transport user will choose the mode that maximizes its utility.

However, this utility is unobserved. What we actually perceive is the modal choice of the user. In this context the variable to be explained will be the choice established by the transport user and not its utility.

This endogenous variable is thus discrete and qualitative which will take a limited number of integer values, whose each value illustrates a particular choice. This is the foundation of the discrete choice model.

We assume that the choice modal set is composed of three modes such as the private car, bus, and taxi (j = 1, 2, 3).

The variable to be explained is expressed by the following system: ∨ i=1…n:

$$\mathbf{Y\_{ij}} = \begin{cases} 1 \text{ if the user i prefers the private car (PC) to other modes} \\ 2 \text{ if the user i prefers the taxi to the other modes} \\ 3 \text{ if the user i prefers the bus to other modes} \end{cases} \tag{15}$$

To avoid collinearity between modal choices, we eliminate the third choice (bus) while considering it as the reference situation. This reference situation will serve us to better interpret our results and evaluate the impact of changing explanatory variables on the probability of choosing the mode j (PC or taxi) rather than the bus mode.

The user i that prefers the private car to the bus mode implies that he gets more satisfaction by using the private car than the bus to get to work. This satisfaction can be systematized by a linear indirect utility function.

Yij = 1 (choice of the PC) if and only if Ui (PC) > Ui (bus) and Ui (PC) > Ui (taxi).

In this section, two case studies will be analyzed and interpreted and treated in the case of my research work and supervision on topics particularly related to transport economics. The first study deals with the modal choice problem and the second with road accidentology. These case studies will allow us to better value the practical interest of these models of discrete choice, to account for the diversity of fields of application of these models and to present real results allowing a better understanding of the coefficient interpretation according to the qualitative and quantitative nature of the explanatory

In the first case study, we will analyze the transport behavior of transport users by estimating an unordered multimodal logit model on a sample of urban transport users from the city of Sousse (Tunisia). This study will allow us to analyze the transport demand and to identify several information about the direct and indirect elasticities of transport demand in relation to the different attributes of the modes envisaged (transport price, travel time, waiting time, etc.)

The behavior of individual choice in the transport market is considered as a selection process between several modes of transport available (car, bus, metro, two-wheeled vehicle, etc.). The

However, this utility is unobserved. What we actually perceive is the modal choice of the user. In this context the variable to be explained will be the choice established by the transport user

This endogenous variable is thus discrete and qualitative which will take a limited number of integer values, whose each value illustrates a particular choice. This is the foundation of the

We assume that the choice modal set is composed of three modes such as the private car, bus,

2 if the user i prefers the taxi to the other modes 3 if the user i prefers the bus to other modes

To avoid collinearity between modal choices, we eliminate the third choice (bus) while considering it as the reference situation. This reference situation will serve us to better interpret our results and evaluate the impact of changing explanatory variables on the probability of choos-

The user i that prefers the private car to the bus mode implies that he gets more satisfaction by using the private car than the bus to get to work. This satisfaction can be systematized by a

1 if the user i prefers the private car ðPCÞ to other modes

(15)

The variable to be explained is expressed by the following system: ∨ i=1…n:

variables.

3.1. Modal choice study

and not its utility.

discrete choice model.

and taxi (j = 1, 2, 3).

Yij ¼

linear indirect utility function.

8 ><

>:

ing the mode j (PC or taxi) rather than the bus mode.

and to calculate the psychological value of transport time.

94 Statistics - Growing Data Sets and Growing Demand for Statistics

transport user will choose the mode that maximizes its utility.

Formally, the indirect utility function Uij depends on a certain number of variables relating to the attributes of the chosen transport mode (Wj ) as well as to the user's socioeconomic characteristics (Xi).

Many explanatory variables can be integrated and tested which characterize as well the individual as the attributes of the mode to choose.

For example, four explanatory variables characterizing the transport user such as income, sex, age, and household size and three explanatory variables characterizing the modes such as the kilometric price of the use of each mode, travel time, and access time to each mode. All variables are continuous except the sex will be expressed as a binary variable coded 0 if the user is female and 1 otherwise. The price, travel time, and access time vary for the same individual from one mode of transport to another, while the variables characterizing the user do not vary according to the mode.

With reference to Eq. (10), our model will be expressed by the following relation:

$$\begin{split} \text{Log}\left(\frac{P\_{\text{ij}}}{P\_{\text{il}}}\right) &= \mathbf{U}\_{\text{ij}} = \alpha\_{0\text{j}} + \sum\_{k=1}^{4} \alpha\_{jk} \mathbf{X}\_{ik} + \sum\_{k=1}^{2} \beta\_{k} \mathbf{W}\_{\text{j}k} \\ &= \alpha\_{0\text{j}} + \alpha\_{1\text{j}} \mathbf{R}\_{\text{i}} + \alpha\_{2\text{j}} \mathbf{S}\_{i} + \alpha\_{3\text{j}} A\_{i} + \alpha\_{4\text{j}} \mathbf{D}\_{\text{i}} + \beta\_{1} \mathbf{P}\_{\text{j}} + \beta\_{2} \text{ tp}\_{\text{j}} + \beta\_{3} \text{ ta}\_{\text{j}} \end{split} \tag{16}$$

where Ri, Si, Ai, Di, Pj , tpj , and taj are, respectively, income, sex, age, household size i, price, travel time, and access time by the mode j.

αjk and β<sup>h</sup> are the coefficients to estimate. The weighting coefficients relating to the socioeconomic characteristics of the users (αjk) are specific to each mode of transport, while those of the attributes (βh) are constant and do not vary according to the mode or the user.

α0j is a constant that varies from one mode to another.

The estimate of this model requires data by user-displacement couple which are collected through the household-displacement survey database dated 2004 for the city of Sousse (Tunisia). Our sample is made up of 500 households distributed homogeneously over the entire agglomeration.

We are interested to a particular aspect of displacement having a professional motive, on a path home-work that converges to the city center during the morning rush hours by bus, private car, and taxi.

Table 1 presents the results of our estimation. It describes the estimated values of the coefficients associated to the explanatory variables; their standard error (in parenthesis), in a second column; their degree of significance in the third column; and their exponential function in the last column.

All variables are statistically significant for thresholds going from 1–10%; several indicators of quality adjustment of the model were developed to evaluate the predictive ability of the model


Concerning the coefficient associated with the gender variable, it is interpreted as follows: a man has 28.5% (1–0.715) and 60.6% (1–0.715) of luck less than a woman to choose, respectively,

The Application of Discrete Choice Models in Transport http://dx.doi.org/10.5772/intechopen.74955 97

The increase of the members of a household of a person increases the probability of choosing PC but brings down the probability of choosing the taxi compared to that of bus. Indeed, one more member in the family increases by 34% the probability of choosing the PC rather than the

In fact, by becoming a householder, we will prefer the car better than the bus thanks to its

For the other explanatory variables characterizing the modes of transport (P, tp, and ta), they negatively affect the probability of choosing both the private car and the taxi to the bus.

The estimated coefficients for these variables are, respectively, �00167, �0.123, and �0.38. This implies that if the cost per kilometer of transport or the travel time or the access time to the mode of transport increases of a unit while keeping all the other variables constant, the probability of choosing the car mode compared to the bus decreases by 1.65% (1-exp (�0.016)), 11.57 and 32%, respectively. The user of the car has a greater sensitivity to the transport time than the cost. This explains well the fundamental reason for the dominance of the car in the modal split, thanks to

So, the cost and the time of transport play a determining role in the decisions of the modal choice and affect negatively the transport demand as well as the modal sharing between the

The weights of the explanatory variables can be interpreted economically as the marginal utilities of each indirect utility function argument (Uij). They indicate the effect of unitary

If Xi = Si is the sex variable, α<sup>31</sup> = �0.33; this implies that the man is less satisfied than the

If Xi = Di, α<sup>41</sup> = 0.29; this implies that the more the household is composed of a larger number of individuals, the greater its satisfaction of the use of a private car is important. One more

The weighting coefficients related to the attribute variables of the PC mode are all negative, implying that the increase in both the cost of transport induced by the increase in the fuel price or the cost of acquisition of the PC, as well as the travel time whether it is in traffic or the search

We can see that the choice probability of the PC is more sensitive to the search time of parking than the travel time and the costs of displacement. The parking search time provides a triple

member in the household increases the satisfaction of PC use by 0.29 units.

for parking caused by congestion, creates a disutility for users of the PC.

disutility compared to that caused by the travel time by the user of the PC:

∂Xk

¼ αk<sup>1</sup>

Umi1PðXkÞ ¼ <sup>∂</sup>Ui1ðXk<sup>Þ</sup>

bus and decreases the probability of choosing the taxi rather than the bus of 22.1%.

its quality of service that is better than the bus particularly in terms of access time.

the PC and the taxi rather than the bus, everything else being equal.

advantages of availability, flexibility, and accessibility.

change of each variable on the utility of the mode (PC).

woman by the use of the particular car.

car and the bus.

Standard error in parentheses:

• Number of observations = 500

• Log likelihood = � 116,6517

• Pseudo R<sup>2</sup> = 0.48.

Table 1. Parameter estimates of modal chose model.

(Mc Fadden's pseudo R2 , Estrella indicator, Ben Akiva and Lerman indicator, etc.) [19]. According to the software used (STATA 11), only the Pseudo R<sup>2</sup> and the log likelihood are calculated. Their values show although overall; the explanatory variables selected explain at high degrees the modal choice:

$$\log\left(\frac{P\_{i(j=1)}}{P\_{i(j=3)}}\right) = -2.014 + 0.218\text{ R}\_i + 0.04\text{ A}\_i - 0.33\text{ S}\_i + 0.29\text{ D}\_i - 0.00167\text{ P} - 0.123\text{ tp} - 0.38\text{ ta}$$

The constant parameter illustrates the heterogeneity in the representativeness of the individual choices in our sample. This coefficient is significantly higher for the PC than the taxi, reflecting thus the higher proportion of taxi users compared to those of the PC.

We can interpret the parameter associated with an explanatory variable by fixing the other variables for a given level and varying the said variable. The exponential function of this coefficient indicates the effect of this variation on the probability of choosing the PC mode rather than the bus mode. For example, when a household's income increases by one unit, the probability of choosing the PC mode instead of the bus mode increases by 24.3% (1.243–1).

For the age variable of the users of the PC, odds ratio is 1.04. This implies that a year furthermore increased by 4% the probability of choosing the PC than the bus.

Concerning the coefficient associated with the gender variable, it is interpreted as follows: a man has 28.5% (1–0.715) and 60.6% (1–0.715) of luck less than a woman to choose, respectively, the PC and the taxi rather than the bus, everything else being equal.

The increase of the members of a household of a person increases the probability of choosing PC but brings down the probability of choosing the taxi compared to that of bus. Indeed, one more member in the family increases by 34% the probability of choosing the PC rather than the bus and decreases the probability of choosing the taxi rather than the bus of 22.1%.

In fact, by becoming a householder, we will prefer the car better than the bus thanks to its advantages of availability, flexibility, and accessibility.

For the other explanatory variables characterizing the modes of transport (P, tp, and ta), they negatively affect the probability of choosing both the private car and the taxi to the bus.

The estimated coefficients for these variables are, respectively, �00167, �0.123, and �0.38. This implies that if the cost per kilometer of transport or the travel time or the access time to the mode of transport increases of a unit while keeping all the other variables constant, the probability of choosing the car mode compared to the bus decreases by 1.65% (1-exp (�0.016)), 11.57 and 32%, respectively. The user of the car has a greater sensitivity to the transport time than the cost. This explains well the fundamental reason for the dominance of the car in the modal split, thanks to its quality of service that is better than the bus particularly in terms of access time.

So, the cost and the time of transport play a determining role in the decisions of the modal choice and affect negatively the transport demand as well as the modal sharing between the car and the bus.

The weights of the explanatory variables can be interpreted economically as the marginal utilities of each indirect utility function argument (Uij). They indicate the effect of unitary change of each variable on the utility of the mode (PC).

(Mc Fadden's pseudo R2

Standard error in parentheses: • Number of observations = 500 • Log likelihood = � 116,6517 • Pseudo R<sup>2</sup> = 0.48.

Log

Sex

Pi jð Þ <sup>¼</sup><sup>1</sup> Pi jð Þ <sup>¼</sup><sup>3</sup> !

high degrees the modal choice:

Table 1. Parameter estimates of modal chose model.

Woman Ref

, Estrella indicator, Ben Akiva and Lerman indicator, etc.) [19].

According to the software used (STATA 11), only the Pseudo R<sup>2</sup> and the log likelihood are calculated. Their values show although overall; the explanatory variables selected explain at

Variable Coefficient Student's T-test Exp (coef)

Income 1 0.218 (0.11) 2.15 1.243 Income 2 0.853 (0.063) 32.14 1.089 Age 1 0.04 (0.013) 14.01 1.04 Age 2 �0.13 (0.0912) �2.06 0.87

Man 1 �0.3341 (0.139) �3.47 0.715 Man 2 �0.93 (0.173) �8.7 0.394 Household size 1 0.2943 (0,112) 2.15 1.34 Household size 2 �0.25 (0.125) �2.25 0.779 Price �0.0167 (0,078) �0.67 0.983 Travel time �0.123 (0,1218) �2.41 0.884 Access time �0.38 (0.105) �4.13 0.68

Constant 1 �2.014 (0.31) �10.66 Constant 2 �12.82 (0.401) �15.1

96 Statistics - Growing Data Sets and Growing Demand for Statistics

The constant parameter illustrates the heterogeneity in the representativeness of the individual choices in our sample. This coefficient is significantly higher for the PC than the taxi, reflecting

We can interpret the parameter associated with an explanatory variable by fixing the other variables for a given level and varying the said variable. The exponential function of this coefficient indicates the effect of this variation on the probability of choosing the PC mode rather than the bus mode. For example, when a household's income increases by one unit, the probability of choosing the PC mode instead of the bus mode increases by 24.3% (1.243–1).

For the age variable of the users of the PC, odds ratio is 1.04. This implies that a year

furthermore increased by 4% the probability of choosing the PC than the bus.

thus the higher proportion of taxi users compared to those of the PC.

¼ �2:014 þ 0:218 Ri þ 0:04 Ai � 0:33 Si þ 0:29 Di � 0:00167 P � 0:123 tp � 0:38 ta

$$\mathcal{U}Im\_{i1P}(\mathbf{X}\_k) = \frac{\partial \mathcal{U}\_{i1}(\mathbf{X}\_k)}{\partial \mathbf{X}\_k} = \alpha\_{k1}$$

If Xi = Si is the sex variable, α<sup>31</sup> = �0.33; this implies that the man is less satisfied than the woman by the use of the particular car.

If Xi = Di, α<sup>41</sup> = 0.29; this implies that the more the household is composed of a larger number of individuals, the greater its satisfaction of the use of a private car is important. One more member in the household increases the satisfaction of PC use by 0.29 units.

The weighting coefficients related to the attribute variables of the PC mode are all negative, implying that the increase in both the cost of transport induced by the increase in the fuel price or the cost of acquisition of the PC, as well as the travel time whether it is in traffic or the search for parking caused by congestion, creates a disutility for users of the PC.

We can see that the choice probability of the PC is more sensitive to the search time of parking than the travel time and the costs of displacement. The parking search time provides a triple disutility compared to that caused by the travel time by the user of the PC:

$$\frac{\mathcal{U}Im\_{i1}(ta)}{\mathcal{U}Im\_{i1}(tp)} = \frac{\beta\_{31}}{\beta\_{21}} = 3.09 = \text{TMS}\_{\text{ta/tp}}$$

to both the socioeconomic characteristics of the driver who is the victim of a road accident, and of his driving behavior, and the circumstances of the traffic (state of the vehicle, infrastructure,

The Application of Discrete Choice Models in Transport http://dx.doi.org/10.5772/intechopen.74955

The objective of this case study is to analyze the severity of road accidents in Tunisia. We seek to estimate a multinomial logit model to predict the probability of a driver's exposure to a given gravity accident. The structure of the estimate is based on disaggregated data collected following the study of survey sheets proposed by the National Observatory of Circulation (Tunisia). Our sample consists of 300 randomly selected traffic accident victims from survey cards dated 2010. In our model, we defined three levels of gravity such as fatal accident, injury

The endogenous variable is an unordered multinomial variable that will be scored from one to three to indicate the severity level of the observed accident. It will be illustrated by the

2 if the observed accident only causes injuries

The objective function of the driver is his risk perception. Each driver seeks to maximize his risk perception to better estimate the danger of the road and consequently reduce the accident severity.

To estimate the probability of exposure of an individual i (such as i = 1, 2, …, 300) to a traffic accident of severity level j (such as j = 1, 2, 3), it is necessary to cross the multinomial variable Y

Referring to the accidentology literature, this gravity may depend on three components: the driver, the vehicle and its condition of use, and infrastructure. These various components constitute the road traffic system and determine the road safety. They interact at a given time

Several quantitative and qualitative variables can be identified and measured to describe these

It is dependent on both the socioeconomic characteristics of the individual i (Xik) such as sex (X1), age (X2), householder (X3), vigilance level (X4), and seat belt wearing (X5); vehicleoperated characteristics (Vih) such as age (V1), size (V2), speed (V3), and airbag equipment (V4); and those of the borrowed road (Rjl) such as road condition (R1), vision (R2), lighting (R3), position of the accident (R4) and the environment (Ejm) such as climate (E1), time (E2), and

The obtained results showed that all the variables retained are statistically and theoretically

We designate by Sij = S (Xik, Vih, Rjl, Ejm) the objective function of the individual i.

significant and explain at different degrees the severity of an accident.

Yij = 1 if the risk perception is minimal, so that the driver may have a serious accident.

3 if the observed accident causes only material damage

(17)

99

1 if the observed accident is fatal

and meteorology).

following system:

components.

agglomeration (E3) (Table 2).

Yij ¼

8 ><

>:

with a number of explanatory variables.

and place to explain the occurrence and severity of an accident.

accident, and accident-causing material damage.

The ratio of the marginal utilities of the two variables ta and tp measures the marginal rate of substitution of waiting time for travel time. The user agrees to spend 3.09 minutes more on his journey to save an extra minute to search for parking to his PC.

The ratio of marginal utilities of the two variables Tp and P measures the marginal rate of substitution of money for travel time:

$$\frac{\mathcal{U}m\_{i1}(tp)}{\mathcal{U}m\_{i1}(P)} = \frac{\overline{\partial \mathcal{U}\_{i1}}}{\overline{\partial tp}} \bigg/ \frac{\mathcal{B}\_{21}}{\frac{\partial \mathcal{U}\_{i1}}{\partial P}} = \frac{\beta\_{21}}{\beta\_{11}} = 73.65^{\circ}$$

The PC user agrees to pay 73.65 currency units to gain a minute in his trips the equivalent of 1.82 USD per hour. The TMSTp/P measures the price of time granted by the user of the PC having given socioeconomic characteristics.

The value of time is defined as the price that the individual is willing to pay to save a unit of time given its motive for displacement and its socioeconomic characteristics.

This value is obtained by comparing the coefficient associated with the time variable and the one associated with the displacement cost variable. It corresponds to the level of disutility associated with the time spent in a given path.

From these results, it is thus possible to detect the most influential determinants on the modal choice of the transport users and consequently determine the function of the transport demand.

#### 3.2. Accidentology study

Discrete choice models were also used to estimate the risk of road accidents. Several authors [15, 16, 20–22] used these models to calculate the probability of occurrence of a road accident and to detect the correlation between driver behavior, the characteristics of the traffic system, and the accident severity. They tried to model the driver's accident risk perception according to a set of factors describing the traffic system. This risk perception expresses a subjective, personal, and psychological assessment of the danger that every motorist seeks to minimize. Usually, the more this risk perception is high, the more lower the accident severity will be. And the more this risk perception is weak, the higher the probability of a serious or fatal accident is high. The risk perception will influence both the occurrence of the accident and the severity of the injuries.

These disaggregated models help to better describe and analyze the risk and severity of an accident by treating each accident separately in Ref. to its circumstances and the driver's individual behavior. The general idea is that the accident severity can be explained according to both the socioeconomic characteristics of the driver who is the victim of a road accident, and of his driving behavior, and the circumstances of the traffic (state of the vehicle, infrastructure, and meteorology).

Umi1ð Þ ta Umi1ð Þ tp <sup>¼</sup> <sup>β</sup><sup>31</sup>

journey to save an extra minute to search for parking to his PC.

Umi1ð Þ tp Umi1ð Þ <sup>P</sup> <sup>¼</sup>

substitution of money for travel time:

98 Statistics - Growing Data Sets and Growing Demand for Statistics

having given socioeconomic characteristics.

associated with the time spent in a given path.

demand.

the injuries.

3.2. Accidentology study

β21

∂Ui<sup>1</sup> ∂tp ,

time given its motive for displacement and its socioeconomic characteristics.

The ratio of the marginal utilities of the two variables ta and tp measures the marginal rate of substitution of waiting time for travel time. The user agrees to spend 3.09 minutes more on his

The ratio of marginal utilities of the two variables Tp and P measures the marginal rate of

∂Ui<sup>1</sup> ∂P

The PC user agrees to pay 73.65 currency units to gain a minute in his trips the equivalent of 1.82 USD per hour. The TMSTp/P measures the price of time granted by the user of the PC

The value of time is defined as the price that the individual is willing to pay to save a unit of

This value is obtained by comparing the coefficient associated with the time variable and the one associated with the displacement cost variable. It corresponds to the level of disutility

From these results, it is thus possible to detect the most influential determinants on the modal choice of the transport users and consequently determine the function of the transport

Discrete choice models were also used to estimate the risk of road accidents. Several authors [15, 16, 20–22] used these models to calculate the probability of occurrence of a road accident and to detect the correlation between driver behavior, the characteristics of the traffic system, and the accident severity. They tried to model the driver's accident risk perception according to a set of factors describing the traffic system. This risk perception expresses a subjective, personal, and psychological assessment of the danger that every motorist seeks to minimize. Usually, the more this risk perception is high, the more lower the accident severity will be. And the more this risk perception is weak, the higher the probability of a serious or fatal accident is high. The risk perception will influence both the occurrence of the accident and the severity of

These disaggregated models help to better describe and analyze the risk and severity of an accident by treating each accident separately in Ref. to its circumstances and the driver's individual behavior. The general idea is that the accident severity can be explained according

<sup>¼</sup> <sup>β</sup><sup>21</sup> β11

¼ 73:65

¼ 3:09 ¼ TMSta=tp

The objective of this case study is to analyze the severity of road accidents in Tunisia. We seek to estimate a multinomial logit model to predict the probability of a driver's exposure to a given gravity accident. The structure of the estimate is based on disaggregated data collected following the study of survey sheets proposed by the National Observatory of Circulation (Tunisia). Our sample consists of 300 randomly selected traffic accident victims from survey cards dated 2010. In our model, we defined three levels of gravity such as fatal accident, injury accident, and accident-causing material damage.

The endogenous variable is an unordered multinomial variable that will be scored from one to three to indicate the severity level of the observed accident. It will be illustrated by the following system:

$$Y\_{\vec{\eta}} = \begin{cases} 1 \text{ if the observed accident is fast} \\ 2 \text{ if the observed accident only causes injiraes} \\ 3 \text{ if the observed accident causes only material damage} \end{cases} \tag{17}$$

The objective function of the driver is his risk perception. Each driver seeks to maximize his risk perception to better estimate the danger of the road and consequently reduce the accident severity.

Yij = 1 if the risk perception is minimal, so that the driver may have a serious accident.

To estimate the probability of exposure of an individual i (such as i = 1, 2, …, 300) to a traffic accident of severity level j (such as j = 1, 2, 3), it is necessary to cross the multinomial variable Y with a number of explanatory variables.

Referring to the accidentology literature, this gravity may depend on three components: the driver, the vehicle and its condition of use, and infrastructure. These various components constitute the road traffic system and determine the road safety. They interact at a given time and place to explain the occurrence and severity of an accident.

Several quantitative and qualitative variables can be identified and measured to describe these components.

We designate by Sij = S (Xik, Vih, Rjl, Ejm) the objective function of the individual i.

It is dependent on both the socioeconomic characteristics of the individual i (Xik) such as sex (X1), age (X2), householder (X3), vigilance level (X4), and seat belt wearing (X5); vehicleoperated characteristics (Vih) such as age (V1), size (V2), speed (V3), and airbag equipment (V4); and those of the borrowed road (Rjl) such as road condition (R1), vision (R2), lighting (R3), position of the accident (R4) and the environment (Ejm) such as climate (E1), time (E2), and agglomeration (E3) (Table 2).

The obtained results showed that all the variables retained are statistically and theoretically significant and explain at different degrees the severity of an accident.


For the vigilance variable (X4), the ratio of relative probabilities is equal to 1.4 (exp (0.33)). This implies that driving without concentration (zero vigilance: alcohol, sleeping while driving, etc.) increases the probability to be the victim of a fatal accident of 40% compared to an intangible accident and increases the probability of being injured in an accident by 55% compared to an intangible accident. Tiredness, driving drowsiness, and alcohol are the factors that increase road insecurity and the probability of having more and more serious accidents. These factors are particularly related to the irresponsible behavior of the

The Application of Discrete Choice Models in Transport http://dx.doi.org/10.5772/intechopen.74955 101

According to the weighting coefficient of the seat belt-wearing variable (X5), the nonuse of the seat belt increases the probability of going from an accident with material damage to a fatal accident of 170%. However, the coefficient of this same variable (X5) relative to the injury accident alternative is negative. This implies that not wearing a seat belt reduces the probability of being an injury accident victim in relation to an intangible accident. Not wearing a seat belt does not prevent injury accident, but it reduces the risk of a fatal accident. Therefore, not

For the age variable (X2), 1 more year in the driver's age reduces the probability of being a fatal accident victim rather than an intangible accident of 48%. The fatal accident risk decreases with the increase of the driver's age. For the variable speed (V3), its coefficient is 0.188 in the event of a fatal accident and 0.167 in the event of an injury accident. These coefficients are interpreted as follows: any increase in the circulation speed of 1 Km/h causes an increase in the probability of the fatal accident risk compared to an intangible accident of 20% (exp (0.133) 1) and a decrease in the injury accident risk of 18% compared to the reference

Concerning the variable airbag equipment (V4), it positively affects the probability of occurrence of a fatal accident, but negatively that of an injury accident. In other words, a car not equipped with an airbag increases the probability of a fatal accident compared to an injury

With regard to the infrastructure characteristic vector (road condition, position of the accident, lighting, and vision at the time of the accident), it represents one of the elements that contrib-

All other things being equal, the driver reduces the probability of a fatal accident compared to an intangible accident by 12.7% when it avoids overtaking on a straight-line trajectory, by 35.6% when he takes a good quality road and by 54% when the road is illuminated and the

In terms of environmental factors, we find that the climate (E1), the time, and the location of the accident negatively affect the probability of occurrence of a fatal accident compared to an intangible accident. In other words, driving in an environment characterized by a normal, sunny day and in an agglomeration zone reduces the probability of a fatal accident in relation to an intangible accident by 30% compared to the driving in the rain, by 60% compared to

wearing a seatbelt is a key factor in the explanation of fatal traffic accidents.

situation. So speed is a risk factor whose excess increases the accident severity.

accident by 10.7%, while it decreases the probability of an injury accident by 45%.

utes to the explanation of the probability of a fatal accident risk.

night driving, and by 54% compared to an out agglomeration driving.

driver.

vision is clear.

Standard error in parentheses.

\*\*\*Significant to only one of 1%; \*\*significant to only one of 5%; \*significant to only one of 10%.

The incorporeal accident is the reference category:

• Number of observations = 300

• Log likelihood = � 195.969

• Pseudo R<sup>2</sup> = 0.405.

Table 2. Parameter estimates of accidentology study.

Referring to Eq. (10), the estimated value of the weighting coefficient of the sex variable (X1) corresponds to the ratio of relative probabilities as follows:

$$\begin{aligned} \log\left(\frac{P(Y=1;X\_1=1)/P(Y=3;X\_1=1)}{P(Y=1;X\_1=0)/P(Y=3;X\_1=0)}\right) &= 0.62\\ \Rightarrow \frac{P(Y=1;X\_1=1)/P(Y=3;X\_1=1)}{P(Y=1;X\_1=0)/P(Y=3;X\_1=0)} &= \exp\left(0.62\right) = 1.86 \end{aligned}$$

The sign of the coefficient is positive. It implies that the gender variable has a positive effect on the probability of being a victim of a fatal bodily injury rather than an intangible accident. We can interpret this coefficient as follows: a man has a probability of 86% to be the victim of a fatal accident rather than an intangible accident. This probability rate is 92.5% in the case of an injury accident.

For the vigilance variable (X4), the ratio of relative probabilities is equal to 1.4 (exp (0.33)). This implies that driving without concentration (zero vigilance: alcohol, sleeping while driving, etc.) increases the probability to be the victim of a fatal accident of 40% compared to an intangible accident and increases the probability of being injured in an accident by 55% compared to an intangible accident. Tiredness, driving drowsiness, and alcohol are the factors that increase road insecurity and the probability of having more and more serious accidents. These factors are particularly related to the irresponsible behavior of the driver.

According to the weighting coefficient of the seat belt-wearing variable (X5), the nonuse of the seat belt increases the probability of going from an accident with material damage to a fatal accident of 170%. However, the coefficient of this same variable (X5) relative to the injury accident alternative is negative. This implies that not wearing a seat belt reduces the probability of being an injury accident victim in relation to an intangible accident. Not wearing a seat belt does not prevent injury accident, but it reduces the risk of a fatal accident. Therefore, not wearing a seatbelt is a key factor in the explanation of fatal traffic accidents.

For the age variable (X2), 1 more year in the driver's age reduces the probability of being a fatal accident victim rather than an intangible accident of 48%. The fatal accident risk decreases with the increase of the driver's age. For the variable speed (V3), its coefficient is 0.188 in the event of a fatal accident and 0.167 in the event of an injury accident. These coefficients are interpreted as follows: any increase in the circulation speed of 1 Km/h causes an increase in the probability of the fatal accident risk compared to an intangible accident of 20% (exp (0.133) 1) and a decrease in the injury accident risk of 18% compared to the reference situation. So speed is a risk factor whose excess increases the accident severity.

Concerning the variable airbag equipment (V4), it positively affects the probability of occurrence of a fatal accident, but negatively that of an injury accident. In other words, a car not equipped with an airbag increases the probability of a fatal accident compared to an injury accident by 10.7%, while it decreases the probability of an injury accident by 45%.

With regard to the infrastructure characteristic vector (road condition, position of the accident, lighting, and vision at the time of the accident), it represents one of the elements that contributes to the explanation of the probability of a fatal accident risk.

Referring to Eq. (10), the estimated value of the weighting coefficient of the sex variable (X1)

P Yð Þ <sup>¼</sup> <sup>1</sup>; <sup>X</sup><sup>1</sup> <sup>¼</sup> <sup>0</sup> <sup>=</sup>Pð<sup>Y</sup> <sup>¼</sup> <sup>3</sup>; X<sup>1</sup> <sup>¼</sup> <sup>0</sup> <sup>¼</sup> exp 0ð Þ¼ :<sup>62</sup> <sup>1</sup>:<sup>86</sup>

The sign of the coefficient is positive. It implies that the gender variable has a positive effect on the probability of being a victim of a fatal bodily injury rather than an intangible accident. We can interpret this coefficient as follows: a man has a probability of 86% to be the victim of a fatal accident rather than an intangible accident. This probability rate is 92.5% in the case of an

¼ 0:62

Fatal accident Injury accident

log P Yð Þ <sup>¼</sup> <sup>1</sup>; <sup>X</sup><sup>1</sup> <sup>¼</sup> <sup>1</sup> <sup>=</sup>Pð<sup>Y</sup> <sup>¼</sup> <sup>3</sup>; X<sup>1</sup> <sup>¼</sup> <sup>1</sup> P Yð Þ ¼ 1; X<sup>1</sup> ¼ 0 =PðY ¼ 3; X<sup>1</sup> ¼ 0 

\*\*\*Significant to only one of 1%; \*\*significant to only one of 5%; \*significant to only one of 10%.

P Yð Þ ¼ 1; X<sup>1</sup> ¼ 1 =PðY ¼ 3; X<sup>1</sup> ¼ 1

corresponds to the ratio of relative probabilities as follows:

Explanatory variables Coefficients

100 Statistics - Growing Data Sets and Growing Demand for Statistics

Constant 0.2472(0.006)\*\*\* 2.5440(0.026)\*\* Sex (X1) 0.6233 (0.082)\* 0.6549 (0.060)\* Driver's age (X2) 0.3968 (0.030)\*\* �0.2925 (0.020)\*\* Householder (X3) �0.1323 (0.744) 0.7078 (0.402) Vigilance level (X4) 0.3375 (0.084)\* 0.4374 (0.086)\* Seat belt wearing (X5) 0. 9995 (0.001)\*\*\* �0.5509 (0.062)\* Vehicle age (V1) 0.6950(0.040)\*\* �0.4719(0.050)\*\* Vehicle size (V2) 0.7906 (0.010)\*\*\* �0.5346 (0.006)\*\*\* Speed (V3) 0.1888 (0.049)\*\* �0.1671 (0.075)\* Airbag equipment (V4) 0.1022 (0.002)\*\*\* �0.6098 (0.020)\*\* Road condition (R1) �0.4400 (0.089)\* 0.4722 (0.093)\* Vision (R2) 0.5127 (0.013)\*\* �0.5983 (0.004)\*\*\* Lighting (R3) �0.7897 (0.080)\* 0.8874 (0.089)\* Position of the accident (R4) �0.1362 (0.060)\* 0.2368 (0.068)\* Climate (E1) �0.2630 (0.050)\*\* 0.2367 (0.049)\*\* Time (E2) �0.9784 (0.009)\*\*\* �0.6947 (0.010)\*\*\* Agglomeration (E3) �0.7772 (0.012)\*\* 0.1086 (0.015)\*\*

)

The incorporeal accident is the reference category:

Table 2. Parameter estimates of accidentology study.

injury accident.

Standard error in parentheses.

• Number of observations = 300 • Log likelihood = � 195.969 • Pseudo R<sup>2</sup> = 0.405.

> All other things being equal, the driver reduces the probability of a fatal accident compared to an intangible accident by 12.7% when it avoids overtaking on a straight-line trajectory, by 35.6% when he takes a good quality road and by 54% when the road is illuminated and the vision is clear.

> In terms of environmental factors, we find that the climate (E1), the time, and the location of the accident negatively affect the probability of occurrence of a fatal accident compared to an intangible accident. In other words, driving in an environment characterized by a normal, sunny day and in an agglomeration zone reduces the probability of a fatal accident in relation to an intangible accident by 30% compared to the driving in the rain, by 60% compared to night driving, and by 54% compared to an out agglomeration driving.
