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在一些发展中国家，道路交通事故增加了。本文的一个问题是致力于特定类型的事故是比十年前更为常见的情况下增加车辆占用。大量的商用车辆事故死亡经常发生。关于发展国家事故和死亡影响因素的研究是本文的主要目的。本文研究了一个仿真环境中的协调系统的建模和实施，以预见未来的事故率。使用的分析方法，必须相应的强大和客观的评估事故率。通过对车辆所有权的变化，数据用于研究这些变化背后的因素如收入、注册的车辆有多远取决于就业，工作和居住区从对方的人口取决于家庭结构的变化。他们不应该太敏感，偏离模型的假设或存在大量的异常值。推荐的稳健回归技术，而不是普通最小二乘回归。因素分析在五个步骤，并通过使用从澳大利亚的数据作为一个案例研究，强大的回归出现最有效的系数，在强大的方程，以防止它，因此，减少死亡。
Road accident is increasing in some developing countries. A matter of this paper is being committed to increasing vehicle occupancy overtime or to the fact that a particular type of accident is much more common than was the case ten years ago. Large numbers of mortalities often occur by accident of commercial vehicles. On developing country impact factors on accidents and fatalities are the main aim of this paper. This paper investigates the modeling and implementation of a coordination system within a simulation environment to foresee future accident rate. The approach of analysis used must be correspondingly robust and objective about evaluating accident rate. By comparing changes in vehicle ownership, data used to investigate the factors behind these changes such as income, registered vehicles depends on employments, how far work and residential area from each other's and population depends on changing household structure. They should not be too sensitive to departures from model assumptions or the presence of a substantial number of outliers. Robust regression techniques are recommended instead of ordinary least square regression. Analysis of factors does in five steps and by using data from Australia as a case study, robust regression appears the most effective coefficient in robust equation to prevent it, consequently, reduce fatalities.
Subject heading; Vehicle ownership, Accident rate, robust regression
Introduction 简介
Contamination growth and increased the one hand vehicles, rising vehicle ownership ratio per capita in society, increased travel demand in household size, to double traffic volume and usage of personal belongings as the root causes of driving accidents and mortalities in come. According to the International Federation of Red Cross and Red Crescent populations, road accidents in 1998 about 500 thousand death and 15 million not wounded, and if social effects to delete about 53 billion dollars of economic damage have left. This paper aims to find a relationship between vehicle ownership and accident rate in a developed country to predict future and make a plan to reduce economic damages and death. By prediction of vehicle ownership growth and relation between its factors and accident, some factors describe are influenced on limitation of accidents in the future by controlling them.
To accomplish this task several objectives were undertaken:
A) Determine the relationship of accident rate with vehicle ownership factors.
B) Determine the regression equation of the ownership factors and accident rate.
C) Forecast accident rate for 2012- short term.
This paper discusses the data collection effort and scope of determining factors of vehicle ownership, identify and describe possible factors that may effect by accident rate, in addition collect reliable information of vehicle ownership in case study to analysis obtains data with a statistical method.
The key finding of this paper comes from a number of vehicles per households; Population-Based Accident Rates consist of Area population, Number of registered vehicles, Number of licensed drivers, and Highway mileage (useful on fatality accident rate).
Background 背景
Little guidance is available with regard to research of TRRL which in 1972 a small team was formed within the Overseas Unit at TRRL to undertake research on road safety in Third World countries in order to establish the nature and extent of the problem and, in the longer tirm to assess the effectiveness of remedial measures.
The number of fatalities as opposed to casualties or injury accidents has been used because the poor accident recording systems in most Third World countries mean that only fatalities are recorded to any reasonable degree of accuracy. In addition, numbers of vehicles licensed to have been used, contrary to millions of vehicle kilometers travelled per annum because very rarely are accurate n-point or trend censes carried out in developing countries to provide such data.
In examining the relationship between deaths and vehicle ownership for three different developed countries. The two parameters are not linearly related over time. For the periods chosen there is an apparent difference between each country in the sensitivity of deaths to changes in the number of vehicles. Thus to double the number of road deaths in each country would require an eight-fold increase in the number of vehicles in the USA, a four-fold increase in Australia and a two-fold increase in New Zealand.
High vehicle ownership in low income households, combined with a lack of alternatives such as good walk accessibility or public transport, suggest that some households may be „forced into car ownership and use. The use of urban public transport is still only a small component of total passenger transport, the largest component being travel by private car. As young people enter relationships their income rises as they often have two income earners contributing to their family income. Population and median income of household depend on the territory. Growth in car ownership has largely been through the increase in the number of households with two or more cars as the proportion of one car households has remained remarkably constant at 44% since the mid 1960(Figure1).
The size of households has declined as people are getting married or cohabiting later, there are more divorces and separations, and people are living longer in single person households. The other factor affecting demand for car ownership is the possession of a driving license.
Types of Statistics
Accident statistics generally address and describe one of three principal informational elements:
* Accident occurrence
* Accident involvements
* Accident severity
Accident occurrence relates to the numbers and types of accidents that occur, which are often described in terms of rates based on population or vehicle-miles travelled. Accident involvement concerns the numbers and types of vehicles and drivers involved in accidents, with population-based rates a very popular method of expression. Accident severe is generally dealt with by proxy: the numbers of fatalities and fatality rates are often used as a measure of the seriousness of accidents.
Accident rates generally fall into one of two broad categories: population-based rates, and exposure-based rates. The number of motor vehicles registered is increasing, and urban design tends to encourage their use with the construction of freeways and dispersed housing. First one is the case study of this paper, which relates to most effective factors f vehicle ownership without measuring facility of roads (highway mileage). Hence, by this assumption, future results concentrate on short term influence time.
The principal source of demographic data in Australia is the Census of Population, and Housing conducted every five years by the Australian Bureau of Statistics (ABS).
Data collected from the registered vehicle in Australia's state by state in any types, which gather in Australia Bareau. Moreover, new vehicles sales and registration from Australian Automotive Intelligence, Yearbook 2009
People aged 20-24 years also had the highest adjudication rate of all age groups for dangerous or negligent driving. The rate for men of this age (712 adjudications per 100,000) was about seven times higher than that for women (97 per 100,000).
Accident Rate
The largest and most complete accident database is the General Estimates System (GES) which was extensively used for the development of this report. According to the Australian Transport Safety Bureau, there were 1601 people killed in 1,456 road accidents in the year 2006. Thus over 130 people are killed in crashes each month. During this same time period about 22,500 people were seriously injured. The number of crashes on Australian roads has been consistent with the past three years and is higher than European roads. For a crash to be eligible for the GES sample.
The crash statistics recorded by the Roads and Traffic Authority and included in this Statistical Statement are confined to those crashes which conform to the national guidelines for reporting and classifying road vehicle crashes. The main criteria are:#p#分页标题#e#
1 The crash was reported to the police.
2 The crash occurred on a road open to the public.
3 The crash involved at least one moving road vehicle.
4 The crash involved at least one person being killed or injured or at least one motor vehicle being towed away.
Reports for some crashes are not received until well into the following year and after the annual crash database has been finalized. These amount to less than 1% of recorded crashes and are counted in the following year's statistics.
MM-Robust Regression (s-estimator)
MM-Robust Regression is performed in two steps. In the first step, the subset of observations constituting the dominant trend is identified by use of the S-estimate of location and scale. In the second step, the regression is performed with points further from the dominant trend having their influence discounted. The kernel function ρc will give a greatly inflated value to points situated „far from the dominant location. When the sum of the kernels is minimized the distant points (outliers) will contribute large terms in the sum, and therefore, will have little influence on the regression parameters. The kernel function used in this application of MM-Robust regression is the bi-square function. The weights for the bisquare decline as soon as e departs from 0, and are 0 for |e| > k. The value k for the bisquare estimators is called a tuning constant; smaller values of k produce more resistance to outliers, but at the expense of lower efficiency when the errors are normally distributed.
The tuning constant is generally picked to give reasonably high efficiency in the normal case; in particular,
k = 4.685σ for the bisquare (where σ is the standard deviation of the errors) produce 95-percent efficiency when the errors are normal, and still offer protection against outliers. specifying the argument method='MM' to rlm requests bisquare estimates with start values determined by a preliminary bounded-influence regression.
A more objective method is to use the goodness of fit. The scatter plot of the original un-smoothed data against the predicted curve shows that MM-Robust regression with local polynomial smoothing gives a good fit to the data.
Compute the vehicle ownership level by using generated observation times and prior parameter values from logistic model
Gaussian noise add to the solution
On above methodology flowchart, a sample size of 108 and a standard deviation of 35 (vehicles per thousand persons) is used in all of the simulations. Stage 1 Linear Regression, apply the linearization transformation to the logistic differential equation, from which is obtained, by robust regression, a value of the saturation parameter (α) and the growth parameter (κ). Stage 2 non-Linear Regression, using the values obtained from the first stage as initial values; solve the nonlinear least-squares problem (algorithm: Gauss-Newton).
The saturation parameter (α) is accurately inferred by non-linear regression the mean absolute error (MAE) is approximately 1%. For MMRR the MAR is approximately 30%. Both methods are less accurate for the growth parameter (κ). For MMRR the MAE is in excess of 100%. In contrast, for the nonlinear method the MAE is about 3%. The time parameter (γ) is most accurate (MAE 0.1%). Non-linear regression clearly out-performs the other inference methods. Nonlinear robust regression proper is worth investigating.
Yi=xi1θ1+…+ xipθp+ei (i=1, …, n)
As in simple regression, the least squares (LS) technique for estimating the unknown parameters θ1, …, θp is quite sensitive to the presence of outlying points. ei is error term which is captured the effect of all omitted variables. The identification of such points becomes more difficult, because it is no longer possible to spot the influential points in a scatter plot. Therefore, it is important to have a tool for identifying such points. In the last few decades, several statisticians have given consideration to robust regression, whereas others have directed their attention to regression diagnostics.
Regression diagnostics first attempt to identify points that have to be deleted from the data set, before applying a regression method. Robust regression tackles these problems in the inverse order, by designing estimators that dampen the impact of points that would be highly influential otherwise. A robust procedure tries to accommodate the majority of the data. Bad points, lying far away from the pattern formed by the good ones, will consequently possess large residuals from the robust fit. So in addition to insensitivity to outliers, a robust regression estimator makes the detection of these points an easy job.
r1,..,rm - β1, … ,βn m≥n
Gauss-Newton algorithm finds the minimum the sum of squares.
= Solution to the normal equations
SO Equation 4
Analysis
Analysis of factors that are related to vehicle ownership is a role of finding equation among accident rate and vehicle ownership factors.
Data Collection
Income, Registered Veh, Population
Formula vehicle ownership factors and year
Formula vehicle ownership factors and accident rate
Accident on 2012 individually
Predict amount of vehicle ownership factors on 2012
Chang scale of data by Rate
Regression formula among vehicle ownership factors and accident rate
Accident rate on 2012 by scaled data
Results
By data that are collected from Australia, and MM-Robust regression analysis by Excel to find the relationship between them on past 19 years and use it to improve data to next 2 years to forecast accident rate. Below some results of the regression show and it is acceptable for linear equation, therefore, regression equation follows them.
Relationship between vehicle ownership factors and accident rate individually;
Y1= Income of household ïƒ AI= -10-4 y1+13.694
Y2= registered Vehicles ïƒ AR= -7.41E-6 y2 +15.163
Y3=youth population ïƒ AP= -1.3E-3y3+34.228
Regression equation among accident rate and vehicle ownership factors which have most effective on accident rate;
Y= -2.090.22 θ1 -3.614 θ2+ 0.178 θ3+1570
- θ1= Income of household (per 1000$)
- θ2 = population (per 100000 people)
- θ3 = Registered vehicles (per 10000 vehicle)
- Y= Accident rate (per 1000 vehicle)
To forecast future vehicle ownership parameters, use equation between each one and accident rate independently;
Figure 2 Accident rate against time related to vehicle ownership factors (x= year, y= accident number)
Rate which are measured from equation 4 change as below:
θ1= Income per one thousand dollar in accident= 19.14
θ2= Registered vehicles per 10000 number in accident= 35.24
θ3= Population per 100,000 people in accident rate = 24196
Accident on 2012 = Input all θ1, θ2, θ3 on regression formula = 5553
Conclusion 结论
To sum up, using this formula can help urban organizations to predict accident rate and control them by traffic safety. In this paper, three factors which are most effective in vehicle ownership to accident rate conclude; Income of household, the amount of youth in household, and number of registered vehicles are focused.
An assumption of this paper uses fatality accidents instead of accident statistics because in a developed country these two parameters have same rate, which occurs of same culture in their countries. Moreover, Australia selected as the study area since it has the real statistics for several years ago. Besides, survivors solve problems of vehicle ownership factors to decrease an accident rate.
Relationship between vehicle ownership factors and accident rate individually:
- Y4 = -0.0001y1 + 13.694 ïƒ y1= Income of household
- Y5 = -7.41E-06y2 + 15.163 ïƒ y2= Registered vehicles
- Y6 = -0.0013y3 + 34.228 ïƒ y3= Population
- Yi= Accident rate that relate to each factors of vehicle ownership individually
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