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Abstract

Factor analysis refers to a collection of statistical methods for reducing correlational data into a smaller number of dimensions or factors. In this study, factor analysis theory was used to determine the main influential factors of road traffic crashes with massive casualties. Twenty variables related to personnel, vehicles, roads, and environment were collected, and the significance of their correlations was tested for validity. A correlation coefficient matrix R was calculated, and its latent root $λ$ was obtained based on the characteristic equation. A number of common factors were determined according to the value of latent root $λ$ . Factor loading was used to express the relationship of each variable to the underlying main influential factors. An index system of accident factors was developed based on the results of factor loading, and the weight of each factor was calculated to classify the factor influence. The main influential factors of accidents were determined to be fault behavior, driving experience, condition of vehicle safety, purpose of vehicle, road lighting, driver, road surface condition, roadside protection facilities, and road terrain.

Keywords

Factor analysis crashes with massive casualties factor loading main influential factors

Introduction

With increasing vehicle ownership in China, transport infrastructure weakness has become a growing problem, and traffic safety is very important. How to reduce road traffic accidents has become a significant issue. Road traffic accident statistics of some countries are summarized in Table 1. This table shows that the mortality per 10,000 vehicles in China is much higher than that in other developed countries.¹ Serious traffic accidents are those that involve more than 3 deaths or 11 serious injuries, cause 1 person to die or injure more than 8 persons seriously, or cause 2 persons to die and injure more than 5 persons seriously. The mortality of road traffic crashes with massive casualties (CMCs) (more than 10 deaths in 1 crash) is around 50% in China.² With such high mortality and serious consequences, more attention should be paid to CMCs. A CMCs database should be established to master the characteristics and distribution of CMCs accurately and put forward prevention measures to alleviate the severity of CMCs.

Table 1.

Traffic accidents data in 2011.

Country	Number of accidents	Number of fatalities	Mortality per 10,000 vehicles
China	4,727,000	59,997	2.50
United States	5,338,000	32,367	1.26
Japan	692,000	4612	0.57
Germany	157,000	1960	0.56
Italy	306,000	4009	0.80
France	206,000	3860	0.80
Britain	83,000	3963	1.00

Many studies have been conducted to study CMCs, and the Haddon matrix was developed to express the correlation of driver–vehicle–road in traffic accidents.³ The Haddon matrix is summarized in Table 2. The National Highway Traffic Safety Administration (NHTSA) established the Fatality Analysis Reporting System (FARS) to conduct in-depth analysis of accidents that resulted in a security evaluation in 1975.⁴ In 1992, the Traffic Accident Research and Analysis Center was established in Japan to collect information on road traffic accidents in Japan and build a road traffic accident analysis system based on geographic information system (GIS).⁵ The European Transport Safety Council (ETSC)⁶ focused on the application of traffic accident data mining and determined the main influence factors of accidents since 1993; reports for the most recent 10 years were issued in 2001. In 2008, a questionnaire by Japanese scholars was completed by 1987 drivers to study the effects of driving behavior on traffic accidents. The results showed that there was a significant relationship between illegal driving behaviors and accidents.⁷ Hassan and Al-Faleh⁸ explored the risk factors associated with the size and severity of roadway crashes in Riyadh. The results revealed that crash reason, damage to public property, day of week, crash location, and point of collision were the significant variables affecting the binary target variable (fatal and non-fatal crashes).

Table 2.

Haddon matrix.

Element	Before accident	In accident	After accident
Person	Training, safety education, driving attitude, dress	Location and sitting posture	Exigency succor
Vehicle	Active safety (brake, performance, speed, vision), related factor (traffic, pedestrian, etc.)	Passive safety (anti-collision structure, safety belt, etc.)	Rescue
Road	Road traffic signs and markings, geometric alignment, road performance, stopping sight distance, safety evaluation	Roadside safety, guardrail	Repair of road traffic facilities

The Traffic Accident Information System developed by China’s Ministry of Public Security is used by the Traffic Police Department for road traffic accident analysis in China and has certain superficial data processing functions.⁹ Ma et al.¹⁰ reviewed four national-level data sources used to estimate the burden of road traffic injuries, including mortality, injury, and crashes in China. Zhou et al.¹¹ investigated road traffic safety in the mountain areas of Southwest China and suggested that the high incidence of severe crashes closely relates to imperfect road design, defective execution of traffic laws, imperfect management, and environmental factors. Wang et al.¹² developed a driver safety approach behavioral model based on driver human factors analysis to prevent rear-end collisions in car-following situations. Xu et al.¹³ studied the speed distribution of mixed bicycle traffic for highway systems. Jiang et al.^14,15 investigated intercultural differences of time-to-collision (TTC) distribution and relationships between TTC and vehicle–pedestrian (VEH-PED) conflicts to improve vehicle and pedestrian safety in critical situations. Pedestrian behavior was analyzed in the conflict process to reduce accident frequency and severity for pedestrians. Li et al.¹⁶ presented an improved cellular automata model to analyze traffic congestion propagation properties to evaluate the effectiveness of traffic control strategies.

Xu¹⁷ studied data mining methods such as correlation analysis, cluster analysis, and decision tree analysis to analyze road traffic accident data. Sun et al.¹⁸ proposed the concept of driver safety margin and built an analytic hierarchy process (AHP) model considering causes and the influence of people, vehicles, road, and environment on traffic accidents. Cheng¹⁹ collected traffic accident data in Kunming from 1997 to 2001 and analyzed the correlation between 11 factors and road traffic accidents; the results showed that the number of motor vehicles, drivers, and population had a significant correlation with accidents. Deng²⁰ put forward the concept of accident background factors and set up an index system of background factors. The background factors system of China was built based on the Oracle database.

The data mining method of factor analysis was used in this article to analyze influential factors of CMCs. A total of 250 cases of CMCs in China from 2005 to 2012 were collected to analyze the influential factors. A factor analysis model based on personnel, vehicles, roads, and environmental elements was developed, and common factors were obtained through factor analysis. The weight of common factor elements was determined by the weighted model to determine the main influential factors of accidents.

Method

Database

Fatal road traffic CMCs are discussed in this article (more than 10 deaths in 1 crash). A total of 250 accident cases from 2005 to 2012 in China are summarized in Table 3. The accident type and modality distribution of fatal road traffic accidents with massive casualties are summarized in Table 4. The percentage of single-vehicle accidents was 51.6%, and most of the accidents were dropping accidents; vehicle–vehicle accidents accounted for 32.8% and mainly were caused by frontal impact.

Table 3.

Data of CMC.

Year	Number of accidents	Fatalities	Number of injuries
2005	47	807	705
2006	38	558	463
2007	26	389	449
2008	29	476	504
2009	24	329	345
2010	34	461	432
2011	27	455	404
2012	25	361	367
Total	250	3836	3669

Table 4.

Relative proportion of accident type.

Accident type (%)	Specific type	Number of accidents	Proportion of total accidents (%)
Single-vehicle accident (51.6)	Dropping accident	98	39.2
	Roll-over accident	22	8.8
	Vehicle fixtures	6	2.4
	Fire	3	1.2
Vehicle–vehicle accident (32.8)	Frontal impact	33	13.2
	Rear-end impact	20	8
	Side impact	12	4.8
	Scratch	10	4
	Impact stagnant vehicle	7	2.8
Multiple vehicle accident (13.6)	Multiple impact	34	13.6
Vehicle–pedestrian accident (2.0)	Multiple impact	5	2

Basic principle of factor analysis

Factor analysis²¹ is a kind of mining method aimed to study the correlation for each attribute, identify the underlying dimensions that explain these correlations, and group together the close attributes into one pattern. The attributes of each pattern are called “common factors.” The influential factors of CMCs are distributed in four aspects: personnel, vehicles, roads, and environment. Common factors were obtained through factor analysis, the weight of common factor elements was determined by the weighting model, and the main influential factors of accidents were determined.

The general model of factor analysis²² is

\begin{matrix} X = AF + B \\ {\begin{matrix} x_{1} = a_{11} F_{1} + a_{12} F_{2} + \dots + a_{1 m} F_{m} + ε_{1} \\ x_{2} = a_{21} F_{1} + a_{22} F_{2} + \dots + a_{2 m} F_{m} + ε_{2} \\ ⋮ \\ x_{p} = a_{p 1} F_{1} + a_{p 2} F_{2} + \dots + a_{pm} F_{m} + ε_{p} \end{matrix} \end{matrix}

(1)

where X is the observable random vector (original observed variables), F is the common factor of X, A is the coefficient of F (factor loading matrix), a_ij is the correlation coefficient, ε_i is the error factor, and B is a special factor of X. a_ij expresses the degree of linear relationship between the row and column variables of the matrix; the higher the correlation coefficient, the stronger the relationship. B is the special factor of X, ignore it when analyzing

x_{i} = a_{i 1} F_{1} + a_{i 2} F_{2} + \dots + a_{im} F_{m} + ε_{i}

(2)

Normalize the X matrix, making its mean value 0 and variance value 1. Assume F and ε_i are independent, the mean value is 0, and variance value is 1. X is called the factor model with m common factors. Then, the correlation coefficient matrix R = (r_ij)_p*p and its latent root $λ$ are obtained. Determine the number of common factors, sum common variance $h_{i}^{2}$ , and rotate the loading matrix to obtain the common factors.

Factor analysis

A total of 20 indexes of factors related to personnel, vehicles, roads, and environment are summarized in Table 5. Original data of the accident influential factors index are shown in Appendix 1.

Table 5.

Index of accident influential factor.

No.	Index
ZX1	Personnel type
ZX2	Driving license type
ZX3	Driver’s gender
ZX4	Driving experience
ZX5	Driver’s fault behavior
ZX6	Means of transportation
ZX7	Vehicle safety situation
ZX8	Purpose of vehicle
ZX9	Vehicle driving state
ZX10	Load excess
ZX11	Road condition
ZX12	Road surface condition
ZX13	Road alignment
ZX14	Road section (intersection)
ZX15	Roadside facility
ZX16	Road type
ZX17	Weather
ZX18	Terrain
ZX19	Lighting condition
ZX20	Dangerous goods

Data were normalized, and the correlation was analyzed before factor analysis. In the analysis of correlation, if most of the coefficients are larger than 0.3 and pass the correlation test, the results of factor analysis seem to be valid.

Normalize the original data by Z-score standard method.²³ The equation is

Z_{ij} = (x_{ij} - {\bar{x}}_{j}) / S_{j}, i = 1, 2, \dots, n; j = 1, 2, \dots, p

(3)

where ${\bar{x}}_{j} = (Σ_{i = 1}^{n} x_{ij}) / n$ is the mean value, $S_{j}^{2} = Σ_{i = 1}^{n} (x_{ij} - {\bar{x}}_{j})^{2} / n - 1$ is variance, $S_{j}$ is the standard deviation, $i = 1, 2, \dots, n$ is the number of samples, $j = 1, 2, \dots, p$ is the number of index, $x_{ij}$ is the value of index, $n = 250$ , $p = 20$ . The normalized matrix of accident influential factors is shown in Appendix 2.

The following equation is used to calculate the correlation coefficient

\begin{array}{l} r_{j k} = \frac{1}{n - 1} \sum_{i = 1}^{n} [{(x_{i j} - {\bar{x}}_{j})}^{2} / S_{j}] [{(x_{i k} - {\bar{x}}_{k})}^{2} / S_{k}], \\ i = 1, 2, \dots, n; j = 1, 2, \dots, p; k = 1, 2, \dots, p \end{array}

(4)

r_{jk} = \frac{1}{n - 1} \sum_{i = 1}^{n} Z_{ij} \cdot Z_{ik}

(5)

where r_jk is the correlation coefficient of index, r_ii = 1, r_jk = r_kj. Correlation coefficient matrix R is shown in Appendix 3

C_{i} = \frac{λ_{i}}{\sum_{i = 1}^{p} λ_{i}}

(6)

According to characteristic equation $| R - λ E | = 0$ , the latent root $λ$ of the correlation coefficient matrix was obtained. Factor contribution proportion C_i means the degree of change of each common factor and all factors. When the cumulative contribution proportion is larger than 85% or the latent root is not less than 1, the common factor number can be determined.²⁴ The variance contribution percentage and cumulative contribution proportion were based on the rotation of the square load.

An index system model of CMCs influential factors based on the outcome of the rotating component matrix was built to calculate how secondary indexes rates on primary indexes, tertiary indexes rates on secondary indexes, and primary indexes. The results are shown in Table 9

A_{i} = \frac{C_{i}}{\sum_{i = 1}^{n} C_{i}}

(7)

A_{ij} = \frac{| a_{ij} |}{\sum_{j = 1}^{m} | a_{ij} |}, i = 1, 2, \dots, n, j = 1, 2, \dots, m

(8)

w_{j} = A_{i} \cdot A_{ij}

(9)

where A_i is the weight value of secondary indexes out of primary indexes, n is the number of main factors, C_i is contribution percentage of main factor to primary index level, A_ij is the weight value of tertiary indexes rate on secondary indexes, m is the amount of tertiary indexes in each main factor, and w_j is the weight value of tertiary indexes rate on primary indexes.

Calculate the importance degree of each index based on the obtained index weight value and group the indexes into four patterns of “very important,”“important,”“less important,” and “unimportant” valued in 4, 3, 2, and 1, respectively, based on the effects in an accident. This research mainly focuses on the importance of tertiary indexes (the second layer of the factors hierarchical tree)

N_{j} = 4 \times w_{j}

(10)

where N_j is the section value of the j tertiary indexes.

Classification formulas based on index importance are given by

T_{j} = {\begin{matrix} 1 & N_{j} \in [0, 0.1) \\ 2 & N_{j} \in [0.1, 0.2) \\ 3 & N_{j} \in [0.2, 0.25) \\ 4 & N_{j} \in [0.25, + \infty) \end{matrix}

(11)

where T_j is the importance degree of the j tertiary index.

Results and discussion

Common factors

Normalized indexes data from part of the cases are shown in Appendix 2. Appendix 3 shows the correlation coefficient matrix of the index data, and we can see that most of the matrix coefficients are higher than 0.3.

The explanation of total variance is shown in Table 6. We can see that there are seven factors whose latent root is not less than 1; thus, seven common factors were obtained. The scree test is shown in Figure 1, and we can see that the curves become smooth after the seventh point. Therefore, it was appropriate to select seven common factors. As X = AF, matrix A varies across the method of parameter estimation; therefore, principal component analysis was used to estimate factors. Varimax orthogonal rotation was also used to make the common factors more diffuse by factor rotation.²⁵ The rotational component matrix is shown in Table 7.

Table 6.

Total variance explained.

Component	Initial eigenvalues			Extraction sums of squared loadings			Rotation sums of squared loadings
Component	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %
1	3.116	15.581	15.581	3.116	15.581	15.581	2.849	14.243	14.243
2	2.398	11.989	27.571	2.398	11.989	27.571	2.307	11.537	25.780
3	1.617	8.083	35.654	1.617	8.083	35.654	1.730	8.649	34.429
4	1.306	6.530	42.183	1.306	6.530	42.183	1.353	6.767	41.196
5	1.243	6.214	38.397	1.243	6.214	48.397	1.289	6.447	47.643
6	1.172	5.858	54.255	1.172	5.858	54.255	1.223	6.117	53.760
7	1.090	5.448	59.703	1.090	5.448	59.703	1.189	5.943	59.703
8	0.992	4.960	64.663
9	0.928	4.639	69.302
10	0.850	4.249	73.551
11	0.779	3.895	77.446
12	0.710	3.551	80.998
13	0.670	3.351	84.349
14	0.654	3.272	87.621
15	0.516	2.579	90.200
16	0.493	2.467	92.667
17	0.456	2.282	94.949
18	0.375	1.877	96.825
19	0.320	1.598	98.423
20	0.315	1.577	100.00

Figure 1.

Characteristic value of scree test.

Table 7.

Rotational component matrix.

Index	Component
Index	F1	F2	F3	F4	F5	F6	F7
ZX8	0.844	−0.106	0.091	0.049	−0.085	0.007	−0.040
ZX1	0.748	0.031	−0.105	0.039	−0.073	0.107	0.093
ZX6	0.736	0.025	−0.083	−0.087	−0.001	−0.174	0.106
ZX10	0.689	0.350	−0.073	−0.070	0.116	0.114	−0.123
ZX2	0.448	−0.176	0.135	0.117	0.369	0.336	0.044
ZX7	−0.022	0.794	0.056	0.002	0.178	0.046	−0.057
ZX13	0.019	0.774	0.108	0.067	−0.044	−0.044	−0.016
ZX9	0.044	0.764	0.137	0.013	−0.106	−0.038	0.179
ZX16	0.338	0.384	−0.215	0.246	0.293	0.162	−0.199
ZX14	−0.009	0.295	−0.184	0.221	−0.262	0.248	0.056
ZX15	0.076	0.054	0.811	0.021	0.089	−0.090	−0.119
ZX12	−0.101	0.219	0.806	0.063	0.021	−0.100	−0.003
ZX17	−0.241	−0.030	0.480	−0.145	−0.293	0.276	0.198
ZX19	0.018	0.091	0.036	0.764	0.118	−0.237	−0.050
ZX20	0.026	−0.010	−0.007	0.758	0.073	−0.203	−0.103
ZX5	−0.082	0.058	0.012	0.011	0.723	−0.080	0.024
ZX4	0.017	0.050	−0.106	−0.027	−0.082	0.705	−0.071
ZX3	−0.390	0.130	−0.044	−0.060	−0.337	0.413	−0.006
ZX18	0.092	0.006	0.007	0.122	−0.150	−0.208	0.770
ZX11	−0.007	0.101	−0.118	−0.085	0.386	0.232	0.637

Table 7 shows that the seven common factors with which every index corresponds have a different load number. The factor of the maximum load numbers is the main factor. According to the results of the rotating component matrix, the structure of the CMCs’ influential factors was established and is shown in Table 8. The first floor is the target floor used as the first index floor, the second is the main factor floor used as the second index floor, and the third floor is the details floor used as the third index floor.

Table 8.

Index system of accident factors.

First index	Second index	Third index
Accident influential factors	First factor	Purpose of vehicle, personnel type, means of transportation, load excess, driving license type
	Second factor	Vehicle safety situation, road alignment, vehicle driving state, road type
	Third factor	Roadside protection facility, road surface condition, weather
	Fourth factor	Road lighting condition, dangerous goods inside or not
	Fifth factor	Driver’s fault behavior
	Sixth factor	Driving experience, driver’s gender
	Seventh factor	Terrain, road condition

Factor weights calculation results

The system of CMCs’ influential factors shows that seven main factors were obtained according to the analysis of factors, and their accumulating contribution percentages are 59.703%; their values are 14.243%, 11.537%, 8.649%, 6.767%, 6.447%, 6.117%, and 5.943%. We acquired the weight A_i of second index through the first index, the same as the weight of third index, and the weight of third index through the second index. The results are shown in Table 9.

Table 9.

Weights of different index floors.

First index	Second index/second index rate on first index (A_i)	Third index	Factor coefficient (a_ij)	Third index rate on second index (A_ij)	Third index rate on first index (w_j)
Accident influential factors	Main factor 1/0.239	Purpose of vehicle	0.332	0.288	0.069
		Personnel type	0.291	0.253	0.060
		Means of transportation	0.229	0.199	0.048
		Load excess	0.182	0.158	0.038
		Driving license type	0.118	0.102	0.024
	Main factor 2/0.193	Vehicle safety situation	0.427	0.325	0.063
		Road alignment	0.335	0.255	0.049
		Vehicle driving state	0.268	0.204	0.039
		Road type	0.151	0.115	0.022
		Road section (intersection)	0.132	0.101	0.019
	Main factor 3/0.145	Roadside protection facility	0.479	0.388	0.056
		Road surface condition	0.458	0.371	0.054
		Weather	0.296	0.240	0.035
	Main factor 4/0.113	Road lighting condition	0.577	0.563	0.064
	Main factor 4/0.113	Dangerous goods inside or not	0.448	0.437	0.049
	Main factor 5/0.108	Driver’s fault behavior	0.597	1.000	0.108
	Main factor 6/0.102	Driving experience	0.599	0.663	0.068
	Main factor 6/0.102	Gender	0.304	0.337	0.034
	Main factor 7/0.100	Terrain	0.543	0.507	0.507
	Main factor 7/0.100	Road condition	0.527	0.493	0.493

Results of factor importance

The index weight was calculated through the factor weight, which is shown in Table 10. Table 10 shows that the most important factors are personnel type, driving experience, and driver fault behavior. Vehicle safety conditions and purpose of vehicle are important factors for vehicles. Terrain and lighting condition are important factors for environment.

Table 10.

Factor weight.

Factors	$w_{j}$	$N_{j}$	$T_{j}$
Driver’s fault behavior	0.108	0.432	4
Driving experience	0.068	0.272	4
Vehicle safety situation	0.069	0.276	4
Purpose of vehicle	0.063	0.252	4
Lighting condition	0.064	0.256	4
Personnel type	0.060	0.240	3
Road surface condition	0.054	0.216	3
Roadside facility	0.056	0.224	3
Terrain	0.507	2.028	3
Gender	0.034	0.136	2
Means of transportation	0.048	0.192	2
Vehicle driving state	0.039	0.156	2
Load excess	0.038	0.152	2
Road condition	0.493	1.972	2
Road alignment	0.049	0.196	2
Weather	0.035	0.140	2
Dangerous goods	0.049	0.196	2
Driving license type	0.024	0.096	1
Road section (intersection)	0.019	0.076	1
Road type	0.022	0.088	1

The model provides factor weight values of personnel, vehicle, road, and environment. All the factors were ordered according to the rule of weight value; factors with a value of 4 or 3 are the main factors related to the CMCs shown in Table 11, where 1 refers to not important, 2 refers to less important, 3 refers to important, and 4 refers to very important.

Table 11.

Main influential factor of fatal traffic crashes with massive casualty.

Main influential factor	Weight value
Driver’s fault behavior	4
Driving experience	4
Vehicle safety situation	4
Purpose of vehicle	4
Lighting condition	4
Personnel type	3
Road surface condition	3
Roadside facility	3
Terrain	3

Conclusion

This article used the analysis of 20 variables of CMCs to determine the main influential factors. According to the weight value, the main influential factors are fault behavior, driving experience, condition of vehicle safety, purpose of vehicle, road lighting, personnel type, road surface condition, roadside protection facilities, and road terrain.

Among these factors, personnel type, driving experience, and driver fault behavior are related to personnel, driver fault behavior, and driving experience, with a high weight value of 4, proving that driver is the most important role responsible for CMCs. It can be inferred that fatigued driving, speeding, and less driving experience are the main causes. Others factors, such as condition of vehicle, can infer that vehicles with safety problems such as brake fade can cause CMCs. Vehicles used for passengers or freight transport and drivers with a poor education background are more likely to be involved in CMCs. Rough surfaces and rugged terrain of roads can make it difficult to handle a vehicle and cause an accident. Dim road lighting is the main cause for night CMCs. Roads with no roadside protection facilities may have a higher CMCs rate.

This analysis of the main influential factors shows that to prevent CMCs, first, educating drivers, especially those who drive for passenger or freight transport, should be improved to reduce fault behavior and improve the driving experience. Second, vehicles should be inspected and maintained periodically to eliminate any mechanical breakdowns. Third, road surfaces and lighting conditions should be perfected, and roadside protection facilities should be implemented to improve traffic safety.

Footnotes

Appendix

Appendix 3.

Correlation coefficient matrix.

Correlation coefficient	ZX1	ZX2	ZX3	ZX4	ZX5	ZX6	ZX7	ZX8	ZX9	ZX10	ZX11	ZX12	ZX13	ZX14	ZX15	ZX16	ZX17	ZX18	ZX19	ZX20
ZX1	1.000	0.256	0.621	0.772	0.478	0.402	0.378	0.721	0.690	0.367	0.406	0.556	0.991	0.365	0.378	0.298	0.467	0.496	0.691	−0.389
ZX2	0.256	1.000	0.562	0.367	0.411	0.521	−0.706	0.490	0.731	0.692	0.496	0.307	0.658	−0.489	0.444	0.571	0.397	0.662	0.502	0.481
ZX3	0.621	0.562	1.000	−0.211	0.572	0.598	0.762	0.821	0.602	−0.554	0.474	0.503	0.449	0.630	0.581	0.388	0.489	0.770	0.631	0.550
ZX4	0.772	0.367	−0.211	1.000	0.366	0.788	0.492	0.551	0.720	0.833	0.466	0.910	0.820	0.599	0.481	0.637	0.672	0.811	0.709	0.766
ZX5	0.478	0.411	0.572	0.366	1.000	0.554	0.592	0.737	0.658	0.440	0.580	0.433	0.529	0.641	0.638	−0.692	0.578	0.829	0.434	0.541
ZX6	0.402	0.521	0.598	0.788	0.554	1.000	0.772	0.824	0.765	0.683	0.429	0.478	0.361	0.542	−0.773	0.429	0.589	0.678	0.663	0.673
ZX7	0.378	−0.706	0.762	0.492	0.592	0.772	1.000	0.286	0.476	0.775	0.674	0.772	0.456	0.463	0.551	0.893	0.782	0.397	0.833	0.782
ZX8	0.721	0.490	0.821	0.551	0.737	0.824	0.286	1.000	0.551	0.458	0.492	0.770	0.498	0.588	0.678	0.323	0.495	0.664	0.529	0.558
ZX9	0.690	0.731	0.602	0.720	0.658	0.765	0.476	0.551	1.000	0.677	0.453	0.820	0.782	0.699	0.481	0.321	0.287	0.445	0.762	0.558
ZX10	0.367	0.692	−0.554	0.833	0.440	0.683	0.775	0.458	0.677	1.000	0.338	0.769	0.652	0.477	0.489	0.580	0.527	0.668	0.629	0.881
ZX11	0.406	0.496	0.474	0.466	0.580	0.429	0.674	0.492	0.453	0.338	1.000	0.592	0.661	0.739	0.487	0.524	0.583	0.763	0.748	0.553
ZX12	0.556	0.307	0.503	0.910	0.433	0.478	0.772	0.770	0.820	0.769	0.592	1.000	0.372	0.469	0.583	−0.477	0.781	0.685	0.774	0.674
ZX13	0.991	0.658	0.449	0.820	0.529	0.361	0.456	0.498	0.782	0.652	0.661	0.372	1.000	0.772	0.594	0.755	0.287	0.466	0.409	0.588
ZX14	0.365	−0.489	0.630	0.599	0.641	0.542	0.463	0.588	0.699	0.477	0.739	0.469	0.772	1.000	0.659	0.439	0.622	0.478	0.578	0.543
ZX15	0.378	0.444	0.581	0.481	0.638	−0.773	0.551	0.678	0.481	0.489	0.487	0.583	0.594	0.659	1.000	0.773	0.585	0.542	0.343	0.663
ZX16	0.298	0.571	0.388	0.637	−0.692	0.429	0.893	0.323	0.321	0.580	0.524	−0.477	0.755	0.439	0.773	1.000	0.598	0.676	0.337	0.462
ZX17	0.467	0.397	0.489	0.672	0.578	0.589	0.782	0.495	0.287	0.527	0.583	0.781	0.287	0.622	0.585	0.598	1.000	0.369	0.467	0.664
ZX18	0.496	0.662	0.770	0.811	0.829	0.678	0.397	0.664	0.445	0.668	0.763	0.685	0.466	0.478	0.542	0.676	0.369	1.000	0.773	0.659
ZX19	0.691	0.502	0.631	0.709	0.434	0.663	0.833	0.529	0.762	0.629	0.748	0.774	0.409	0.578	0.343	0.337	0.467	0.773	1.000	0.884
ZX20	−0.389	0.481	0.550	0.766	0.541	0.673	0.782	0.558	0.558	0.881	0.553	0.674	0.588	0.543	0.663	0.462	0.664	0.659	0.884	1.000

Academic Editor: Xiaobei Jiang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially supported by Science Foundation of Chinese Ministry of Transport (2015319812200), the Open Project Program of the Key Laboratory of Road Traffic Safety of the Ministry of Public Security in China (2015ZDSYSKFKT07), Chinese Universities Scientific Fund (310822162018), and Program for Changjiang Scholars and Innovative Research Team in University (IRT1286).

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Factor analysis of fatal road traffic crashes with massive casualties in China

Abstract

Keywords

Introduction

Method

Database

Basic principle of factor analysis

Factor analysis

Results and discussion

Common factors

Factor weights calculation results

Results of factor importance

Conclusion

Footnotes

Appendix

Declaration of conflicting interests

Funding

References