CN103218668B - A kind of county-level road accident Forecasting Methodology based on geographical weighting Poisson regression - Google Patents

Abstract

The invention discloses the Forecasting Methodology of a kind of county-level road accident based on geographical weighting Poisson regression；First pass through data survey and gather the historical traffic accident frequency data in research range Nei Ge county, then the geographical position matrix form of the influence coefficient of the relationship model between accident frequency at county level and influence factor and each variable is set, and carry out the geographical weighting function in parameter estimation procedure, thereafter the Poisson regression model according to geographical weight carries out parameter estimation, overcome and the prediction of conventional county-level road accident does not account for special heterogeneity and causes the problem that prediction precision is not high, offer science is specified for county-level road accident prediction and safe prevention policy, reasonably instruct.

Description

A kind of county-level road accident Forecasting Methodology based on geographical weighting Poisson regression

Technical field

The present invention relates to field of traffic safety, especially relate to a kind of county-level road accident Forecasting Methodology based on geographical weighting Poisson regression.

Background technology

Traffic safety problem is one of basic problem of promoting social harmony, improving People's livelihood, is a global difficult problem.Alleviate traffic safety problem and be that one long-term, very long and difficult task.Traffic safety generally also exists contacting of inherence with the socio-economic development of countries and regions.The course that some developed countries pass by from the world, it all lives through the period that road traffic accident is occurred frequently, the low-level developing period that the accident that then enters is more stable.The 50-60 age in 20th century is developed country's Prevention of Road Traffic Fatalities " occurred frequently " period；Thereafter, in order to contain that road traffic worsens, developed country have adjusted road traffic safety management pattern in early 1970s, has promulgated series of road traffic safety code, formulates traffic safety strategical planning, road traffic accident is carried out comprehensive control.From early 1980s, these measures win initial success, and toll on traffic begins to decline.At present, the road traffic safety management of these countries has stepped into the foundation of four-stage emphasis elimination death and grievous injury long-term safety system and has undertaken the responsibility altogether.Traffic safety is a comprehensive social management job, according to the national communication security strategy worked out, plan is improved in interim major tasks target and the examination of working out all departments of governments at all levels, move in circles, constantly setting about from height and the macro policy level of National Security Strategy, strengthening traffic safety is administered, it is ensured that the completeness of laws and regulations and continual and steady fund input, through the concerted effort of the whole society long-term, comprehensive, it is only possible to containment road traffic accident.

In recent years, along with traffic safety problem is more and more paid attention to, traffic safety planning is put in the middle of overall city planning as a substance.County-level road accident forecast model can according to the economics of population feature at each county town, road and traffic attribute, evaluate rational vehicle accident quantity in each territory, county, thus judging the theoretical foundation important with traffic safety regulation offer for traffic safety situation at county level.Between generalized linear model supposition accident quantity and the predictor variable of in the past widely used vehicle accident quantitative forecast, relation is constant, do not account for the special heterogeneity of relation between county-level road accident quantity and each predictor variable, it is impossible to space heterogeneity in explanation accident quantitative forecast.Actually the space various social factors in area, geographic factor, Humanistic Factors all interacting thus having influence on the accuracy of traffic accident prediction, therefore result in the precision of prediction to county-level road accident quantity not high.

Summary of the invention

Goal of the invention: be constant for relation between generalized linear model supposition accident quantity and the predictor variable of in the past widely used vehicle accident quantitative forecast, it is impossible to space heterogeneity in explanation accident quantitative forecast；Actually the space various social factors in area, geographic factor, Humanistic Factors all interacts thus having influence on the accuracy of traffic accident prediction.The present invention proposes the county-level road accident Forecasting Methodology based on geographical weighting Poisson regression, the Spatial Heterogeneous Environment sex chromosome mosaicism in county-level road accident prediction can be considered, the difference that in different spatial, predictor variable affects can be simulated for accident number, thus being effectively increased the precision of county-level road accident quantitative forecast.

Technical scheme: a kind of county-level road accident Forecasting Methodology based on geographical weighting Poisson regression, including step:

1) the historical traffic accident frequency data in research range Nei Ge county are gathered by data survey, and demographic attributes, social economy's attribute, road infrastructure attribute and volume of traffic attribute data in territory, each county, extract the vehicle accident frequency, the volume of traffic, road attribute, social population's statistical nature, quantity of registering vehicle and hold driving license number scale parameter information；

2) Poisson distribution model form is adopted to set the relationship model between accident frequency at county level and influence factor:

Ln (Y)=ln (β₀(u_i))+β₁(u_i)ln(DVMT)+β₂(u_i)X₂+β₃(u_i)X₃+…+β_J(u_i)X_J+□(1)

Wherein, accident number Y is the predictive value of county-level road accident quantity；β_J(u_i) represent the coordinate position u of county town geographic center_i=(u_xi,u_yi)；X₂…X_JBeing the 1st ... J independent variable, is random error variable.

3) the geographical position matrix form of the influence coefficient of each variable is set, the geographical weighting function in line parameter estimation procedure of going forward side by side:

$\mathrm{\β}=\left[\begin{array}{cccc}{\mathrm{\β}}_0(u_{x1},u_{y1})& {\mathrm{\β}}_1(u_{x1},u_{y1})& \mathrm{...}& {\mathrm{\β}}_J(u_{x1},u_{y1})\\ {\mathrm{\β}}_0(u_{x2},u_{y2})& {\mathrm{\β}}_1(u_{x2},u_{y2})& \mathrm{...}& {\mathrm{\β}}_J(u_{x2},u_{y2})\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ {\mathrm{\β}}_0(u_{xn},u_{yn})& {\mathrm{\β}}_1(u_{xn},u_{yn})& \mathrm{...}& {\mathrm{\β}}_J(u_{xn},u_{yn})\end{array}\right]---\left(2\right)$

Wherein, n is county town quantity；

$\widehat{\mathrm{\β}}\left(i\right){\left(X^{T}W\right(u_{xi},u_{yi}\left)X\right)}^{-1}{X}^{T}W(u_{xi},u_{yi})Y---\left(3\right)$

W(u_xi,u_yi) represent a n by n spatial weighting matrix, it is expressed as by W (i):

$W\left(i\right)=\left[\begin{array}{cccc}{w}_{i1}& 0& ...& 0\\ 0& w_{i2}& ...& 0\\ ...& ...& ...& ...\\ 0& ...& ...& w_{in}\end{array}\right]---\left(4\right)$

Wherein w_ij(j=1,2 ..., it is n) to the weight at j county town in the model calibration of i county town；

Gaussian sum Bi Fang computing is used to provide the county town weight on its impact around:

Gauss: $w_{ij}=\exp (-\frac{1}{2}\×\frac{\left|\right|u_i-u_j\left|\right|}{G_i})---\left(5\right)$

Bi Fang: $w_{ij}=\left\{\begin{array}{cc}{\&lsqb;1-{\left(\right||u_i-u_j||/G_i)}^2\&rsqb;}^2& if\left|\right|u_i-u_j\left|\right|<G_i\\ 0& otherwise\end{array}\right.---\left(6\right)$

Wherein, G_iFor bandwidth variant, for determining that target county town is produced the spatial dimension of impact by around county town,

G_iLevel off to infinity time, w_ijClose to 1, it was shown that all there is impact at target county town by all county towns；

4) Poisson regression model based on geographical weight carries out parameter estimation, draws the changing value of each variation coefficient with geographic location and the significance level of each variable；

5) property value of variable notable in certain territory, Nian Ge county is input in model, each vehicle accident frequency at county level is predicted；

6) check whether the residual error of each accident frequency predictive value at county level has spatial coherence, if without spatial coherence, it was shown that the Poisson regression model based on geographical weight of foundation may be used for effectively prediction county-level road accident number；As having spatial coherence, then should reselect property variable, from step 4) start to repeat, until the residual error of predictive value does not have spatial coherence；The spatial coherence detection method of the residual error of described predictive value is a kind of method studying spatial auto-correlation developed by Mo Lan, Moran ' sI:

${\mathrm{Moran}}^{\&prime;}sI=\frac{{\mathrm{N\&Sigma;}}_i{\mathrm{\&Sigma;}}_j{\mathrm{\&omega;}}_{ij}(Y_i-\stackrel{\&OverBar;}{Y})(Y_j-\stackrel{\&OverBar;}{Y})}{{\mathrm{\&Sigma;}}_i{\mathrm{\&Sigma;}}_j{\mathrm{\&omega;}}_{ij}{\mathrm{\&Sigma;}}_i{(Y-\stackrel{\&OverBar;}{Y})}^2}$

Wherein, N is county town quantity；Y_iAnd Y_jIt it is accident remaining for county town i and county town j；Be all county towns average residual more than, ω_ijIt is the weight to j county town in the model calibration of i county town, is the element of Spatial weight matrix, the spatial coherence structure presented；

Moran ' the sI of one plus or minus value represents that the spatial auto-correlation of the plus or minus at each county town is many；The scope of Moran ' sI is from-1 to+1；Null value represents a random spatial framework；For testing statistical hypothesis, Moran ' sI being converted into Z-value, this value represents the confidence level of statistically significant 5% more than 1.96 or less than-1.96.

Beneficial effect: the Forecasting Methodology of the county-level road accident based on geographical weighting Poisson regression that the present invention proposes；First pass through data survey and gather the historical traffic accident frequency data in research range Nei Ge county, then the geographical position matrix form of the influence coefficient of the relationship model between accident frequency at county level and influence factor and each variable is set, and carry out the geographical weighting function in parameter estimation procedure, thereafter the Poisson regression model according to geographical weight carries out parameter estimation, overcome and the prediction of conventional county-level road accident does not account for special heterogeneity and causes the problem that prediction precision is not high, the difference that in different spatial, predictor variable affects can be simulated for accident number, thus being effectively increased the precision of county-level road accident quantitative forecast, offer science is specified for county-level road accident prediction and safe prevention policy, reasonably instruct.

Accompanying drawing explanation

Fig. 1 is the method flow diagram of the embodiment of the present invention；

Fig. 2 is county town DVMT Parameters variation schematic diagram, California (a) and parameter significant level change schematic diagram (b) in the embodiment of the present invention；

Fig. 3 is the parameter space distribution schematic diagram of the Poisson regression model predictor variable in the embodiment of the present invention based on geographical weight.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, it is further elucidated with the present invention, it should be understood that following detailed description of the invention is merely to illustrate the present invention rather than restriction the scope of the present invention, after having read the present invention, the amendment of the various equivalent form of values of the present invention is all fallen within the application claims limited range by those skilled in the art.

As it is shown in figure 1, based on the county-level road accident Forecasting Methodology of geographical weighting Poisson regression, including step:

The first step is the historical traffic accident frequency data being gathered research range Nei Ge county by data survey, and the data of four kinds of types such as demographic attributes, social economy's attribute, road infrastructure attribute and volume of traffic attribute have been studied in territory, each county, including the vehicle accident frequency, the volume of traffic, road attribute, social population's statistical nature, quantity of registering vehicle with hold driving license number ratio etc..

Second step, sets the relationship model between accident frequency at county level and influence factor, and acquiescence adopts Poisson distribution model form；

Ln (Y)=ln (β₀(u_i))+β₁(u_i)ln(DVMT)+β₂(u_i)X₂+β₃(u_i)X₃+…+β_J(u_i)X_J+□(1)

Wherein, accident number Y is the predictive value of county-level road accident quantity；β_J(u_i) represent the coordinate position u of county town geographic center_i=(u_xi,u_yi)；X₂…X_JBeing the 1st ... J independent variable, is random error variable.

3rd step, arranges the geographical position matrix form of the influence coefficient of each variable, and carries out the geographical weighting function in parameter estimation procedure:

$\mathrm{\&beta;}=\left[\begin{array}{cccc}{\mathrm{\&beta;}}_0(u_{x1},u_{y1})& {\mathrm{\&beta;}}_1(u_{x1},u_{y1})& \mathrm{...}& {\mathrm{\&beta;}}_J(u_{x1},u_{y1})\\ {\mathrm{\&beta;}}_0(u_{x2},u_{y2})& {\mathrm{\&beta;}}_1(u_{x2},u_{y2})& \mathrm{...}& {\mathrm{\&beta;}}_J(u_{x2},u_{y2})\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ {\mathrm{\&beta;}}_0(u_{xn},u_{yn})& {\mathrm{\&beta;}}_1(u_{xn},u_{yn})& \mathrm{...}& {\mathrm{\&beta;}}_J(u_{xn},u_{yn})\end{array}\right]---\left(2\right)$

Wherein, n is county town quantity.

$\widehat{\mathrm{\&beta;}}\left(i\right)={\left(X^{T}W\right(u_{xi},u_{yi}\left)X\right)}^{-1}{X}^{T}W(u_{xi},u_{yi})Y---\left(3\right)$

W(u_xi,u_yi) represent a n by n spatial weighting matrix, it is expressed as by W (i):

$W\left(i\right)=\left[\begin{array}{cccc}{w}_{i1}& 0& ...& 0\\ 0& w_{i2}& ...& 0\\ ...& ...& ...& ...\\ 0& ...& ...& w_{in}\end{array}\right]---\left(4\right)$

Wherein w_ij(j=1,2 ..., it is n) to the weight at j county town in the model calibration of i county town；

Use gaussian sum Bi Fang computing can provide the county town weight on its impact around:

Gauss: $w_{ij}=\exp (-\frac{1}{2}\&times;\frac{\left|\right|u_i-u_j\left|\right|}{G_i})---\left(5\right)$

Bi Fang: $w_{ij}=\left\{\begin{array}{cc}{\&lsqb;1-{\left(\right||u_i-u_j||/G_i)}^2\&rsqb;}^2& if\left|\right|u_i-u_j\left|\right|<G_i\\ 0& otherwise\end{array}\right.---\left(6\right)$

Wherein, G_iFor bandwidth variant, for determining that target county town is produced the spatial dimension of impact by around county town,

G_iLevel off to infinity time, w_ijClose to 1, it was shown that all there is impact at target county town by all county towns；

4th step carries out parameter estimation based on the Poisson regression model of geographical weight, draws the changing value of each variation coefficient with geographic location and the significance level of each variable；

The property value of variable notable in certain territory, Nian Ge county is input among model by the 5th step, is predicted for each vehicle accident frequency at county level；

6th step checks whether the residual error of each accident frequency predictive value at county level has spatial coherence, if without spatial coherence, it was shown that the Poisson regression model based on geographical weight of foundation may be used for effectively prediction county-level road accident number；As having spatial coherence, then should reselect property variable, start to repeat from the 4th step, until prediction residual does not have spatial coherence.

Moran ' sI is a kind of method studying spatial auto-correlation developed by Mo Lan, Moran ' sI:

${\mathrm{Moran}}^{\&prime;}sI=\frac{{\mathrm{N\&Sigma;}}_i{\mathrm{\&Sigma;}}_j{\mathrm{\&omega;}}_{ij}(Y_i-\stackrel{\&OverBar;}{Y})(Y_j-\stackrel{\&OverBar;}{Y})}{{\mathrm{\&Sigma;}}_i{\mathrm{\&Sigma;}}_j{\mathrm{\&omega;}}_{ij}{\mathrm{\&Sigma;}}_i{(Y_i-\stackrel{\&OverBar;}{Y})}^2}---\left(7\right)$

Wherein, N is county town quantity；Y_iAnd Y_jIt it is accident remaining for county town i and county town j；Be all county towns average residual more than, ω_ijIt is the weight to j county town in the model calibration of i county town, is the element of Spatial weight matrix, the spatial coherence structure presented；

One Moran ' sI just (bearing) value represents that the spatial autocorrelation just (born) at each county town is many.The scope of Moran ' sI is from-1 (representing perfection dispersion) to+1 (good dependency).Null value represents a random spatial framework.For testing statistical hypothesis, Moran ' sI can be converted into Z-value, and this value represents the confidence level of statistically significant 5% more than 1.96 or less than-1.96.

Such as Fig. 2 and Fig. 3, the present embodiment selects area, the California data of 2007 to 2009 3 years to be by a definite date analyzed.Acquire the data of four kinds of types, including vehicle accident frequency, the volume of traffic, road network attribute, and social population's statistical nature.

Setting the relationship model between accident frequency at county level and influence factor, acquiescence adopts Poisson distribution model form and arranges the geographical position matrix form of influence coefficient of each variable, and carries out the geographical weighting function in parameter estimation procedure.

The Poisson regression model being then based on geographical weight carries out parameter estimation (estimated result is in Table 1), draws the changing value of each variation coefficient with geographic location.As shown in Figure 2, the design parameter DVMT in all counties, the significant level 95% demonstrates the Poisson regression model of geographical weight can the heterogeneous impact of capture space.

Thereafter every attribute in certain territory, Nian Ge county is input among model, each vehicle accident frequency at county level is predicted；Whether the residual error checking each accident frequency predictive value at county level has spatial coherence, it has been found that without spatial coherence, it was shown that the Poisson regression model based on geographical weight of foundation may be used for effectively prediction county-level road accident number.Each variation parameter space that the Poisson regression model of geographical weight calculates is distributed as shown in Figure 3.

Being calculated according to identical data with broad sense line style model, and the Poisson regression model by result with based on geographical weight predicts the outcome and contrasts, the contrast for accident quantitative forecast precision at county level is as shown in table 2.Poisson regression model based on geographical weight is more accurate compared to former broad sense line style model.

Geographical weighting Poisson regression (GWPR) catches the relation of those spatial variations in the face of complicated variable impact, Forecasting Methodology defect on special heterogeneity before overcoming, substantially increase the accuracy of county-level road accident prediction, prevent and treat policy for traffic safety at county level and prediction provides scientific and rational guidance.

Table 1 is summed up based on the variable estimated result of the Poisson regression model of geographical weight

Table 2 is based on geographical weight Poisson regression model precision of prediction and generalized linear model comparing result

Illustrating: Pearson came r is more big, and precision is more high, mean error and the more little precision of average error sum of squares are more high.

Claims (1)

1., based on a county-level road accident Forecasting Methodology for geographical weighting Poisson regression, it is characterized in that including step:

1) the historical traffic accident frequency data in research range Nei Ge county are gathered by data survey, and demographic attributes, social economy's attribute, road infrastructure attribute and volume of traffic attribute data in territory, each county, extract the vehicle accident frequency, the volume of traffic, road attribute, social population's statistical nature, quantity of registering vehicle and hold driving license number scale parameter information；

2) Poisson distribution model form is adopted to set the relationship model between accident frequency at county level and influence factor:

Ln (Y)=ln (β₀(u_i))+β₁(u_i)ln(DVMT)+β₂(u_i)X₂+β₃(u_i)X₃+…+β_J(u_i)X_J+□(1)

Wherein, accident number Y is the predictive value of county-level road accident quantity；β_J(u_i) represent the coordinate position u of county town geographic center_i=(u_xi,u_yi)；X₂…X_JBeing the 2nd ... J independent variable, is random error variable；

3) the geographical position matrix form of the influence coefficient of each variable is set, the geographical weighting function in line parameter estimation procedure of going forward side by side:

$\mathrm{\&beta;}=\left[\begin{array}{cccc}{\mathrm{\&beta;}}_0(u_{x1},u_{y1})& {\mathrm{\&beta;}}_1(u_{x1},u_{y1})& \mathrm{...}& {\mathrm{\&beta;}}_J(u_{x1},u_{y1})\\ {\mathrm{\&beta;}}_0(u_{x2},u_{y2})& {\mathrm{\&beta;}}_1(u_{x2},u_{y2})& \mathrm{...}& {\mathrm{\&beta;}}_J(u_{x2},u_{y2})\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ {\mathrm{\&beta;}}_0(u_{xn},u_{yn})& {\mathrm{\&beta;}}_1(u_{xn},u_{yn})& \mathrm{...}& {\mathrm{\&beta;}}_J(u_{xn},u_{yn})\end{array}\right]---\left(2\right)$

Wherein, n is county town quantity；

$\widehat{\mathrm{\&beta;}}\left(i\right)={\left(X^{T}W\right(u_{xi},u_{yi}\left)X\right)}^{-1}{X}^{T}W(u_{xi},u_{yi})Y---\left(3\right)$

W(u_xi,u_yi) represent a n by n spatial weighting matrix, it is expressed as by W (i):

$W\left(i\right)=\left[\begin{array}{cccc}{w}_{i1}& 0& \mathrm{...}& 0\\ 0& w_{i2}& \mathrm{...}& 0\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 0& \mathrm{...}& \mathrm{...}& w_{in}\end{array}\right]---\left(4\right)$

Wherein w_ijIt is the weight to j county town in the model calibration of i county town, j=1,2 ..., n；

Gaussian sum Bi Fang computing is used to provide the county town weight on its impact around:

Gauss:

Bi Fang:

Wherein, G_iFor bandwidth variant, for determining that target county town is produced the spatial dimension of impact, G by around county town_iLevel off to infinity time, w_ijClose to 1, it was shown that all there is impact at target county town by all county towns；

4) Poisson regression model based on geographical weight carries out parameter estimation, draws the changing value of each variation coefficient with geographic location and the significance level of each variable；

5) property value of variable notable in certain territory, Nian Ge county is input in model, each vehicle accident frequency at county level is predicted；

6) check whether the residual error of each accident frequency predictive value at county level has spatial coherence, if without spatial coherence, it was shown that the Poisson regression model based on geographical weight of foundation may be used for effectively prediction county-level road accident number；As having spatial coherence, then should reselect property variable, from step 4) start to repeat, until the residual error of predictive value does not have spatial coherence；The spatial coherence detection method of the residual error of described predictive value is a kind of method studying spatial auto-correlation developed by Mo Lan, Moran ' sI:

${\mathrm{Moran}}^{\&prime;}sI=\frac{N{\&Sigma;}_i{\&Sigma;}_j{\mathrm{\&omega;}}_{ij}(Y_i-\stackrel{\&OverBar;}{Y})(Y_j-\stackrel{\&OverBar;}{Y})}{{\&Sigma;}_i{\&Sigma;}_j{\mathrm{\&omega;}}_{ij}{\&Sigma;}_i{(Y_i-\stackrel{\&OverBar;}{Y})}^2}---\left(7\right)$

Wherein, N is county town quantity；Y_iAnd Y_jIt it is accident remaining for county town i and county town j；Be all county towns average residual more than, ω_ijIt is the weight to j county town in the model calibration of i county town, is the element of Spatial weight matrix, the spatial coherence structure presented；

Moran ' the sI of one plus or minus value represents that the spatial auto-correlation of the plus or minus at each county town is many；The scope of Moran ' sI is from-1 to+1；Null value represents a random spatial framework；For testing statistical hypothesis, Moran ' sI being converted into Z-value, this value represents the confidence level of statistically significant 5% more than 1.96 or less than-1.96.