CN103218668A - County-level road accident forecasting method based on geographic weighting Poisson regression - Google Patents

Abstract

The invention discloses a county-level road accident forecasting method based on geographic weighting Poisson regression. Firstly history road accident frequency data of each county in a research scope are collected through data survey; then a model relation between county-level accident frequencies and influencing factors and a geographic position matrix form of influence coefficients of each variable quantity are set, and a geographic weighting function in a parameter estimation process is carried out; and parameter estimation is carried out on a Poisson regression model according to geographic weighting. A problem that existing county-level road accident forecasting does not give consideration to spatial heterogeneity to cause not-high forecasting accuracy is solved, and scientific and reasonable guidance is provided for county-level road accident forecasting and safety prevention and control policy formulating.

Description

A kind of Forecasting Methodology of the traffic hazard at county level that returns based on geographical weighting Poisson

Technical field

The present invention relates to the traffic safety field, especially relate to a kind of traffic accident prediction method at county level that returns based on geographical weighting Poisson.

Background technology

The traffic safety problem is one of basic problem that promotes social harmony, improves People's livelihood, and is a global difficult problem.Alleviate the traffic safety problem and be long-term, a very long and difficult task.The common socio-economic development with countries and regions of traffic safety exists inherent getting in touch.The course that some developed countries pass by from the world, it all lives through road traffic accident period occurred frequently, has then entered accident more stable low-level developing period.The 50-60 age in 20th century is developed country's road traffic accident death " occurred frequently " period; Thereafter, worsen in order to contain road traffic, developed country has adjusted the traffic safety management mode in early 1970s, has issued the series of road traffic safety code, formulates the traffic safety strategic planning, and road traffic accident is carried out the comprehensive regulation.From early 1980s, these measures win initial success, and toll on traffic begins to descend.At present, four-stage has been stepped in these national traffic safety management---pay attention to eliminating the foundation of dead and grievous injury long-term safety system and undertaking the responsibility altogether.Traffic safety is a comprehensive social management job, according to the national communication security strategy of working out, work out the interim major tasks target and the examination of all departments of governments at all levels and improve plan, move in circles, constantly set about, strengthen traffic safety and administer, guarantee the completeness of laws and regulations and continual and steady fund input from the height and the macro policy level of National Security Strategy, through concerted effort long-term, the comprehensive whole society, just may contain 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 the overall city planning as a substance.Traffic Accident Forecast Model at county level can be according to economics of population feature, road and the traffic attribute at each county town, estimate in each territory, county reasonably traffic hazard quantity, thereby judge and traffic safety is renovated the important theory foundation is provided for traffic safety situation at county level.It is constant closing between the generalized linear model supposition accident quantity of the traffic hazard quantitative forecast that extensively adopts and the predictive variable in the past, do not consider the special heterogeneity that concerns between traffic hazard quantity at county level and each predictive variable, can't explanation accident quantitative forecast in the heterogeneous problem in space.In fact various social factors in space area, geographic factor has influence on the accuracy of traffic accident prediction thereby all interact on the humane factor, has therefore caused the precision of prediction of traffic hazard quantity at county level not high.

Summary of the invention

Goal of the invention: at close between the generalized linear model supposition accident quantity of the traffic hazard quantitative forecast that extensively adopted and the predictive variable in the past is constant, can't explanation accident quantitative forecast in the heterogeneous problem in space; In fact various social factors in space area, geographic factor has influence on the accuracy of traffic accident prediction thereby all interact on the humane factor.The present invention proposes the traffic accident prediction method at county level that returns based on geographical weighting Poisson, can consider the special heterogeneity problem in the traffic accident prediction at county level, can simulate the difference that predictive variable influences for the accident number in the different spatial, thereby effectively improve the precision of traffic hazard quantitative forecast at county level.

Technical scheme: a kind of traffic accident prediction method at county level that returns based on geographical weighting Poisson comprises step:

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

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

ln(Y)=ln(β ₀(u _i))+β ₁(u _i)ln(DVMT)+β ₂(u _i)X ₂+β ₃(u _i)X ₃+…+β _J(u _i)X _J+□ (1)

Wherein, accident is counted the predicted value that Y is a traffic hazard quantity at county level; β _J(ui) the coordinate position ui=(u of expression county town geographic center _Xi, u _Yi); X ₁X _JBe the 1st ... J independent variable, are the stochastic error variable.

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

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

Wherein, n is a county town quantity;

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

W (u _Xi, u _Yi) by n of n spatial weighting matrix representation, be expressed as by W (i):

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

W wherein _Ij(j=1,2 ..., n) be the weight of giving the j county town in the model calibration of i county town;

Utilization gaussian sum Bi Fang computing provides on every side the county town to the weight of its influence:

Gauss: $\mathrm{wij}=\exp (-\frac{1}{2}\×\frac{\left|\right|u_i-u_j\left|\right|}{G})---\left(5\right)$

Bi Fang: $\mathrm{wij}=\left\{\begin{array}{cc}[1-{\left(\right||u_i-u_j||/G_i)}^2{]}^2& \mathrm{if}\left|\right|u_i-u_j\left|\right|<G_i\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

Wherein, G _iBe the bandwidth variable, the spatial dimension that the county town exerts an influence to the target county town around being used for determining,

G _iWhen leveling off to infinity, w _IjNear 1, show that all county towns are all influential to the target county town;

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

5) with in certain year each territory, county significantly the property value of variable be input in the model, predict for each traffic hazard frequency at county level;

6) check the residual error of each the accident frequency predicted value at county level correlativity of whether having living space, if no spatial coherence shows that the Poisson regression model based on geographical weight of foundation can be used for effectively predicting traffic hazard number at county level; As have spatial coherence, and then should reselect the attribute variable, begin repetition from step 4), do not have spatial coherence until the residual error of predicted value; Serve as reasons a kind of method of studying spatial autocorrelation of Mo Lan exploitation of the spatial coherence detection method of the residual error of described predicted value, Moran ' s I:

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

Wherein, N is a county town quantity; Y _iAnd Y _jIt is county town i and county town j remnants' accident;

Be the average remnants at all county towns, ω _IjBeing the weight of giving the j county town in the model calibration of i county town, is space weight entry of a matrix element, the spatial coherence structure that presents;

Moran ' the s I of a plus or minus value represents that the spatial autocorrelation of plus or minus at each county town is many; The scope of Moran ' s I is from-1 to+1; Null value is represented a spatial framework at random; For testing statistical hypothesis, Moran ' s I is converted into the Z-value, this value is greater than 1.96 or be illustrated on the statistics very significant 5% confidence level less than-1.96.

Beneficial effect: the Forecasting Methodology of the traffic hazard at county level that returns based on geographical weighting Poisson that the present invention proposes; At first gather the historical traffic hazard frequency data in research range Nei Ge county by data survey, set the geographic position matrix form of the influence coefficient of relationship model between the accident frequency at county level and the influence factor and each variable then, and carry out geographical weighting function in the parameter estimation procedure, thereafter the Poisson regression model according to geographical weight carries out parameter estimation, overcome and do not considered special heterogeneity in the traffic accident prediction at county level in the past and cause the not high problem of pre-measuring precision, can simulate the difference that predictive variable influences for the accident number in the different spatial, thereby effectively improved the precision of traffic hazard quantitative forecast at county level, for traffic accident prediction at county level and the safety policy of preventing and treating is provided by the science that provides, reasonably instruct.

Description of drawings

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

Fig. 2 is that county town, California DVMT parameter changes synoptic diagram (a) and parameter level of signifiance variation synoptic diagram (b) in the embodiment of the invention;

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

Embodiment

Below in conjunction with the drawings and specific embodiments, further illustrate the present invention, should understand following embodiment only is used to the present invention is described and is not used in and limit the scope of the invention, after having read the present invention, those skilled in the art all fall within the application's claims institute restricted portion to the modification of the various equivalent form of values of the present invention.

As shown in Figure 1, the traffic accident prediction method at county level based on geographical weighting Poisson returns comprises step:

The first step is the historical traffic hazard frequency data of gathering research range Nei Ge county by data survey, and the data of four types of demography attribute, social economy's attribute, road infrastructure attribute and volume of traffic attributes etc. are studied in each territory, county, comprise the traffic hazard frequency, the volume of traffic, road attribute, social population's statistical nature, the quantity of registering vehicle and hold driving license number ratio etc.

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

ln(Y)=ln(β ₀(u _i))+β ₁(u _i)ln(DVMT)+β ₂(u _i)X ₂+β ₃(u _i)X ₃+…+β _J(u _i)X _J+□ (1)

Wherein, accident is counted the predicted value that Y is a traffic hazard quantity at county level; β _J(ui) the coordinate position ui=(u of expression county town geographic center _Xi, u _Yi); X ₁X _JBe the 1st ... J independent variable, are the stochastic error variable.

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

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

Wherein, n is a county town quantity.

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

W (u _Xi, u _Yi) by n of n spatial weighting matrix representation, be expressed as by W (i):

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

W wherein _Ij(j=1,2 ..., n) be the weight of giving the j county town in the model calibration of i county town;

Utilization gaussian sum Bi Fang computing can provide on every side the county town to the weight of its influence:

Gauss: $\mathrm{wij}=\exp (-\frac{1}{2}\&times;\frac{\left|\right|u_i-u_j\left|\right|}{G})---\left(5\right)$

Bi Fang: $\mathrm{wij}=\left\{\begin{array}{cc}[1-{\left(\right||u_i-u_j||/G_i)}^2{]}^2& \mathrm{if}\left|\right|u_i-u_j\left|\right|<G_i\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

Wherein, G _iBe the bandwidth variable, the spatial dimension that the county town exerts an influence to the target county town around being used for determining,

G _iWhen leveling off to infinity, w _IjNear 1, show that all county towns are all influential to the target county town;

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

The 5th step with in certain year each territory, county significantly the property value of variable be input among the model, predict for each traffic hazard frequency at county level;

The residual error of the 6th each accident frequency predicted value at county level of the step check correlativity of whether having living space is if no spatial coherence shows that the Poisson regression model based on geographical weight of foundation can be used for effectively predicting traffic hazard number at county level; As have spatial coherence, and then should reselect the attribute variable, since the 4th step repetition, do not have spatial coherence until prediction residual.

Moran ' s I is a kind of method of studying spatial autocorrelation by the Mo Lan exploitation, Moran ' s I:

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

Wherein, N is a county town quantity; Y _iAnd Y _jIt is county town i and county town j remnants' accident;

Be the average remnants at all county towns, ω _IjBeing the weight of giving the j county town in the model calibration of i county town, is space weight entry of a matrix element, the spatial coherence structure that presents;

A Moran ' s I who just (bears) value represents that the spatial autocorrelation of just (bearing) at each county town is many.The scope of Moran ' s I is to+1 (well correlativity) from-1 (the perfect dispersion of expression).Null value is represented a spatial framework at random.For testing statistical hypothesis, Moran ' s I can be converted into the Z-value, and this value is greater than 1.96 or be illustrated on the statistics very significant 5% confidence level less than-1.96.

As Fig. 2 and Fig. 3, present embodiment select area, California 2007 to 2009 by a definite date the data in 3 years analyze.Gathered four types data, comprised the traffic hazard frequency, the volume of traffic, road network attribute and social population's statistical nature.

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

Poisson regression model based on geographical weight carries out parameter estimation (estimated result sees Table 1) then, draws the changing value of each variation coefficient with geographic location.By shown in Figure 2, the concrete parameter DVMT in all counties, the level of signifiance 95% has proved the influence that the Poisson regression model of geographical weight can the capture space heterogeneity.

Certain year each county territory in every attribute be input to model among, predict for each traffic hazard frequency at county level thereafter; Check the residual error of each the accident frequency predicted value at county level correlativity of whether having living space, find no spatial coherence, show that the Poisson regression model based on geographical weight of foundation can be used for effectively predicting traffic hazard number at county level.Each variation parameter space that the Poisson regression model of geographical weight calculates distributes as shown in Figure 3.

Calculate according to identical data with broad sense line style model, and compare with the result with based on the Poisson forecast of regression model result of geographical weight, as shown in table 2 for the contrast of accident quantitative forecast precision at county level.Based on the Poisson regression model of geographical weight compared to before broad sense line style model more accurate.

Geographical weighting Poisson returns (GWPR) catches those spatial variations in the face of complicated variable influence relation, overcome the defective of former Forecasting Methodology on special heterogeneity, improved the accuracy of traffic accident prediction at county level greatly, for traffic safety at county level prevents and treats policy 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 forecast of regression model precision and generalized linear model comparing result

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

Claims (1)

1. traffic accident prediction method at county level that returns based on geographical weighting Poisson is characterized in that comprising step:

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

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

ln(Y)=ln(β ₀(u _i))+β ₁(u _i)ln(DVMT)+β ₂(u _i)X ₂+β ₃(u _i)X ₃+…+β _J(u _i)X _J+□ (1)

Wherein, accident is counted the predicted value that Y is a traffic hazard quantity at county level; β _J(ui) the coordinate position ui=(u of expression county town geographic center _Xi, u _Yi); X ₁X _JBe 1J independent variable, is the stochastic error variable;

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

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

Wherein, n is a county town quantity;

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

W (u _Xi, u _Yi) by n of n spatial weighting matrix representation, be expressed as by W (i):

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

W wherein _Ij(j=1,2 ..., n) be the weight of giving the j county town in the model calibration of i county town;

Utilization gaussian sum Bi Fang computing provides on every side the county town to the weight of its influence:

Gauss: $\mathrm{wij}=\exp (-\frac{1}{2}\&times;\frac{\left|\right|u_i-u_j\left|\right|}{G})---\left(5\right)$

Bi Fang: $\mathrm{wij}=\left\{\begin{array}{cc}[1-{\left(\right||u_i-u_j||/G_i)}^2{]}^2& \mathrm{if}\left|\right|u_i-u_j\left|\right|<G_i\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

Wherein, G _iBe the bandwidth variable, the spatial dimension that the county town exerts an influence to the target county town around being used for determining,

G _iWhen leveling off to infinity, w _IjNear 1, show that all county towns are all influential to the target county town;

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

5) with in certain year each territory, county significantly the property value of variable be input in the model, predict for each traffic hazard frequency at county level;

6) check the residual error of each the accident frequency predicted value at county level correlativity of whether having living space, if no spatial coherence shows that the Poisson regression model based on geographical weight of foundation can be used for effectively predicting traffic hazard number at county level; As have spatial coherence, and then should reselect the attribute variable, begin repetition from step 4), do not have spatial coherence until the residual error of predicted value; Serve as reasons a kind of method of studying spatial autocorrelation of Mo Lan exploitation of the spatial coherence detection method of the residual error of described predicted value, Moran ' s I:

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

Wherein, N is a county town quantity; Y _iAnd Y _jIt is county town i and county town j remnants' accident; Y is the average remnants at all county towns, ω _IjBeing the weight of giving the j county town in the model calibration of i county town, is space weight entry of a matrix element, the spatial coherence structure that presents;

Moran ' the s I of a plus or minus value represents that the spatial autocorrelation of plus or minus at each county town is many; The scope of Moran ' s I is from-1 to+1; Null value is represented a spatial framework at random; For testing statistical hypothesis, Moran ' s I is converted into the Z-value, this value is greater than 1.96 or be illustrated on the statistics very significant 5% confidence level less than-1.96.

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