CN102103715A - Negative binomial regression-based maritime traffic accident investigation analysis and prediction method - Google Patents

Abstract

The invention discloses a negative binomial regression-based maritime traffic accident investigation analysis and prediction method, which comprises the following steps of: first determining the most substantial factors and the most important factors which may influence an accident, determining a plurality of independent variables and selecting a proper model type according to the characteristics of data; then performing model hypothesis on such a basis, and determining a basic model which describes problems; and finally performing parameter evaluation and verification on the model by using a series of criterions, and correcting the model to establish a more accurate model. The analysis and prediction model has relatively higher prediction accuracy, and provides a good way for analyzing and predicting maritime traffic accidents.

Description

Waterborne traffic accident investigation analysis and Forecasting Methodology based on negative binomial recurrence

Technical field

The present invention relates to a kind of overwater accident investigation and analysis and Forecasting Methodology that returns based on negative binomial.

Background technology

The accuracy of accident forecast is mainly based on two basic premises: the one, and information as can be known, countries in the world government recognizes the importance of setting up the disaster data storehouse with organizing at present, also carries out the work just energetically; The 2nd, correct accident forecast method.

The analysis of marine incident, prediction, evaluation and prevention Decision Control technology have become the core of modern ships safety management.There is great danger in maritime traffic safety actually, may cause great loss to society, acceptable value-at-risk is much, and how carrying out Safety Support for Marine Traffic could be reduced to the hazard level of system in the safety index, and these all depend on accident investigation and analysis and research.

Explore pregnant calamity body in the catastrophe conductive process, cause the calamity body, fragility, infectiousness and the stability of disaster-stricken body, extract and condensed its mechanism mechanism is safe and scientific most crucial problem.Transfer to the aristogenesis of exploration accident when the emphasis of safe and scientific research from exploration accident reason, indicate that the accident forecast technology becomes one of problem in science the most basic in the research of current safety safeguards technique day by day.How accident is investigated and analysed it after taking place effectively, prevents that similar accident from taking place once more, and it is crucial selecting suitable analytical approach.

Analyze domestic and international present Research and development trend thereof, accident forecast mainly shows the following aspects at present:

1) qualitative forecasting method

Qualitative forecasting is meant that the dopester relies on personnel and the expert who is familiar with professional knowledge, has rich experiences and comprehensive analytical capacity, according to historical summary of having grasped and audio-visual materials, utilization individual's experience and analysis and judgement ability, judgement on the nature and extent is made in the future development of things, then, pass through the suggestion of the comprehensive each side of a definite form again, as following main foundation of prediction.

2) quantitative forecasting technique

Quantitative forecast is meant and adopts certain mathematical model, utilizes history and existing concrete data to calculate and finally obtain concrete numerical method.The mathematical model and the method for accident forecast have various ways, and commonly used and more feasible mathematical method has Regression Forecast, time series forecasting, markov predicted method, grey method, Bayesian network predicted method, neural network prediction method, SVM prediction method etc.

3) security of system assay method has obtained extensively pushing away factory, but all is to carry out method research at system and industry characteristic, formulates relevant criterion, promulgation relevant regulations and way, and limitation is bigger.What just mainly adopting at the safe evaluation method of research and development is the qualitative forecasting method, and the expert utilizes working experience to judge according to existing information and data, and these are judged quantification.The weights number needs of some quantitative targets is progressively perfect.

4) main intuitive forecasting technique and methods of comparative analysis of adopting of some accident statistical analysis prediction at present can only be carried out short-term forecasting or with comparing in the past.The foundation of assessment indicator system and evaluation synthetic technology etc. are by the mathematical theory analysis, set up model and carry out accident statistical analysis and be in the research trial period, still do not have at present the comparatively accident forecast and the safety analysis evaluation method of the security incident statistical number reason aspect of system.

Accident investigation analytical technology in recent years and method become the focus of research gradually.Modern accident investigation was used and is interpenetrated with the intersecting of the multiple often investigation and analysis method of development of analytical approach, therefore, was difficult to carry out absolute division.At present, scholars' achievement in research is as follows:

Zhang Ling reduces 5 big classes according to reason results model, process model, energy model, logic tree model, the SHE administrative model of accident with the accident investigation analytical technique, and multiple technique for investigation combinatory analysis is applicable to the investigation of complex accident; The investigation method of consideration incident order and influence factor thereof is convenient to the suggestion that proposes to prevent accident and take place once more and reduce risks.

Yang Jiaxuan proposes to adopt the electronic chart technology to set up waterborne traffic accident information system, attribute and spatial character according to casualty data, determine content characteristic based on the waterborne traffic risk (accident) management system of electronic chart, design accident Functions of Management System structure and technological development flow process, become an advanced effective technical means of marine traffic control, crash analysis.

Huang Zhi proposes by adopting the association analysis principle in the gray system theory, set up accident kind and the grey correlation matrix that causes culprit, Ship's Dimension size, reason position, place where the accident occurred and accident time of origin, and utilization the Taiwan Straits boats and ships marine accident statistical data, characteristics and rule that the Taiwan Straits have an accident are analyzed, provided new method for analyzing Maritime Traffic Accident.

Xu Guoyu proposes utilization grey correlation system and analyzed the casualty that all boats and ships and 300gt and above boats and ships take place in the waters respectively near the Taiwan Straits reaches, and to collision, hit a submerged reef or stranded, touch, catch fire or blast, mechanical fault, tilt or six class casualties such as topple, carried out grey correlation matrix operation and analysis.

Bear is peaceful by analyzing China and IMO and the world other countries classification, the difference of statistical method of traffic hazard on the water, point out the deficiency of China on classification, statistical method, point out classification, statistics lack of standardization, the imperfection of present China, lack comparability and accuracy accident.

He Yipei sorts out statistics and pursues the case analysis by 10 great fishing collision accidents that relate to that Ningbo-sea area, Zhoushan is taken place, and makes up and relates to the multiple reason structural model of fishing collision accident, has proposed early warning targetedly and has prevented pre-control means.

Mu Junmin proposes to overcoming data multidimensional in the casualty data storehouse, sparse, not congruent adverse effect, discern and find the new model and the inherent law thereof of casualty data effectively, propose the thought that the inland navigation craft traffic hazard was put comprehensively, analyzed to the application data digging technology in order.

Liu Zhengjiang is on the basis of collecting 100 collision accident survey reports, utilize the correlation rule in the data mining technology relation between human error and its influence factor is excavated, tentatively determined the corresponding relation between the human error and priming factors in the Collision Avoidance of Ships.

Wang Fengwu proposes the marine accident at the generation of high sea weather, association analysis method in the utilization gray system theory, set up the incidence matrix between high sea marine accident and its reason, carried out the grey correlation analysis of culprit, drawing the main cause that causes marine accident from quantitative angle is boats and ships unseaworthiness and human factor.

Yu Weihong proposes to have analyzed the meaning of setting up perils of the sea data warehouse, has proposed the snowflake model of perils of the sea data warehouse, and the result shows, utilizes data mining technology that perils of the sea historical data is done profound the analysis, can excavate a large amount of knowledge, for safety of maritime navigation is offered reference.

More than research to the accident reason research carried out more detailed elaboration, but still the research of shortage accident casualty quantitative test and prediction aspect.

Summary of the invention

At above-mentioned problems of the prior art, the present invention proposes a kind of waterborne traffic accident investigation analysis and Forecasting Methodology, by to the water surface traffic hazard analyze, set up the analyses and prediction model, reach and improve the prevention level, the purpose that the minimizing accident takes place.

To achieve these goals, the present invention adopts following technical scheme:

A kind of waterborne traffic accident investigation analysis and Forecasting Methodology that returns based on negative binomial, carry out as follows:

A) variable and data are selected: carried out the statistics and the correlation analysis of multitude of descriptive before modeling, determine the of paramount importance factor of fundamental sum the most that the accident that may influence takes place, final definite variable that can enter the several independent of model; Characteristics according to dependent variable and independent variable are selected the proper model type.When dependent variable is a counting variable, when promptly getting the number of incident generation, should consider usage count (Count Data) model.Model is applied to dependent variable to be the integer that disperses and to have that numerical value is little, to get zero number more and independent variable is the situation of the nominal variable of representation attribute mostly, need improve common least square method with the model form that can reflect this characteristics, EViews provides the multiple method of estimation of enumeration data, except that standard Poisson and negative binomial maximum-likelihood method (ML), also has lopar maximum-likelihood method (QML).When explanatory variable was qualitative variable, test or observations are called enumeration data, for example the waterborne traffic casualty investigation findings: accident played number, a shipwreck number, death and missing toll, number of injured people, direct economic loss etc.

B) model hypothesis: the common distribution pattern of qualitative variable has binomial distribution, multinomial distribution, Poisson distribution, negative binomial distribution etc.; Because it is any nonnegative integer that accident plays number, death and missing toll, number of injured people, it is typical enumeration data, disobey normal distribution, and may be to obey Poisson distribution or negative binomial distribution, so when quantitative analysis, adopt the counting model to be more suitable for than linear model, suppose that the discrete value of explained variable obeys certain Poisson distribution, its distribution function is:

$P(Y=y_i)=\frac{\exp (-\mathrm{\λ}){\mathrm{\λ}}^{y_i}}{y_i!},$ y _i＝1，2，3，Λ

E (y wherein _i)=λ, Var (y _i)=λ, promptly the average of stochastic variable y and variance are λ, if with X=(x ₁, x ₂, Λ, x _m) expression influence m the independent variable of λ, the Poisson regression model is exactly the regression model that concerns between the average λ of target variable y of description obedience Poisson distribution and the explanatory variable X, can be expressed as:

logλ＝Xβ

Wherein β is a parameter to be estimated, it can adopt iteration nonlinear weight least square method or maximum-likelihood method to estimate.At given x _iCondition under, y _iSigma-t be exactly:

$f\left(y_i\right|x_i,\mathrm{\β})=\frac{e^{-\mathrm{\λ}(x_i,\mathrm{\β})}\mathrm{\λ}(x_i,\mathrm{\β}{)}^{y_i}}{y_i!}$

If stochastic variable y _iAverage equal variance, the Poisson maximal possibility estimation is exactly to make peace effectively so, and actual accident time logarithmic data often had discrete (over-dispersion) feature, if stochastic variable y _iExcessively disperse, variance is greater than average, and promptly variance is greater than average.In these cases,, may underestimate the standard error of parameter, over-evaluate its level of significance, thereby in model, keep unnecessary explanatory variable, finally cause irrational result if still use the Poisson regression model.For eliminating this adverse effect, use negative binomial regression model (Negative Binomial Regression) to replace the Poisson regression model to estimate, by introducing the error term structure negative binomial distribution that gamma distributes, negative binomial regression model has been introduced an independently stochastic effects u in conditional mean μ, thereby expanded the Poisson regression model, that is: log μ _i=log λ _i+ logu _i, then the recurrence form of negative binomial regression model is:

logμ _i＝x _iβ+e _i

In the following formula, e _iBe stochastic error, exp (e _i) obey the Γ distribution, in negative binomial regression model, y _iTo x _i, u _iCondition distribute and still to be Poisson distribution:

$f\left(y_i\right|x_i,u_i)=\left[\exp (-{\mathrm{\λ}}_i{u}_i){\left({\mathrm{\λ}}_i{u}_i\right)}^{y_i}\right]/y_i!$

At this moment, stochastic variable y _iConditional mean and variance be respectively λ, λ (1+ η ²λ), η wherein ²=1/y _i, be that conditional variance is exceeded the measurement that the conditional mean degree is a degree of divergence.

C) parameter estimation and checking:

1) carry out parameter estimation with lopar maximum-likelihood function method (QML):

Lopar maximum-likelihood function method is could realize that its estimation is more sane under a series of distribution supposition, even the distribution specify error also can produce the consistent Estimation of correct definite condition Mean Parameters.Result's this robustness is similar to common recurrence: even residual error distribution abnormal, it also is consistent that ML estimates.In the common least square method, coherence request be conditional mean m (x, β)=x ' β, and in QML, coherence request have m (x, β)=exp (x ' β).

The method of standard error of estimate is to calculate with the contrary of information matrix, unless but the condition that does not possess consistance y distribute specify correct.Even yet specify error is still possible with a kind of sane mode standard error of estimate.

2) parameter estimation check:

The parameter estimation of discrete data counting model is estimated to realize that the check of estimated parameter is mainly checked by Wald and finished by maximum likelihood.Parametric test helps that the average of sample population is made some infers that the Wald check is similar to the t check in the linear regression model (LRM), therefore often is called as broad sense t check.Being assumed to be of Wald check: H ₀: β _j=0.Setting up the t statistic is:

$t_{{\mathrm{\β}}_j}=\frac{{\widehat{\mathrm{\β}}}_j}{\mathrm{se}\left({\widehat{\mathrm{\β}}}_j\right)}$

Wherein,

Be the estimates of parameters that will check, It is the standard deviation of a row estimates of parameters.The t statistic is the approximate standardized normal distribution of obeying under the situation of large sample.

3) introducing of pressing goodness of fit calibration, checking and the variable of following criterion model is differentiated:

(1) Pesudo R ²Statistic is carried out the test of fitness of fot, R to model ²The bigger explanation match of value gets better;

(2) Log likelihood (LL) logarithm maximum likelihood function value is based on the statistic that the maximum likelihood estimation obtains, and the log-likelihood value is used to illustrate the accuracy of model, and big more explanation model is accurate more;

(3) conspicuousness of t estimated parameter is in 5% level;

(4) ratio of Pearson chi-square value and degree of freedom is between 0.8-1.2;

(5) Akaike ' s information criteria (AIC) criterion is used for the quality of evaluation model, generally requires the AIC value the smaller the better.

The analyses and prediction model that uses technique scheme to obtain, owing to introduce the decision rule of the introducing of the calibration of model fitting goodness, checking and variable in the modeling process, make the forecast model of final acquisition have the goodness of fit preferably, thereby the precision of prediction of model is improved, for the analyses and prediction of water surface traffic hazard provide a kind of good method.

Embodiment

In order to make technological means of the present invention, creation characteristic, to reach purpose and effect is easy to understand,, further set forth the present invention below in conjunction with embodiment.

The present invention has determined the of paramount importance factor of fundamental sum the most that the accident that may influence takes place from the principle of generality, simplicity, practicality on the basis of literature reading, data preparation analysis and correlative study.The waterborne traffic accident be result of various factor comprehensive action, each influence factor is interrelated, and the bigger independent variable of correlativity can not enter model simultaneously.Therefore, before modeling, carry out the statistics and the correlation analysis of multitude of descriptive, finally determine 11 separate variablees, as shown in table 1.Choose the injures and deaths number as output variable, choose parameter registration of ships ground that the accident that influences takes place, accident pattern, Ship Types, accident occurrence positions etc. as explanatory variable, these 5 explanatory variables have 2,3,3,3 and 2 risk levels respectively, totally 36 risk levels carry out match at above risk level utilization EVIEWS software to data.

Table 1

At first adopt the negative binomial distribution form to carry out regression forecasting, whole independents variable are brought into model, regression result shows, some variable is inapparent on statistical model, can not refuse its coefficient and be 0 hypothesis, the regression coefficient of some variable runs counter to convention, simultaneously, find because multicollinearity too much appears in qualitative index, the present invention takes progressively to return the elimination multicollinearity, respectively the match explained variable is with respect to the simple regression of each explanatory variable, and with the goodness of fit R of each regression equation ²Sort according to size order; Then with R ²Big explanatory variable adds in the model to be estimated, carries out the t check of estimates of parameters according to the model estimated result, if the t check significantly, then keeps, otherwise rejects this variable, constantly repeats this process up to adding all significant variablees.The final registration of ships ground a1 that keeps removes a2, a3, keeps 2 accident pattern variable b1, b3, and 2 Ship Types variable c2, c3,2 accident waters location variable d1, d2, accident time of origin only use e1 in model, rebulid model.Utilization EVIEWS software carries out match to data, and fitting result is as shown in table 2.

Table 2

α is the regression parameter of negative binomial distribution, is used for representing the mistake dispersion degree of data, the big more data of α discrete more (variance is greater than average), and α is 0 o'clock, data are obeyed Poisson distribution.Odds choosing between model is criterion with AIC statistic, log likelihood, and by the recurrence index of 2 kinds of distributed models shown in the comparison sheet 2, the forecast model of negative binomial distribution form is better as can be seen.Relatively the match situation of two models shows that the goodness of fit of negative binomial regression model is better than the Poisson regression model.

More than show and described ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that describes in the foregoing description and the instructions just illustrates principle of the present invention; the present invention also has various changes and modifications without departing from the spirit and scope of the present invention, and these changes and improvements all fall in the claimed scope of the invention.The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (1)

1. based on the waterborne traffic accident investigation analysis and the Forecasting Methodology of negative binomial recurrence, carry out as follows:

A) variable and data are selected: carried out the statistics and the correlation analysis of multitude of descriptive before modeling, determine the of paramount importance factor of fundamental sum the most that the accident that may influence takes place, final definite variable that can enter the several independent of model; Characteristics according to dependent variable and independent variable are selected the proper model type, when dependent variable is a counting variable, when promptly getting the number of incident generation, consider usage count (Count Data) model;

B) model hypothesis: the common distribution pattern of qualitative variable has binomial distribution, multinomial distribution, Poisson distribution, negative binomial distribution etc.; Because it is any nonnegative integer that accident plays number, death and missing toll, number of injured people, it is typical enumeration data, disobey normal distribution, and may be to obey Poisson distribution or negative binomial distribution, so when quantitative analysis, adopt the counting model to be more suitable for than linear model, suppose that the discrete value of explained variable obeys certain Poisson distribution, its distribution function is:

$P(Y=y_i)=\frac{\exp (-\mathrm{\λ}){\mathrm{\λ}}^{y_i}}{y_i!},$ y _i＝1，2，3，Λ

E (y wherein _i)=λ, Var (y _i)=λ, promptly the average of stochastic variable y and variance are λ, if with X=(x ₁, x ₂, Λ, x _m) expression influence m the independent variable of λ, the Poisson regression model is exactly the regression model that concerns between the average λ of target variable y of description obedience Poisson distribution and the explanatory variable X, can be expressed as:

logλ＝Xβ

Wherein β is a parameter to be estimated, it can adopt iteration nonlinear weight least square method or maximum-likelihood method to estimate, at given x _iCondition under, y _iSigma-t be exactly:

$f\left(y_i\right|x_i,\mathrm{\β})=\frac{e^{-\mathrm{\λ}(x_i,\mathrm{\β})}\mathrm{\λ}(x_i,\mathrm{\β}{)}^{y_i}}{y_i!}$

If stochastic variable y _iAverage equal variance, the Poisson maximal possibility estimation is exactly to make peace effectively so, and actual accident time logarithmic data often had discrete (over-dispersion) feature, if stochastic variable y _iExcessively disperse, variance is greater than average, be that variance is greater than average, in these cases, if still use the Poisson regression model, may underestimate the standard error of parameter, over-evaluate its level of significance, thereby in model, keep unnecessary explanatory variable, finally cause irrational result, for eliminating this adverse effect, use negative binomial regression model (Negative Binomial Regression) to replace the Poisson regression model to estimate, by introducing the error term structure negative binomial distribution that gamma distributes, negative binomial regression model has been introduced an independently stochastic effects u in conditional mean μ, thereby expanded the Poisson regression model, that is: log μ _i=log λ _i+ logu _i, then the recurrence form of negative binomial regression model is:

logμ _i＝x _iβ+e _i

In the following formula, e _iBe stochastic error, exp (e _i) obey the Γ distribution, in negative binomial regression model, y _iTo x _i, u _iCondition distribute and still to be Poisson distribution:

$f\left(y_i\right|x_i,u_i)=\left[\exp (-{\mathrm{\λ}}_i{u}_i){\left({\mathrm{\λ}}_i{u}_i\right)}^{y_i}\right]/y_i!$

At this moment, stochastic variable y _iConditional mean and variance be respectively λ, λ (1+ η ²λ), η wherein ²=1/y _i, be that conditional variance is exceeded the measurement that the conditional mean degree is a degree of divergence;

C) parameter estimation and checking:

1) carry out parameter estimation with lopar maximum-likelihood function method (QML): lopar maximum-likelihood function method is could realize under a series of distribution supposition, its estimation is more sane, even the distribution specify error also can produce the consistent Estimation of correct definite condition Mean Parameters, result's this robustness is similar to common recurrence: even residual error distribution abnormal, it also is consistent that ML estimates, in the common least square method, coherence request is conditional mean m (x, β)=x ' β, and in QML, coherence request have m (x, β)=exp (x ' β);

2) parameter estimation check: the parameter estimation of discrete data counting model is estimated to realize by maximum likelihood, the check of estimated parameter is mainly checked by Wald and is finished, parametric test helps the average of sample population is made some deductions, the Wald check is similar to the t check in the linear regression model (LRM), therefore often be called as broad sense t check, what Wald checked is assumed to be: H ₀: β _j=0, set up the t statistic and be:

$t_{{\mathrm{\β}}_j}=\frac{{\widehat{\mathrm{\β}}}_j}{\mathrm{se}\left({\widehat{\mathrm{\β}}}_j\right)}$

Wherein,

Be the estimates of parameters that will check, Be the standard deviation of a row estimates of parameters, the t statistic is the approximate standardized normal distribution of obeying under the situation of large sample, carries out the t check of estimates of parameters according to the model estimated result, if the t check significantly, then keep, otherwise reject this variable, constantly repeat this process up to adding all significant variablees;

3) introducing of carrying out goodness of fit calibration, checking and the variable of model by following criterion is differentiated:

(1) Pesudo R ²Statistic is carried out the test of fitness of fot, R to model ²The bigger explanation match of value gets better;

(2) Log likelihood (LL) logarithm maximum likelihood function value is based on the statistic that the maximum likelihood estimation obtains, and the log-likelihood value is used to illustrate the accuracy of model, and big more explanation model is accurate more;

(3) conspicuousness of t estimated parameter is in 5% level;

(4) ratio of Pearson chi-square value and degree of freedom is between 0.8-1.2;

(5) Akaike ' s information criteria (AIC) criterion is used for the quality of evaluation model, generally requires the AIC value the smaller the better.