CN107657377A

CN107657377A - A kind of public transportation lane policy evaluation method returned based on breakpoint

Info

Publication number: CN107657377A
Application number: CN201710881294.7A
Authority: CN
Inventors: 钟绍鹏; 王仲; 程荣; 刘佳超; 邹延权; 李旭丰
Original assignee: Dalian University of Technology
Current assignee: Dalian University of Technology
Priority date: 2017-09-26
Filing date: 2017-09-26
Publication date: 2018-02-02
Anticipated expiration: 2037-09-26
Also published as: CN107657377B

Abstract

The invention provides a kind of public transportation lane policy evaluation method returned based on breakpoint, belong to public transportation lane policy evaluation technical field.Breakpoint recurrence is carried out to the speed of two kinds of different type motor vehicles using measured data, with reference to the catastrophe of outcome variable before and after graphical analysis discontinuous point, influence of the qualitative assessment special lane to bus and public vehicles speed, city traffic management department is aided in formulate and optimize dedicated bus lanes policy, this method cost is very low, the conclusion drawn is directly effective, has certain promotional value.

Description

A kind of public transportation lane policy evaluation method returned based on breakpoint

Technical field

The invention belongs to Urban Traffic Planning technical field, is related to public transportation lane policy evaluation field, more particularly to disconnected The technical methods such as point recurrence.

Background technology

For the assessment of public transportation lane effect, existing research method mainly have practical experience summary, microscopic traffic simulation, Three kinds of traffic assignation theory analysis.Cox exists《RESERVED BUS LANES IN DALLAS,TEXAS》It has studied and reach in one text The applicable cases of Lars city public transportation lane；ThamizhArasan and P.Vedagi exist《Microsimulation Study of the Effect of Exclusive Bus Lanes on Heterogeneous Traffic Flow》Constructed in one text Simulation model of microscopic HETEROSIM under new mixed traffic stream mode simulates the motor line in reality as spy Point, so as to assess public transportation lane effect；Shuguang Li and YongfengJu exist《Evaluation of Bus- Exclusive Lanes》A kind of multimode Dynamic traffic assignment model is proposed in one text to assess the effect of public transportation lane.

Summary of experience method practicality is stronger, may be directly applied to example；Microscopic traffic simulation tries close to random Test, but due to actual conditions can not be reflected, it is impossible to the means as evaluation real effect；Traffic assignation theory is then more focused on reason By analysis, real case is difficult to apply to, and the assumed condition of method can not reflect road network time of day.By contrast, it is based on The research that real example data are assessed special lane Policy Effect is also very insufficient.

Breakpoint proposed by the present invention returns, and is a kind of statistical research method based on real example data, can pass through reality The measured data of road is evaluated special lane true effect, and existing research is carried out from the angle of practical application effect Supplement, while the checking of theory analysis can be carried out.

The content of the invention

The technical problem to be solved in the present invention is to propose that a kind of public transportation lane Policy Effect based on measured data is assessed Method, quantify influence of the public transportation lane to bus and public vehicles speed, and then propose corresponding suggest.

Technical scheme：

A kind of public transportation lane policy evaluation method returned based on breakpoint, step are as follows：

(1) variable determination and hypothesis testing

Research object is peak period public transportation lane, only public transit vehicle is opened in daily specific time period, in opening Moment and finish time produce discontinuous point, and the front and rear only path resource distribution of breakpoint produces change；

Time t is driving variable, and its value directly affects the change of path resource distribution, is observable；It is small when the time When the open moment, public transportation lane is identical with common track, is used for any vehicle；It is public when the time exceeding the open moment Special lane is handed over only to allow bus to use, other public vehicles only allow using other common tracks；

Road average-speed S is outcome variable, S^bRepresent the average speed of bus, S^cRepresent the average speed of taxi；

The key point that breakpoint returns is disposition effect valuation, and the expression disposed in regression model is by introducing one two Member disposal variable EBL_tCome what is realized, the binary variable shares 0 and 1 two value.1 represents public transportation lane in when opening Section, research object receive disposal, and 0 expression public transportation lane is closed, and research object does not receive disposal；

Under the urban traffic status of reality, the time that bus and public vehicles reach assessment section has randomness, Driver can not accurately control arrival time deliberately to evade or receive disposal, meet effective first bar of breakpoint homing method Part：Research object has no ability to accurately control the driving variable around discontinuous point；Breakpoint homing method effective second Individual condition：Other control variables for influenceing outcome variable must be continuous at discontinuous point, due to the condition of continuity of these variables It is often bad directly to verify, so first being proposed before recurrence successional it is assumed that verifying that assumed condition is by regression result again No establishment；

(2) graphical analysis

Before breakpoint recurrence is carried out, the data being collected into are handled, drawn with speed s (m/s) as ordinate, when Between t (min) be abscissa scatter diagram, then data point is fitted.When more than the global data and mixed and disorderly, using Bin side Method is handled global data, is removed the noise in global data, is made the curve of fitting smoother.By the data point after conversion Carry out linear or polynomial regression, it is possible to which preliminary observation whether there is the jump of data at breakpoint, if it does not, connecing down The regression result come may be unreliable；

(3) it is global to return

Underlying parameter regression model

S_t=alpha+beta₀·EBL_t+β₁t+β₂t·EBL_t+γX_t+ε_t (1)

The underlying parameter regression model represents to open average operation of the front and rear vehicle in target road section in public transportation lane Speed；Wherein, t represents the number of minutes since breakpoint, to drive variable, the t=0 at discontinuous point；Dependent variable S_tIt is at t points Target road section average speed in clock；EBL_tIt is a binary disposal variable, has 0 and 1 two kind of value, if discontinuous point t=0 is Special lane opens the moment, then when the durations of t ＞ 0 are 1, the vehicle on expression section receives the disposal that track resource allocation changes, and works as t The durations of ＜ 0 are 0, and vehicle does not receive the disposal of track resource allocation on expression section；If discontinuous point t=0 closes for special lane Moment, then when the durations of t ＞ 0 are 0, represent that track resource allocation returns to normal condition, when the durations of t ＜ 0 are 1, represent, represent public Special lane is handed over also in open state.X_tFor the vector of other control variable compositions；∈_tFor white noise.

The coefficient of each variable in regression model, embody influence degree of each variable to outcome variable；Wherein, return It is β to return most important target component₀, its value directly reflects the size of the disposition effect at discontinuous point.β₁And β₂It is that driving becomes T regression coefficient is measured, outcome variable (speed) is with the entire change for driving variable (time) before and after its size determines discontinuous point Trend.γ is the vector of the regression coefficient composition of other control variables, reflects other influences of control variable to outcome variable Degree, although not being the main object of research, the change when size and Robustness Test of A of its value can verify that breakpoint returns It is assumed that verify other control variables it is whether relevant with disposition effect.

Taxi and bus are separated, calculate both average speed respectively, the model applied when returning is also Difference, it is mainly reflected in the selection of other control variables；For taxi, there is two kinds of carrying and zero load in it when runing State, speed is fast under passenger carrying status in theory, so carrying to be used for one in other control variables；In urban road On, when public transportation lane is not open, bus and public vehicles mix row, and bus has an impact to taxi, if on section Bus quantity is excessive, and bus relative velocity is smaller, and the phenomenon that lane change and on-board and off-board out of the station wait be present, to hiring out The operation of car is had an impact, and the quantity of bus and taxi is used for into a control variable；In addition, road in the unit interval Taxi and bus Floating Car quantity in section also serve as controlling variable；Linear regression model (LRM) for taxi is：

In formula：

P, γ_P--- taxi ratio and its regression coefficient in the unit interval；

C, γ_C--- taxi Floating Car quantity and its regression coefficient in the unit interval；

B, γ_B--- public transport Floating Car quantity and its regression coefficient in the unit interval；

R, γ_R--- bus and taxis quantity ratio and its regression coefficient in the unit interval.

Recurrence for bus, other control variable to be public transport Floating Car quantity, hire out Floating Car quantity and both Quantity ratio, therefore be for the regression model of bus：

In formula：

C, γ_C--- Floating Car quantity and its regression coefficient are hired out in the unit interval；

R, γ_R--- taxi and bus quantity ratio and its regression coefficient in the unit interval.

Regression result obtains the regression coefficient of each variable and corresponding standard error, by comparing regression coefficient and standard error Size evaluate the effect of disposal；The positive and negative and relative size of regression coefficient is reflected to influence of the dependent variable to outcome variable Degree, when regression coefficient all very littles or it is stable within the specific limits when, it is believed that these control variables are right in the range of selected data Disposition effect size is not related, it was demonstrated that the reliability of breakpoint regressive appraisement result；

After global linear regression, typically also need to add multiple item progress polynomial regression, in order to more preferable Ground fitting result variable versus time curve, while can also be as a part for Robustness Test of A.Can be with when returning Increase the high-order term of time t on the basis of direct-on-line regression model.The global polynomial of degree n regression expression of bus is (4), the global polynomial of degree n regression expression of taxi is (5)：

(4) local linear smoothing

Assuming that t₀For discontinuous point, in discontinuous point both sides, selection width is returned for h data point, and what it is less than discontinuous point is Control group, it is disposal group more than discontinuous point.It is assumed that the regression function of disposal group (on the right side of discontinuous point) is linear forms：

S_i=α_r+β_r·t_i+ε_i (6)

The target of recurrence be by discontinuous point on the right side of data be worth to value at discontinuous point, due to different data points Distance to breakpoint is different, and the nearlyer influence to estimating point value of spacing should be bigger, so needing to each data point Different weights is assigned, nearer apart from discontinuous point, weight is bigger, otherwise weight is smaller, and this weight distribution passes through specific core Function K is realized.Final choice (α_r, β_r) make it that the data on the right side of breakpoint obtain local weighted quadratic sum minimum for value, i.e.,

So, point estimate of the disposal group at discontinuous point is

S_r(t₀)=α_r+β_r·(t₀-t₀)=α_r (8)

Similarly control group can also obtain regression coefficient

It is so as to obtain estimate of the control group at discontinuous point

S_l(t₀)=α_l+β_l·(t₀-t₀)=α_l (10)

Final disposition effect valuation is

τ=α_r-α_l (11)

(5) Robustness Test of A of valuation

When carrying out breakpoint recurrence, Robustness Test of A is carried out, there is certain stability to test the valuation of disposition effect And reliability；Robustness Test of A is broadly divided into two major classes：

1) it is directed to the Robustness Test of A of global polynomial regression

It is mainly real by changing the degree of polynomial and change data scope for the Robustness Test of A of global polynomial regression It is existing；

Global polynomial regression can carry out valuation using the data of breakpoint distant place, thus by the data influence away from breakpoint It is larger, to examine the reliability of disposition effect valuation, it is necessary to constantly reduce window width centered on breakpoint, make the data area used The sufficiently small width being reduced to around breakpoint.Disposition effect valuation under the different pieces of information scope difference degree of polynomial is compared Compared with if data area and the degree of polynomial change, disposition effect valuation can also be maintained in certain scope, fluctuation Less, illustrate that valuation has certain reliability；

2) it is directed to the Robustness Test of A of local linear smoothing

Mainly realized for the Robustness Test of A of local linear smoothing by changing kernel function type and amount of bandwidth；

The type of kernel function determines the weighted value of valuation point ambient data, in this method mainly using rectangle kernel function, Triangle kernel function and Ye Panieqi Nico husbands kernel function carry out Robustness Test of A；The selection of bandwidth needs to reach accuracy and deviation Balance.Disposition effect valuation under different IPs type function and different bandwidth is compared, if kernel function type and band When width changes, putting effect valuation can also maintain in certain scope, and fluctuation is little, illustrate that the valuation can with certain By degree；

In addition, the special lane policy driving variable that the present invention studies is the time, for policy execution person and traffic driver For, the time is difficult to carry out unification, that is to say, that disposal might not be just in fixed opening moment, this meeting at the time of generation The valuation of disposition effect is set to produce certain deviation.Thus when carrying out Robustness Test of A, it is necessary to which front and rear adjustment breakpoint location enters Row regressive appraisement, the situation of change of valuation is investigated to determine the actual position of breakpoint.

Beneficial effects of the present invention：Breakpoint based on real example data returns, using the measured data of real road to special Road true effect is evaluated, and city traffic management department can be aided in formulate and optimize dedicated bus lanes policy, Er Qiefang Method cost is very low, and the conclusion drawn is directly effective, has certain promotional value.

Brief description of the drawings

Fig. 1 is that breakpoint returns application schematic diagram.

Fig. 2 is the electronic map of target road section.

Fig. 3 (a) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 1, polynomial fitting Number is 1.

Fig. 3 (b) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 1, polynomial fitting Number is 2.

Fig. 3 (c) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 1, polynomial fitting Number is 3.

Fig. 3 (d) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 2, polynomial fitting Number is 1.

Fig. 3 (e) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 2, polynomial fitting Number is 2.

Fig. 3 (f) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 2, polynomial fitting Number is 3.

Fig. 3 (g) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 3, polynomial fitting Number is 1.

Fig. 3 (h) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 3, polynomial fitting Number is 2.

Fig. 3 (i) is that public transportation lane opens moment bus breakpoint fitted figure picture, box width 3, polynomial fitting Number is 3.

Note：In Fig. 3 (a) -3 (i), t=0 is discontinuous point 7:30AM, t=1 7:31AM, t=-1 7:29AM, with such Push away.

Fig. 4 (a) is from 7 by breakpoint:30AM shifts to an earlier date the bus breakpoint fitted figure picture that 1min is obtained.

Fig. 4 (b) is from 7 by breakpoint:30AM shifts to an earlier date the bus breakpoint fitted figure picture that 5min is obtained.

Fig. 4 (c) is from 7 by breakpoint:30AM shifts to an earlier date the bus breakpoint fitted figure picture that 7min is obtained.

Fig. 4 (d) is from 7 by breakpoint:30AM shifts to an earlier date the bus breakpoint fitted figure picture that 10min is obtained.

Fig. 5 (a) is public transportation lane close moment bus breakpoint fitted figure picture, box width 1, polynomial fitting Number is 1.

Fig. 5 (b) is public transportation lane close moment bus breakpoint fitted figure picture, box width 1, polynomial fitting Number is 2.

Fig. 5 (c) is public transportation lane close moment bus breakpoint fitted figure picture, box width 1, polynomial fitting Number is 3.

Fig. 5 (d) is public transportation lane close moment bus breakpoint fitted figure picture, box width 2, polynomial fitting Number is 1.

Fig. 5 (e) is public transportation lane close moment bus breakpoint fitted figure picture, box width 2, polynomial fitting Number is 2.

Fig. 5 (f) is public transportation lane close moment bus breakpoint fitted figure picture, box width 2, polynomial fitting Number is 3.

Fig. 5 (g) is public transportation lane close moment bus breakpoint fitted figure picture, box width 3, polynomial fitting Number is 1.

Fig. 5 (h) is public transportation lane close moment bus breakpoint fitted figure picture, box width 3, polynomial fitting Number is 2.

Fig. 5 (i) is public transportation lane close moment bus breakpoint fitted figure picture, box width 3, polynomial fitting Number is 3.

Note：In Fig. 5 (a) -5 (i), t=0 is discontinuous point 9:30AM, t=1 9:31AM, t=-1 9:29AM, with such Push away.

Fig. 6 (a) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 1, polynomial fitting Number is 1.

Fig. 6 (b) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 1, polynomial fitting Number is 2.

Fig. 6 (c) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 1, polynomial fitting Number is 3.

Fig. 6 (d) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 2, polynomial fitting Number is 1.

Fig. 6 (e) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 2, polynomial fitting Number is 2.

Fig. 6 (f) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 2, polynomial fitting Number is 3.

Fig. 6 (g) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 3, polynomial fitting Number is 1.

Fig. 6 (h) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 3, polynomial fitting Number is 2.

Fig. 6 (i) is that public transportation lane opens moment taxi breakpoint fitted figure picture, box width 3, polynomial fitting Number is 3.

Note：In Fig. 6 (a) -6 (i), t=0 is discontinuous point 7:30AM, t=1 7:31AM, t=-1 7:29AM, with such Push away.

Fig. 7 (a) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 1, polynomial fitting Number is 1.

Fig. 7 (b) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 1, polynomial fitting Number is 2.

Fig. 7 (c) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 1, polynomial fitting Number is 3.

Fig. 7 (d) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 2, polynomial fitting Number is 1.

Fig. 7 (e) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 2, polynomial fitting Number is 2.

Fig. 7 (f) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 2, polynomial fitting Number is 3.

Fig. 7 (g) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 3, polynomial fitting Number is 1.

Fig. 7 (h) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 3, polynomial fitting Number is 2.

Fig. 7 (i) is public transportation lane close moment taxi breakpoint fitted figure picture, box width 3, polynomial fitting Number is 3.

Note：In Fig. 7 (a) -7 (i), t=0 is discontinuous point 9:30AM, t=1 9:31AM, t=-1 9:29AM, with such Push away.

Fig. 8 is the overview flow chart of breakpoint homing method.

Fig. 9 is regression data processing flow chart.

Embodiment

Below in conjunction with the embodiment of the technical scheme narration present invention, and simulate the implementation result of invention.

1st, the selection of target road section and the preparation of regression data

It is target road section to choose positioned at the deep east southeast road of In Luohu District of Shenzhen Municipal, and its public transportation lane is arranged on road outermost Side, open hour are bigger 7 of the daily volume of traffic:30—9:30 and 17:30—19:30.Pass through the bus routes in section Totally 16, there are two roadside formula bus stops.Fig. 2 is target road section electronic map.

Extract on June 9th, 2014 to five days on the 13rd 6:00 to 11:In 00 5 hours, taxi and bus are in depth The data point on east southeast road carries out the calculating of average speed as basic data is returned in SPSS softwares.Calculated according to Floating Car Model, selection unit time period are 1min, calculate the Road average-speed of bus per minute in 5 hours and taxi, and Count bus and taxis quantity per minute, the cabin factor of taxi.

Moment and finish time are opened as breakpoint progress breakpoint regression analysis, global data width using public transportation lane respectively For each 1.5h before and after breakpoint.7:30 be breakpoint, data area 6:00 to 9:00, each 90min before and after breakpoint.Table 1 to table 4 is Hire a car, compare before and after bus regression data breakpoint.

The taxi regression data breakpoint of table 1 is front and rear relatively (with 7:30 be breakpoint)

The taxi regression data breakpoint of table 2 is front and rear relatively (with 9:30 be breakpoint)

The bus regression data breakpoint of table 3 is front and rear relatively (with 7:30 be breakpoint)

The bus regression data breakpoint of table 4 is front and rear relatively (with 9:30 be breakpoint)

2nd, breakpoint regression analysis

(1) bus regression result is analyzed

For the situation that breakpoint occurs from figure, the image of global data, and logarithm are depicted before recurrence Strong point is fitted.Fig. 3 (a) -3 (i) show respectively the road under different casing quantity and different polynomial fitting times conditions Section average speed changes with time, the bus average speed of corresponding the number of minutes of each point representative in figure, and the line in figure is The time trend line of fitting.Fig. 3 (a), 3 (b), the casing quantity of 3 (c) are 90, box width 1min；Fig. 3 (d), 3 (e), 3 (f) casing quantity is 45, box width 2min；Fig. 3 (g), 3 (h), the casing quantity of 3 (i) are 30, and box width is 3min.Fig. 3 (a), 3 (d), the polynomial fitting number of 3 (g) are 1；Fig. 3 (b), 3 (e), the polynomial fitting number of 3 (h) are 2； Fig. 3 (c), 3 (f), the polynomial fitting number of 3 (i) are 3.By this nine images, can be intuitive to see very much：Except linear Outside three figures (Fig. 3 (a), 3 (d), 3 (g)) of fitting, other secondary and cubic polynomial fitted figures are all shown, Public transportation lane opens the moment (7:30AM), the average speed of bus, which experienced, is once lifted, and lifting amplitude is about 0.5- 0.8m/s。

We have found that when casing quantity reduces (i.e. box width increases), song of the scatterplot data closer to polynomial regression Line.In the case where not introducing other control variables, the degree of polynomial used with fitting increases (increasing to 3 times from 1 time), The breakpoint being mutated upwards is gradually obvious, and this shows that the average speed of target road section is with the time when not considering other control variables Change is not linear.Be fitted using secondary above multinomial and obvious breakpoint occur, but only by image not The presence of breakpoint can be absolutely proved, because the degree of polynomial that fitting uses is higher, is more likely to occur the situation of data over-fitting. Also possible in the presence of one kind, breakpoint is not 7:30AM occurs on time, and public vehicles may be opened to evade punishment in Policy Conditions The moment begin before it is avoided that driving into public transportation lane, causes breakpoint to occur in advance, but the time in advance can't be oversize.Fig. 4 (a), 4 (b), 4 (c), 4 (d) are by original breakpoint 7 respectively:30AM shifts to an earlier date the line obtained after 1min, 5min, 7min and 10min Property fitted figure picture, find and compare and do not change significantly (occur unstable small size downward be mutated) before, this can be with Illustrate, because breakpoint causes the unconspicuous possibility of linear fit mutation very low in advance, not considering.

In order to determine whether that the disposition effect at breakpoint whether there is, the OLS for having carried out four global datas successively is (general Logical least square method) experiment is returned, regression result is shown in Table 5.OLS (1) is common least square method linear regression, has only introduced two Member disposal variable and time driving variable, obtained disposition effect value is 0.006, is represented after breakpoint, the section of bus There is 0.006m/s lifting in average speed, and this numerical value can not prove the necessary being of disposition effect close to zero.OLS(2) Return on the basis of OLS (1), introduce target road section public transport per minute and hire out Floating Car quantity and the two ratio three Variable, obtained disposition effect result are -0.03, are illustrated after other control variables are considered, disposition effect is negative on the contrary Value, but numerical value is too small, can not also prove the presence of disposition effect, but confirmed the result of graphical analysis：Linear regression fit Obvious breakpoint can not be observed.When OLS (3) is returned, time t quadratic term is introduced on the basis of OLS (2), is obtained Regression result such as table (3) arrange, disposition effect now is 0.34, relatively before linear regression have and be obviously improved, it is overall R side's value (0.363) increase of recurrence, illustrate for global data, the recurrence of quadratic polynomial is imitated than linear regression fit Fruit is more preferable.OLS (4), which is returned, increases to the multinomial on time t 3 times, and obtained result is returned with quadratic polynomial and differed Less (0.212), it is believed that the valuation of disposition effect has tended towards stability.

The public transport car data overall situation regression result of table 5 is (with 7:30AM is breakpoint)

In addition, the regression coefficient combination image of its dependent variable can also reflect some information in global recurrence.Four times OLS is complete It is all negative value that office, which returns obtained " time " variable regression coefficient, is illustrated before breakpoint, with the operation of the increase bus of time Speed gradually reduces, and illustrates that the traffic of target road section progresses into the morning peak of commuting, traffic starts to be deteriorated.Image This point is confirmed, the tendency of fitted trend line constantly declines before breakpoint." time × disposal variable " variable can represent breakpoint Speed changes over time the change situation of trend afterwards, and the valuation that preceding linear regression twice obtains is negative value, illustrates that public transport is special After being opened up with road, speed is accelerated with the decline of time, and traffic deteriorates, such as Fig. 3 (a), 3 (d), 3 (g), straight line after breakpoint Slope diminishes；Then polynomial regression result twice shows, speed declines with the time and slowed down after breakpoint, and traffic has changed It is kind, but overall downward trend does not change, and figure also reflects similar situation.But from numerical values recited, " when Between " and " time × disposal variable " the two variables coefficient value all very littles, even if there is certain change increasedd or decreased to become Gesture, also very faint, this can illustrate that public transportation lane has some effects to lifting public transport operation speed, but effect and little, together When illustrate before and after breakpoint in minizone outcome variable with driving variable variation tendency it is not significant change, from speed The traffic reflected does not produce great variety, and certain degree is integrally simply offset downward after breakpoint, this side Face reflects disposition effect caused by only because special lane opens up the change of this single factors.

The regression coefficient value of " taxi number per minute " and " bus number per minute " two variables is just, to illustrate bus Speed and bus and taxis quantity have positive correlation, but due to numerical value all very littles, it is believed that in the research period Interior Floating Car quantity influences and little on the speed of service of bus.The quantity of two kinds of motor vehicles is also than the regression coefficient of variable On the occasion of being approximately equal to 0.04, the speed of service of bus and two kinds of motor vehicle relative populations liken to being proportionate, but due to numerical value simultaneously Less, influence also very faint.These results all illustrate, are opened in public transportation lane around the moment in the range of 1.5h, bus Operation is influenceed and little by taxi.Meanwhile we can be understood as in the range of global data, other controls of introducing are returned Influence of the variable processed to outcome variable is all very faint, and this also just has the reasons why certain to illustrate that disposition effect is that public transportation lane opens Caused by this single factors changes.

In order to further examine the robustness of disposition effect valuation, we carried out again different pieces of information scope once with two The recurrence experiment of order polynomial.Regression result such as table 6.It can be sent out by the disposition effect result under the conditions of more different recurrence Existing, as each 60min before and after data area is breakpoint, the disposition effect valuation difference that two kinds of regression equation numbers obtain is minimum, Illustrate the size of disposition effect during 60min data bandwidths is not influenceed by number is returned；But when data bandwidth becomes big or becomes small, The result that linear regression obtains is respectively less than quadratic regression result, and the result of quadratic regression is closer to the knot under 60min bandwidth Fruit, this shows again when carrying out OLS recurrence, and the result for selecting high-order moment to obtain is better than linear regression, confidence level It is higher, and change little with the change of data area, it is believed that regressive appraisement is sane believable.Compared to the overall situation The result of (table 5) is returned, the disposition effect valuation in the range of small data is bigger, and the discovery of this result is not unexpected, because making The valuation obtained with polynomial regression can be had a great influence by away from breakpoint data, and only constantly be contracted to data area to break It can just be obtained closer to real disposition effect value in certain section around point.

Bus data regression results contrast under the different pieces of information scope of table 6 is (with 7:30AM is breakpoint)

(bus is with 7 for the disposition effect valuation of the local regression of table 7:30AM is breakpoint)

After traditional OLS parametric regressions have been carried out, we have also carried out under different condition (different kernel functions, different band It is wide) local linear smoothing, the desired value of recurrence is disposition effect.Regression result such as table 7.Disposed in contrast table under different condition The difference of effect, it can be found that：When bandwidth is excessive, obtained disposition effect valuation very little, almost it is considered that disposition effect It is not present；And when bandwidth is gradually reduced, valuation starts to increase, and can stablize in the range of 0.55 to 0.7, is returned with OLS before It is close to sum up fruit, shows that parametric regression and non parametric regression obtain result and have similitude, thus there is certain reliability.

Then to public transportation lane close moment 9:30AM, identical graphical analysis and regression analysis are carried out.Fig. 5 (a)- The presence of breakpoint can be significantly found in 5 (i), even if changing the degree of polynomial and casing quantity, the mutation at breakpoint is all compared It is relatively stable.Linear fit image intuitively shows the slope variation of Trendline before and after breakpoint, and speed is constantly lifted before breakpoint, and Speed tends to be steady after breakpoint；Secondary fitted figure picture three times all shows that speed is in rising trend before breakpoint, and fast after breakpoint There is slight decline in degree.

Return the presence that obtained data result (table 8, table 9, table 10) also demonstrates breakpoint, breakpoint forward backward averaging speed drop Low about 0.6m/s, and data, about close to breakpoint, obtained disposition effect value is bigger, and maximum is about -0.8, this phenomenon With before with 7:30AM is that the result of breakpoint is similar.Compared to public transportation lane start time, the disposition effect phase of finish time To larger, illustrate in the period around carving at the end, the effect of public transportation lane becomes apparent.

The bus average speed overall situation regression result (9 of table 8:30AM)bandwidth:180min

Compare the regression result of two above breakpoint, the influence to bus of target road section special lane can be analyzed. Before and after public transportation lane opens the moment, target road section bus average running speed has a certain upgrade, before breakpoint Average speed, population mean lifting amplitude is about 8.2%；And before and after special lane close moment, target road section bus is averaged The speed of service has declined, and compared to the average speed before breakpoint, overall fall is 9.9%.By contrast, the open moment Public transport vehicle speed lifting amplitude be less than the reduction amplitude of close moment, that is to say, that when the effect at open moment is not turned off The positive effect at quarter.Analyze the reason for this result occurs：Open moment, the volume of traffic of target road section just start to increase, not yet But peak period is going into, the at this moment opening of public transportation lane is to carry out the standard that reply peak period current demand increases severely in advance It is standby, and the regression coefficient of " bus and taxis quantity ratio per minute " this variable is little, also illustrate that now taxi With interfering simultaneously less for bus, because the traffic circulation of section entirety is more unobstructed, the phase of public vehicles and bus Very little is mutually influenceed, thus special lane is to the speed-increasing effect and unobvious of bus；Secondly, the upstream and downstream intersection of target road section is equal It is not provided with the signal priority rule of bus, the delay of intersection may be also one of the reason for causing DeGrain, due to The influence of intersection delay, bus are not shortened too many by the time in section；In addition, entering the process of peak period The volume of the flow of passengers of middle bus can be amid a sharp increase, and the duration that berths of each car can also increased, and this is also likely to be that speed is lifted not Obvious some reasons.Analyze the change of special lane close moment again, now peak period may not yet pass by, the volume of traffic is also High level is maintained, but being now likely to occur many public vehicles needs to take the situation of public transportation lane traveling, especially It is that the right-hand rotation of taxi on-board and off-board, the interim stop of other private cars and upstream intersection enters the public vehicles of target road section. This just forces bus to have to mix row using other tracks and other public vehicles, so as to reduce passage rate.In addition, by No longer it is outermost dedicated Lanes in the track that bus uses, the current situation out of the station is necessary to cross over more multilane, and other tracks Wagon flow conflict, cause the time out of the station increased, cause the speed of service in section to reduce, so at this moment closing suddenly public Special lane is handed over, the speed of service of bus can produce more obvious decline.

Bus data regression under the different pieces of information scope of table 9 compares (with 9:30AM is breakpoint)

(bus is with 9 for the disposition effect valuation of the local regression of table 10:30AM is breakpoint)

(2) taxi regression result is analyzed

Although opening up for public transportation lane is provided convenience to bus, for public vehicles, may produce not Profit influences, therefore is also required to consider the influence to public vehicles during the effect of assessment public transportation lane.We are represented with taxi Public vehicles, analysis public transportation lane caused by it on influenceing.The step of with analysis bus result, is identical, is returned carrying out data Before returning, image is first passed through to observe the situation of breakpoint.Fig. 6 (a), 6 (b), the box width of 6 (c) are 1min；Fig. 6 (d), 6 (e), the box width of 6 (f) is 2min；Fig. 6 (g), 6 (h), the box width of 6 (i) are 3min.Fig. 6 (a), 6 (d), 6 (g) Polynomial fitting number is 1；Fig. 6 (b), 6 (e), the polynomial fitting number of 6 (h) are 2；Fig. 6 (c), 6 (f), 6 (i) fitting The degree of polynomial is 3.The result of image fitting and the result of bus before are different, it has been found that when fitting number by Cumulative added-time, the mutation size at breakpoint are gradually reduced.

The result (table 11) that global data returns also has confirmed the feature that image reflects：With the increasing of the degree of polynomial Add, the value of disposition effect has reduced.OLS (1) and OLS (2) is linear regression, and the former does not introduce its dependent variable, then Person introduces carrying ratio, taxis quantity, bus quantity and the two quantity, and than this four, other control variables, but return twice Obtained disposition effect valuation is sufficiently close to, and is -1.045 and -0.969 respectively, and standard error all very littles, and this shows linearly returning Gui Shi, other influences of control variable to disposition effect valuation are very faint, i.e. influence of its dependent variable to taxi average speed Very little.But when recurrence number increases to 2 times, the value of disposition effect reduces nearly half, is only -0.493, when number increases to 3 When secondary, disposition effect value has risen, and is -0.627.Although 2 times and 3 times recurrence R side's value be all higher than before two sublinears Return, but obtained value measurement basis is by mistake all excessive, and obtained disposition effect valuation does not simultaneously have certain confidence level.

The taxi average speed overall situation regression result of table 11 is ((with 7:30AM is breakpoint) bandwidth:180min

In order to examine the robustness of valuation, We conducted the OLS of different pieces of information scope to return with comparing, and is shown in Table 12. As a result find：Data bandwidth is 60min and 120min, and disposition effect valuation is essentially identical, and other control variable regression coefficients Valuation is also very close, illustrates that the regression result that is obtained under the two bandwidth conditions is more stable；And data bandwidth is 30min When, disposition effect value is obviously reduced, and becomes in taxi than this variable regression coefficient for negative value, and this result is seemingly Disagreed with the fact, because carrying than reflection is by the carrying taxi number and taxi total amount in section in the unit interval Ratio, for experience, speed when speed during taxi should be more than unloaded, such carrying ratio is bigger, section Average speed should be bigger, and both are into positive correlation, but regression result is opposite with this experience.There is the reason for this case Be probably selection bandwidth it is too small when, comprising data volume can not reflect general trend situation of change.

Taxi data regression under the different bandwidth of table 12 compares (with 7:30AM is breakpoint)

The result of local linear smoothing also reflects the problem of same, is shown in Table 13.The effect obtained during with a width of 30min is estimated Value is significantly less than the value that other bandwidth obtain, but the value that rectangle kernel function obtains is also relatively, is -1.07.Under other bandwidth Result fluctuated between -0.868 to -1.235, and the standard error of result is also within the acceptable range.

(taxi is with 7 for the disposition effect valuation of the local regression of table 13:30AM is breakpoint)

For special lane close moment, same breakpoint analysis has also been carried out.Figure in Fig. 7 (a) -7 (i) under different condition As all reflecting the forward mutation assay that speed at breakpoint be present, and the mutation value of linear fit be significantly greater than it is secondary and cubic fit As a result.

From the point of view of the regression result (table 14) of global data, if introduce other control variables to linear OLS regression results Influenceing less, the preceding valuation of disposition effect twice is very close, and respectively 2.039 and 2.161, and secondary and cubic polynomial returns Result it is relatively small, respectively 1.249 and 1.571.Data area is reduced (table 15), it is found that disposition effect valuation is gradual Increase, 2.218 are increased from 1.353.The effect valuation that parametric regression now can not be stablized, it is also necessary to which nonparametric is returned The result returned is contrasted.The result (table 16) of nonparametric local linear smoothing shows：Except the valuation under 90min bandwidth is relative Outside smaller, the valuation under other conditions can be maintained in the range of 1.8 to 2.2, and global OLS (1) before, OLS (2), Linear regression result under 30min with 60min bandwidth is similar, it may be said that disposition effect now is in the range of 1.8 to 2.2.

The taxi average speed overall situation regression result of table 14 is (with 9:30AM is breakpoint) bandwidth:180min

Comprehensive analysis public transportation lane is opened up to the influence using taxi as the public vehicles of representative.Public transportation lane is opened Before and after putting the moment, the taxi average speed of target road section has reduced about 10.0%, it is seen that opening up for public transportation lane is really right Taxi has a certain impact.In special lane close moment, average speed has risen, and ascensional range is about 25.9%, is out More than 2 times of moment fall are put, this explanation was carved in the residing period when closed, influence of the public transportation lane to taxi It is very big, it is understood that to carve when closed (9 in the period of surrounding:00-10:00AM), taxi is to where public transportation lane The demand in track is very big, it is possible the reason for be that the on-board and off-board of taxi need to utilize outermost track.Starting the period (7 on the contrary: 00-8:Do not occur being greatly reduced for speed 00AM), it may be possible to because now resident trip does not have very to the demand of taxi Greatly, and the period traffic circulation it is integrally very fast, taxi receive bus influence and unobvious.Carrying in regression result The regression coefficient of variable has also confirmed this result, and the numerical value of this coefficient is 0.8 or so in start time breakpoint analysis, and In the breakpoint analysis carved at the end, numerical value is risen to close to 2, or even has more than 3 situation, and this explanation is after peak period Period, influence of the passengers quantity to hiring out vehicle speed is very big, so can freely be used by taxi if turned off special lane Kerb lane, prostitution quantity can be greatly increased, so as to increase average running speed.

Taxi data regression under the different pieces of information scope of table 15 compares (with 9:30AM is breakpoint)

(taxi is with 9 for the disposition effect valuation of the local regression of table 16:30AM is breakpoint)

3rd, Assessment of Policy and Optimizing Suggestions

The regression result summarized above obtains table 17, due to the influence of public transportation lane policy, after special lane opening, mesh Mark section bus average speed improves 8.2%, and taxi average speed reduces 9.9%；After special lane is closed, bus Speed reduces 10.0%, hires out vehicle speed and improves 25.9%.

The special lane impact effect conclusive table of table 17

As a result show that the setting of public transportation lane is obviously improved effect, but the difference of open period, shadow to bus Certain difference can be had by ringing effect, and compared to the open period, quarter special lane is bigger to the influence degree of bus when closed, Analysis result draws Optimizing Suggestions：The opening finish time of target road section special lane should suitably be delayed.

Public transportation lane is influenceed on being influenceed using taxi as the public vehicles of representative there is also certain and hires out bus or train route While the demand for on-board and off-board of parking is related, due to 9:After 00AM taxi on-board and off-board park demand increasing, carve rent at the end Vehicle speed, which has, significantly to be lifted.And this also side illustration taxi has certain use to need public transportation lane Ask, in order to not influence the current of bus, the policy that guarantees priorities of buses is implemented, it should carries out phase to public vehicles such as taxis The limitation answered, the POP concentrated such as is set；And simultaneously to bus should the supporting priority facility of setting signal priority scheduling, coordinate The use of special lane, ensure that public transport is current smooth convenient.

Claims

A kind of 1. public transportation lane policy evaluation method returned based on breakpoint, it is characterised in that step is as follows：

(1) variable determination and hypothesis testing

Research object is peak period public transportation lane, and only public transit vehicle is opened in daily specific time period, at the open moment Discontinuous point is produced with finish time, the front and rear only path resource distribution of breakpoint produces change；

Time t is driving variable, and its value directly affects the change of path resource distribution, is observable；Opened when the time is less than When putting the moment, public transportation lane is identical with common track, is used for any vehicle；When the time exceeding the open moment, public transport is special Only bus is allowed to use with road, other public vehicles only allow using other common tracks；

Road average-speed S is outcome variable, S^bRepresent the average speed of bus, S^cRepresent the average speed of taxi；

The key point that breakpoint returns is disposition effect valuation, and the expression disposed in regression model is by introducing at a binary Put variable EBL_tCome what is realized, the binary variable shares 0 and 1 two value；1 represents that public transportation lane is in the open period, grinds Study carefully object and receive disposal, 0 expression public transportation lane is closed, and research object does not receive disposal；

Under the urban traffic status of reality, the time that bus and public vehicles reach assessment section has randomness, drives Member can not accurately control arrival time deliberately to evade or receive disposal, meet effective first condition of breakpoint homing method： Research object has no ability to accurately control the driving variable around discontinuous point；Effective second bar of breakpoint homing method Part：Influence outcome variable other control variables must be continuous at discontinuous point, due to these variables the condition of continuity often It is bad directly verify, so first proposed before recurrence it is successional it is assumed that again by regression result verify assumed condition whether into It is vertical；

(2) graphical analysis

Before breakpoint recurrence is carried out, the data being collected into are handled, drawn with speed s (m/s) as ordinate, time t (min) it is the scatter diagram of abscissa, then data point is fitted；When more than the global data and mixed and disorderly, using Bin methods pair Global data is handled, and is removed the noise in global data, is made the curve of fitting smoother；Data point after conversion is carried out Linear or polynomial regression, it is possible to which preliminary observation whether there is the jump of data at breakpoint, if it does not, ensuing Regression result may be unreliable；

(3) it is global to return

Underlying parameter regression model

S_t=alpha+beta₀·EBL_t+β₁t+β₂t·EBL_t+γX_t+ε_t (1)

The underlying parameter regression model represents to open average running speed of the front and rear vehicle in target road section in public transportation lane； Wherein, t represents the number of minutes since breakpoint, to drive variable, the t=0 at discontinuous point；Dependent variable S_tIt is within t minutes Target road section average speed；EBL_tIt is a binary disposal variable, has 0 and 1 two kind of value, if discontinuous point t=0 is special Road opens the moment, then when the durations of t ＞ 0 are 1, the vehicle on expression section receives the disposal that track resource allocation changes, as t ＜ 0 Duration is 0, and vehicle does not receive the disposal of track resource allocation on expression section；If discontinuous point t=0 is special lane closing Carve, then when the durations of t ＞ 0 be 0, represent track resource allocation return to normal condition, when the durations of t ＜ 0 be 1, represent, represent public transport Special lane is also in open state；X_tFor the vector of other control variable compositions；∈_tFor white noise；

The coefficient of each variable in regression model, embody influence degree of each variable to outcome variable；Wherein, return most Main target component is β₀, its value directly reflects the size of the disposition effect at discontinuous point；β₁And β₂It is driving variable t Regression coefficient, its size determines that outcome variable (speed) becomes with the entire change of driving variable (time) before and after discontinuous point Gesture；γ is the vector of the regression coefficient composition of other control variables, reflects other influence journeys of control variable to outcome variable Degree, although not being the main object of research, the change when size and Robustness Test of A of its value can verify breakpoint recurrence It is assumed that verify whether other control variables are relevant with disposition effect；

Taxi and bus are separated, calculate both average speed respectively, the model applied when returning is also otherwise varied, It is mainly reflected in the selection of other control variables；For taxi, there is carrying and unloaded two states in it when runing, Speed is fast under passenger carrying status in theory, so carrying to be used for one in other control variables；It is public on urban road When handing over special lane not open, bus and public vehicles mix row, and bus has an impact to taxi, if bus on section Quantity is excessive, and bus relative velocity is smaller, and the phenomenon that lane change and on-board and off-board out of the station wait be present, to the fortune of taxi Row is had an impact, and the quantity of bus and taxi is used for into a control variable；In addition, on section in the unit interval Taxi and bus Floating Car quantity also serve as controlling variable；Linear regression model (LRM) for taxi is：

<mrow> <msup> <mi>S</mi> <mi>c</mi> </msup> <mo>=</mo> <msup> <mi>&alpha;</mi> <mi>c</mi> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>0</mn> <mi>c</mi> </msubsup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>1</mn> <mi>c</mi> </msubsup> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>2</mn> <mi>c</mi> </msubsup> <mi>t</mi> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&gamma;</mi> <mi>P</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>C</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mi>P</mi> <mo>,</mo> <mi>C</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <mi>&epsiv;</mi> <mi>t</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

In formula：

P, γ_P--- taxi ratio and its regression coefficient in the unit interval；

C, γ_C--- taxi Floating Car quantity and its regression coefficient in the unit interval；

B, γ_B--- public transport Floating Car quantity and its regression coefficient in the unit interval；

R, γ_R--- bus and taxis quantity ratio and its regression coefficient in the unit interval；

Recurrence for bus, other control variable for public transport Floating Car quantity, hire out Floating Car quantity and both quantity Than, therefore be for the regression model of bus：

<mrow> <msup> <mi>S</mi> <mi>b</mi> </msup> <mo>=</mo> <msup> <mi>&alpha;</mi> <mi>b</mi> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>0</mn> <mi>b</mi> </msubsup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>1</mn> <mi>b</mi> </msubsup> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>2</mn> <mi>b</mi> </msubsup> <mi>t</mi> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&gamma;</mi> <mi>C</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <mi>&epsiv;</mi> <mi>t</mi> <mi>b</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

In formula：

C, γ_C--- Floating Car quantity and its regression coefficient are hired out in the unit interval；

B, γ_B--- public transport Floating Car quantity and its regression coefficient in the unit interval；

R, γ_R--- taxi and bus quantity ratio and its regression coefficient in the unit interval；

Regression result obtains the regression coefficient of each variable and corresponding standard error, by comparing the big of regression coefficient and standard error It is small to evaluate the effect of disposal；The positive and negative and relative size of regression coefficient is reflected to influence journey of the dependent variable to outcome variable Degree, when regression coefficient all very littles or it is stable within the specific limits when, it is believed that these control variables are in the range of selected data to place It is not related to put effect-size, it was demonstrated that the reliability of breakpoint regressive appraisement result；

After global linear regression, typically also need to add multiple item progress polynomial regression, in order to preferably intend Outcome variable versus time curve is closed, while can also be as a part for Robustness Test of A；Can be direct when returning Increase the high-order term of time t on the basis of linear regression model (LRM)；The global polynomial of degree n regression expression of bus is (4), The global polynomial of degree n regression expression of taxi is (5)：

<mrow> <mtable> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mi>b</mi> </msup> <mo>=</mo> <msup> <mi>&alpha;</mi> <mi>b</mi> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>0</mn> <mi>b</mi> </msubsup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>1</mn> <mi>b</mi> </msubsup> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>2</mn> <mi>b</mi> </msubsup> <mi>t</mi> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>3</mn> <mi>b</mi> </msubsup> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>4</mn> <mi>b</mi> </msubsup> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <mn>...</mn> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <msup> <mi>t</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>b</mi> </msubsup> <msup> <mi>t</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <msup> <mi>t</mi> <mi>n</mi> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> <mi>b</mi> </msubsup> <msup> <mi>t</mi> <mi>n</mi> </msup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&gamma;</mi> <mi>C</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <mi>&epsiv;</mi> <mi>t</mi> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mi>c</mi> </msup> <mo>=</mo> <msup> <mi>&alpha;</mi> <mi>c</mi> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>0</mn> <mi>c</mi> </msubsup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>1</mn> <mi>c</mi> </msubsup> <mi>t</mi> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>2</mn> <mi>c</mi> </msubsup> <mi>t</mi> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>3</mn> <mi>c</mi> </msubsup> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mn>4</mn> <mi>c</mi> </msubsup> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <mn>...</mn> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mn>1</mn> </mrow> <mi>c</mi> </msubsup> <msup> <mi>t</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>c</mi> </msubsup> <msup> <mi>t</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>c</mi> </msubsup> <msup> <mi>t</mi> <mi>n</mi> </msup> <mo>+</mo> <msubsup> <mi>&beta;</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> <mi>c</mi> </msubsup> <msup> <mi>t</mi> <mi>n</mi> </msup> <mo>&CenterDot;</mo> <msub> <mi>EBL</mi> <mi>t</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>&gamma;</mi> <mi>P</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>C</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>B</mi> </msub> <mo>,</mo> <msub> <mi>&gamma;</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mi>P</mi> <mo>,</mo> <mi>C</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msubsup> <mi>&epsiv;</mi> <mi>t</mi> <mi>c</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

(4) local linear smoothing

Assuming that t₀For discontinuous point, in discontinuous point both sides, selection width is returned for h data point, is control less than discontinuous point Group, it is disposal group more than discontinuous point；It is assumed that the regression function of disposal group (on the right side of discontinuous point) is linear forms：

S_i=α_r+β_r·t_i+ε_i (6)

The target of recurrence be by discontinuous point on the right side of data be worth to value at discontinuous point, because different data points is to disconnected The distance of point is different, and the nearlyer influence to estimating point value of spacing should be bigger, so needing to assign to each data point Different weights, nearer apart from discontinuous point, weight is bigger, otherwise weight is smaller, and this weight distribution passes through specific kernel function K To realize；Final choice (α_r, β_r) make it that the data on the right side of breakpoint obtain local weighted quadratic sum minimum for value, i.e.,

<mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <mo>,</mo> <msub> <mi>&beta;</mi> <mi>r</mi> </msub> <mo>)</mo> <mo>=</mo> <mi>arg</mi> <mi> </mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>r</mi> </msub> </munderover> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <mo>-</mo> <msub> <mi>&beta;</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <mi>K</mi> <mo>(</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> </mrow> <mi>h</mi> </mfrac> <mo>)</mo> <mo>&CenterDot;</mo> <mn>1</mn> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>></mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

So, point estimate of the disposal group at discontinuous point is

S_r(t₀)=α_r+β_r·(t₀-t₀)=α_r (8)

Similarly control group can also obtain regression coefficient

<mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>l</mi> </msub> <mo>,</mo> <msub> <mi>&beta;</mi> <mi>l</mi> </msub> <mo>)</mo> <mo>=</mo> <mi>arg</mi> <mi> </mi> <mi>min</mi> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>l</mi> </msub> </munderover> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>l</mi> </msub> <mo>-</mo> <msub> <mi>&beta;</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <mi>K</mi> <mo>(</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> </mrow> <mi>h</mi> </mfrac> <mo>)</mo> <mo>&CenterDot;</mo> <mn>1</mn> <mo>(</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo><</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

It is so as to obtain estimate of the control group at discontinuous point

S_l(t₀)=α_l+β_l·(t₀-t₀)=α_l (10)

Final disposition effect valuation is

τ=α_r-α_l (11)

(5) Robustness Test of A of valuation

When carrying out breakpoint recurrence, Robustness Test of A is carried out, there is certain stability and can to test the valuation of disposition effect By property；Robustness Test of A is broadly divided into two major classes：

1) it is directed to the Robustness Test of A of global polynomial regression

Mainly realized for the Robustness Test of A of global polynomial regression by changing the degree of polynomial and change data scope；

Global polynomial regression can using breakpoint distant place data carry out valuation, thus by away from breakpoint data influence compared with Greatly, to examine the reliability of disposition effect valuation, it is necessary to constantly reduce window width centered on breakpoint, the data area for making to use subtracts The small sufficiently small width to around breakpoint；Disposition effect valuation under the different pieces of information scope difference degree of polynomial is compared Compared with if data area and the degree of polynomial change, disposition effect valuation can also be maintained in certain scope, fluctuation Less, illustrate that valuation has certain reliability；

2) it is directed to the Robustness Test of A of local linear smoothing

Mainly realized for the Robustness Test of A of local linear smoothing by changing kernel function type and amount of bandwidth；

The type of kernel function determines the weighted value of valuation point ambient data, and rectangle kernel function, triangle are mainly used in this method Kernel function and Ye Panieqi Nico husbands kernel function carry out Robustness Test of A；The selection of bandwidth needs to reach the flat of accuracy and deviation Weighing apparatus；Disposition effect valuation under different IPs type function and different bandwidth is compared, if kernel function type and bandwidth hair During changing, putting effect valuation can also maintain in certain scope, and fluctuation is little, illustrate that the valuation has necessarily reliable Degree.