presentation 04

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CIVE1219 Transport Engineering 3

Presentation File 4

Sara Moridpour


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Objectives

Understand the meaning of trip production and tripattraction,

Understand the influencing factors on trip production andtrip attraction,

Appreciate the approaches used in trip generation models,

Be aware of the advantages and disadvantages of usingeach approach in trip generation models,

Understand how to evaluate the trip generation models.

After completing this subject, you should be able to:


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Trip Generation Models

Trip generation models relate the intensity of trip makingto, and from, land use parcels (zones) to measures of the

type and intensity of land use.

Trip generation models develop a relationship betweenthe number of trips attracted to, or produced by, a zone

and the characteristics of the zone.

Trip generation models can then be used to predict thefuture number of trips.


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Trip Productions and Attractions

A 'trip' is defined as travel between two places of activity.

Trips are classified as either: home based trips and non

home based trips.

Trip productions are trips generated by residential zonesto serve a need,

Trip attractions are trips generated by activities such

as employment, retail services etc. and are related tosatisfaction of a need.


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It is important to distinguish between whether the tripgeneration analysis considers only trips made by private

vehicle (person trips by car) or total trips regardless of

mode (total person trips).

It is not uncommon for trips made by foot or by bicycleto be excluded from the datasets used to estimate trip

generation models.

Excluding bike and walk trips reduces the complexity ofsubsequent models, i.e. trips distribution and mode choice.

Trip Productions and Attractions Continued


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Home Based Trips

Home Based (HB) trips, meaning that one end of the tripis at home, for instance home based work trips, home

based shopping trips, and trips from work to home.

Finer classifications may be used (e.g. blue collar work,

white collar (office) work, tertiary student) since underling

relationships governing trip generation are expected to be

different for different trip types and therefore more accurate

predictions are obtained.


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Home Based Trips Continued

White Collar

Managers & Administrators

Professionals

Associate Professionals Clerical, Sales & Service

Blue Collar

Tradespersons & Related

Production & Transport

Laborers

Home Based trips

Secondary

PrimaryTertiary

Shopping

Recreation

OtherWhite

Collar

Blue

Collar


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Non Home Based Trips

Non Home Based (NHB) trips, where neither end of thetrip is at home, for instance, a trip from work to shop.

Non Home Based

trips

Work -

Other

Shopping -

Shopping

Shopping -

Other

OtherWork -

Work

Work -

Shopping


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Influencing Factors in Trip Productions

A variety of factors are likely to influence trip production

including:

Population,

Income levels,

Car ownership,

Quality of transport facilities and frequency of service,

Residential density,

Age structure or stage in the family life cycle.


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Question 1

What are the following factors have the main influence on

trip production of a family (can be more than one option)?

1. Number of students in family, Property type, Number of

people aged 65+,

2. Number of people aged 65+, Family size, Property type,

3. Number of students in family, Public transport access,

Property postcode,

4. Price of property, Property type, Property postcode.


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Influencing Factors in Trip Attraction

A variety of factors are likely to influence trip attraction

including:

Employment,

Levels broken down by type of employment,

Educational institution enrolments,

Floor space,

The accessibility provided by the transport system,

Parks and recreation areas.


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Question 2

Which of the following sets are most important in trip

attraction of a traffic zone (can be more than one option)?

1. Number of schools, Number of people aged 18+,

2. Public transport access, Number of shopping centres,

3. Area of shopping centres, Number of employees,

4. Area of medical centres, Number of cinemas.


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Trip Generation Approaches

There are two common approaches to trip generation

analysis:

Category analysis, also known as cross classification

analysis,

Regression modelling.

These two procedures represent the state of practice inrelation to trip generation modelling.


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Category Analysis or Cross Classification Analysis

This approach usually focuses on the household or asmaller unit than the zone.

Households are categorised on the basis of generalcharacteristics (e.g. car ownership, household size and

age structure). Then, the trip rate is calculated for each

category.

Zonal trips are then predicted as the sum of the trips foreach household in the zone.

Category analysis can be applied to the analysis of tripattractions with the categories defined by land use or

employment.


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Cross Classification Analysis Continued

The steps in calibrating a category analysis model are as

follows:

Group the households by the desired characteristics(number of persons, car ownership etc.),

Calculate a trip rate (trips/household) for each category.

The accuracy of the model depends on the number ofhouseholds in each category. At least 20 households are

required in each category to have confidence in the results.


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To predict the future trips for a zone:

Determine the number of households in each category,

Multiply the appropriate trip rate by the number ofhouseholds in the category,

Sum the results across all categories to obtain an

estimate of the total number of trips for the zone.


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To determine the appropriate variables in the model, anumber of variables are initially considered. These are:

Gender (male, female),

Car availability (always, sometimes, never),

Age (< 18, 18 - 40, 41 - 65, > 65),

Employment (employed, unemployed),

Income (low, medium, high),

Type of employment (blue collar, white collar, other),

Family type (single, childless couple, with children).


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The following table shows the results of trip generationmodelling from a category analysis of data from Madison in

the USA (FHWA, 1975):

Cars Owned

Family Size 0 1 2+

1 1.0 2.7 3.1

2 1.5 5.1 7.0

3 3.1 7.2 9.4

4 3.2 8.0 11.7

5+ 5.2 9.2 13.4


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Category analysis is simple to apply and is capable of

capturing the primary influences on trip generation.

It can be estimated using dummy variable regressiontechniques.

This provides the added advantage of access tostatistical tests to assess the significance of the

relationships and the goodness of fit of the model.

Cross classification analysis has a number of advantages:


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While simple to apply, classification analysis has a number

of disadvantages:

The variation in trip-making within an individual category

can be higher than the variation between categories,

It is difficult to find the combination of categories unlesswhere each category is homogeneous enough,

It is hard to include more than just the basic populationand demographic information given the data processing

requirements.


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Question 3

What is not correct about cross classification method?

1. This approach is very complicated for traffic zone analysis,

2.This method can easily be applied at aggregate and

disaggregate levels (for households and traffic zones),

3. The method is less costly than other methods but not very

accurate,

4. The variables used in this method are generally simple ones.


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Regression Modelling

Regression modelling is a common technique for analysingtrip generation. This approach relies on estimating the

parameters of an underlying model relating the number of

trips from/to a zone to the characteristics of the zone. For

instance:

ZTA = 1560 + 14.3 X1+ 10.5 X2+ 3.7 X3

Where,

ZTA = zonal trips attracted,

X1= retail floor area (m),

X2= service and office floor area (m),

X3= manufacturing floor area (m).


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Regression Modelling Continued

Th= 0.53 + 1.53 NPh- 1.42 CH4h+ 0.67 Wh+ 1.72 CAh

Where,

Th= number of person trips for household h,

NPh= number of persons in the household,CH4h= number of children under 4 in the household,

Wh= number of workers in the household

CAh= number of cars available in the household.

The following is an example of a household level model for

home-based trips:


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Traditionally the emphasis has been on linear regression,since it has been more readily available in statistical

analysis packages.

There are strong reasons for exploring non-linearfunctional forms particularly when empirical evidence

suggests that variables such as car ownership have a

non-linear impact on trip generation.

Dramatic improvements in the capabilities of statisticalpackages make it feasible to explore non-linear

formulations and to test these against linear models.

Regression Modelling Characteristics


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Regression modelling provides the advantage of beingable to test the significance of the relationship between

independent variables and trip generation rates using

statistical tests as well as providing a goodness-of-fitmeasure for the model.

The calibration of a regression model requires a set ofdata containing data for the dependent and independent

variables.

Regression Modelling Advantages/Disadvantages


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Question 4

What is not correct about regression method?

1.This approach is applied at aggregate and disaggregatelevels (for households and traffic zones),

2. Different types of variables can be defined in this method,

3. The accuracy of the results depend on the accuracy of the

collected information,

4. There is no limitation for using variables in this method.


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Evaluation of Regression Modelling

Ye= a + b X

Ye= an estimate of Y,

a, b = parameters of the model.

In a simple case, we have information on the number of trips

generated by a number of zones (Y) and the corresponding

zonal population (X). A linear model has the following form:

The Y and X data are fed into a statistics package and the

values for 'a' and 'b are estimated to give the best fit to the data

(Y, X). The approach minimises the prediction error of model

and it aims to minimise the squared errors.


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0 500 1,000 1,500 2,000 2,500 3,000Population

0

1,0002,000

3,000

4,000

5,000

6,000

7,000

Trip

Production

Series 1

Series 2

Evaluation of Regression Modelling Continued

e1

e2

e3

e4

e5

Error = min (e1 + e2 + e3 + e4 + e5)

Error = min [(Y1 - Ye1)+(Y2 - Ye2)+(Y3 - Ye3)+(Y4 - Ye4)+(Y5 - Ye5)]


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Three important tests to evaluate the model are as follows:

First, it is important to reflect on whether we would logically

expect a relationship between the X variable(s) and Y.

Second, the signs of the parameters should be examined. Arethey consistent with expectations?

For instance, we would expect that the number of trips wouldincrease as the zonal population increases and so a positive

value would be expected for the parameter 'b'.

1. Logic Test (Ye= a + b X)


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One of the classic cases is wheresomeone developed a model that

predicted the number of murders occurred

in a city as a function of how many hats

were sold in that city.


What is a good regression model?

While that model may have done well in terms of goodness-of-fit

or statistical tests, the underlying logic would have to be seriously

questioned.


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The goodness of fit statistics (R2) provides a measure ofhow well the model predicts the values of Y.

A perfect model, that is one which predicts the value of Yperfectly for each value of X, would have an R2of 1.0.

The closer the value of R2is to 1.0 the better the fit. Thevalue is also useful for comparing the goodness of fit of

two models.

2. Goodness of Fit (Ye= a + b X)



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The inherent scatter in the data produces someuncertainty in the value of the parameters of the model.

The most popular statistical test relates to the slopeparameter in the model (parameter 'b'). If the true slope

parameter were equal to zero then the explanatory

variable 'X' would not help in predicting 'Y'. This is usually

done with a 't-test.

3. Statistical Tests (Ye= a + b X)



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It is usually of interest to test the null hypothesis that theslope parameter is equal to zero. This is usually done with

a 't-test' and the value of the t-statistic is usually calculated

by the statistics package.

T-test Analysis

Uses t-tests of individual variable slopes,

Shows if there is a linear relationship between thevariable(s) X and Y,

Hypotheses:

H0: b = 0 (no linear relationship)

H1: b 0 (linear relationship does exist between X and Y)


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T-test Analysis

Compare the calculated t-statistic value with the critical

value from statistical tables.

The critical value depends on the size of the data set(n=number of observations), the number of parameters

(in the case of the simple model considered above this is

two: 'a' and 'b') and the confidence level selected.

It is common to work with a 95% confidence interval, sothe critical t value has n - 2 degrees of freedom (for the

simple model considered above) and you would look up a

0.025 level for the statistic (tcrit).

For large sample sizes it is common to use a rule ofthumb that if the t-test value is greater than 2.0 the

variable's coefficient is statistically significant from zero.


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T-test Analysis Continued

For small samples, the critical t-value must be read from thestatistics table and then:

If t > tcrit, reject the null hypothesis and conclude the

slope parameter is significantly different from zero (that isthere is a statistically significant relationship between 'X'

and 'Y'),

If t < tcrit, then it is not possible to reject the null

hypothesis and conclude that the coefficient on the 'X'

variable is not statistically different from zero.


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T-test Analysis Continued

If the signs of the parameters are consistent with

expectations, the parameters are statistically significant and

the goodness-of-fit is reasonable. Then we can have someconfidence that we have a 'good' model and should be able

to use it to predict for future conditions.

a/2 = 0.025 a/2 = 0.025

Reject H0Reject H0 Do not reject H0


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Regression Modelling in Excel

Excel can be used to estimate a regression model.

Plot the raw data and the regression line on a graph.

Data Analysis is an add-in option which you may need to install if you have notalready done so.

When using Excel 2003, from Tools menu, select Add-Ins, and in the Manage

box, select Analysis ToolPack and click OK. Then, select Data Analysis fromthe Tools menu and then select Regression.

When using Excel 2007, click the Microsoft Office Button and then click ExcelOptions. Click Add-Ins, and in the Manage box, select Excel Add-ins and click Go.

Then, in the Add-Ins available box, select the Analysis ToolPak check box, and

then click OK. Select Data Analysis and then select Regression.

When using Excel 2010, Click the File tab, click Options, and then click the Add-Ins category. In the Manage box, click Excel Add-ins, and then click Go. The Add-

Ins dialog box appears. In the Add-Ins available box, select Analysis Toolpack

and then click OK. Click the Data tab, then select Data Analysis and then

select Regression.

Using this approach will generate t-test results for the parameters of the model.


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Multiple Linear Regression Output

Total Trips = 210.835 + 0.247 (Population) + 0.037 (Number of Cars)


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Multiple Linear Regression Output


b1= + 0.247

Total Trips will increase by0.247 for each one person

increase in Population.

b2= + 0.037

Total Trips will increase, onaverage, by 0.037 for each

increase in Number of Cars.

Where

Total Trips is the number of trips produced in each zone.


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Coefficient of Multiple Determination (R2)

Reports the proportion of total variation in Y explained by

all X variables taken together.

squaresofsumtotal

squaresofsumregression

SST

SSRR2Y ==


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squaresofsumtotal

squaresofsumregression

SST

SSRR2Y ==

SSR = Regression sum of squares =the sum of the differences

of each estimation from the overall mean over all observations.

2n

1i

i )Y(ESSR

=

=

Coefficient of Multiple Determination (R2) Continued

SST = total sum of squares = the sum of the differences ofeach observation from the overall mean over all observations.

2n

1i

i )Y(YSST

=

=

E is the predicted value

Y is the observed value


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0.996333173737083.

862173086971.

SST

SSR

R

2

Y ===

99.6% of the variation in Total Trips is

explained by the variation in Population

and Number of Cars

Coefficient of Multiple Determination (R2) Continued



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Adjusted R2

R2 never decreases when a new X variable is added tothe model.

This can be a disadvantage when comparing models.

We lose a degree of freedom when a new X variable isadded.

Did the new X variable add enough explanatory power to

offset the loss of one degree of freedom?


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Adjusted R2 Continued

Shows the proportion of variation in Y explained by all Xvariables adjusted for the number of Xvariables used.

Penalize excessive use of unimportant independent

variables.

Smaller than R2.

Useful in comparing among models.

=

1kn

1n)R(11R 22adj

(n = sample size, k = number of independent variables)


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99.4% of the variation in Total Trips is

explained by the variation in Population

and Number of Cars, taking into

account the sample size and number of

independent variables.

9940R2adj

.=

Adjusted R2 Continued



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Is the Model Significant?

F-test is used for Overall Significance of the Model.

F-test shows if there is a linear relationship between all ofthe X variables considered together and Y.

Use F-test statistic.

Hypotheses:

H0: b1= b2= = bk= 0 (no linear relationship) i = 1 to k

H1: at least one bi 0 (at least one independent variable affects Y)

Y = b0+ b1 x1+ b2 x2+ + bk xk


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F-test for Overall Significance

399.363216703.824

3186543485.9

1-k-n

SSEk

SSR

MSE

MSRF ====

With 2 and 3 degrees of

freedom

P-value for the

F-Test



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F-test for Overall Significance Continued

H0: b1= b2= 0

H1: b1and b2not both zero

= 0.05

df1 = 2 df2= 3

Test Statistic:

Since F test statistic is in

the rejection area (p-value

< 0.05), reject H0

There is evidence that at

least one independent

variable affects Y

399.363MSE

MSRF ==

Critical Value: F= 9.552

Decision:

Conclusion:

F0.05

= 9.552

0

= 0.05

Reject H0Do not reject H0

F


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Are Individual Variables Significant?

Use t-tests of individual variable slopes.

Shows if there is a linear relationship between the variable X iand Y.

Hypotheses:

H0: bi= 0 (no linear relationship) i = 1 to k

H1: bi 0 (linear relationship does exist between Xiand Y)

ib

i

S

bt

0=Test Statistic:

(df = n - k - 1)

Where, biis the Coefficient of variable Xiand Sbiis the Standard Error of

variable Xi.

Y = b0+ b1 x1+ b2 x2+ + bk xk


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Are Individual Variables Significant? Continued

t-value for Population is t = 5.104, with

p-value 0.015

t-value for Number of Cars is t = 0.561,

with p-value 0.614



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H0: bi= 0 i = 1 to k

H1: bi0

= 0.05 df = 6 - 2 - 1 = 3

Reject H0 for Population and do

not reject H0for Number of Cars.

There is evidence that Populationaffect and Number of Cars does

not affect Y (Total Trips).

Critical Value: t/2 = 3.182

Decision:

Conclusion:

Are Individual Variables Significant? Continued

Reject H0Reject H0Do not reject

H0

3.182-3.182

a/2=0.025 a/2=0.025

Note: Number of Cars is generally is a very important variable. However, in

the available dataset, it is insignificant.



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Next Learning Activities

Examples of Trip Generation Models (problem set 3)will be examined in the next tutorial class (please printproblem set 3 as well as lecture week 4 and bring to the

next tutorial class).

Please bring one Laptop per group for the next tutorialclass. You will need it for regression analysis.

Trip Distribution Models will be comprehensively

explained in the next lecture class.

Different approaches in developing Trip DistributionModels are considered and the strengths and

weaknesses of each model type will be explained.


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Questions?


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Assessment Task 2 Continued

Table 1: Population and employment predictions for the year 2020.


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Table 2: Trip generation data.


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Table 3: Current characteristics of each mode.


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1. Peak period directional trips over the current bridge (prior to

construction of the second bridge).

2. Peak period directional trips on both bridges once the new

bridge is built.

3. Write out the utility expression for each mode. Are the signs

and relative magnitudes of the coefficients logical?

4. Use the model to predict the bus ridership and revenue for the

morning service.

5. The bus operator believes it may be possible to lobby the State

Government to install express bus lanes between zones 1 and

7. Under this scenario the in-vehicle time for the bus would be

reduced by 12%. Predict the effects of this on bus ridership and

revenue.


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t14= 22 + 0.015V14 t24= 22 + 0.015V24

t13= 10 + 0.005V13 t34= 8 + 0.005V34

t23= 15 + 0.005V23

V14= 13000 V24= 11000

Part B:


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1. Using all-or-nothing assignment, find the link volumes and

travel times.

2. Using incremental assignment with five increments of 20%,

find the link volumes and travel times.

3. Compare and comment on the results from parts 1 and 2

above.


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Questions?

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