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This is to certify that the

dissertation entitled

TRANSFERABILITY OF MODE CHOICE MODELS
WITHIN SAUDI ARABIA

presented by

HASAN MUSAED AL-AHMADI

has been accepted towards fulﬁllment
of the requirements for

 

 

 

Ph' D° degree in CiVZl-l Engineering
A/é/2~"7‘)v C. . %//’1
Major profegsor

Date November 6 , 1989

 

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Michigan State
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TRAN SFERABILITY OF MODE CHOICE MODELS
WITHIN SAUDI ARABIA

By

Hasan Musaed Al-Ahmadi

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

Docroiz OF PHILOSOPHY

- Department of Civil and Environmental Engineering

1989 .

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ABSTRACT
'I'RANSFERABILITY OF MODE CHOICE MODELS WITHIN
SAUDI ARABIA
By
Hasan Musaed Al-Ahmadi

The main purpose of this research is to determine whether the cost of
developing, calibrating, and testing intercity mode choice models for Saudi Arabia
corridors can be reduced by transferring models across corridors. To accomplish this
purpose, intercity mode choice models were developed and calibrated for two major
corridors in Saudi Arabia: the Dhahran—Riyadh corridor and the Jeddah-Riyadh
corridor. A general model was developed using data from both corridors, and the
accuracy of transferring each specific model was compared with that of the general
model.

Several approaches were used to test the transferability of intercity mode
choice models. The ﬁrst approach was to determine if the calibrated model could
be used ”as is" to predict intercity mode choice in another corridor in Saudi Arabia.
The second approach was to determine the accuracy achieved by updating the
coefﬁcients and constants of the model using sample data from the corridor where
the model was being transferred. In the third approach, it was assumed that the
specification of the original model could be used with re-estimated parameters from

the test corridor. Finally a modiﬁed approach was used. This modiﬁed approach

consist
scaling

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Hasan Musaed Al-Ahmadi
consisted of two forms. One form of the modiﬁed approach was to use a separate
scaling factor for each variable, while the other form used distance as the scaling
factor.

The results of the attempt to transfer models between corridors without
modiﬁcation was not encouraging. However, the modiﬁed approach gave an
acceptable goodness of fit. Furthermore, by using the Bayesian updating method,
the goodness of ﬁt measure improved in both corridors.

The conclusion reached in this study was that transferring models across
corridors in Saudi Arabia is feasible, and the potential cost saving to the kingdom
can be signiﬁcant. It is recommended that additional corridors be studied to verify

the universal application of the transfer techniques.

Hanee

 

To my parents, whose love, support, and constant prayer
helped me greatly in my achievement.

To my wife Ebtisam who gave her love, affection, and understanding
in times of stress and strain, and to my son Basam and my daughter
Haneen for giving me continuous enjoyment and numerous laughs

during the difﬁcult time while I was writing this dissertation.

iv

ACKNOWLEDGMENTS

I am deeply grateful to several people who contributed by their effort and
support in the development of this dissertation. My profound gratitude is to Dr.
William Taylor, the chairman of the doctoral committee, for his commitment,
support, continuous advice and encouragement throughout this research, who gave
me unlimited time and support. I never felt that he treated me as a student only.
Without the willing of "Allah" in the ﬁrst place, and the help of Dr. William Taylor,
this research would not have been completed.

Gratitude are also extended to Dr. Lidia Kostyniuk for her suggestions which
contributed immeasurably both to the research and writing of this dissertation, and
to the other members of my doctoral dissertation committee, Dr. K. Rajendra, and
Dr. Manderkar for their careful reading of the drafts and speciﬁc suggestions.

I wish to express my gratitude to Dr. Richard Lyles for his stimulation,
friendly relationship, and help when it was needed. Knowledge grasped from the
courses I took with him assisted me throughout this research, and hopefully in my
future career.

Appreciation is expressed from the bottom of my heart to Dr. Khalid
Abdulghani the Mayor of Jeddah for suggesting this topic and for his help in

carryingout this research.

Malec

Islamic

suppor

Hazmi 1

bmm

With my
mcmber:
WMkIV
Ebtlsam
CDCOUrag,
also CXprf
Smiles am

bless all c

 

 

I would also like to express my appreciation to several fellow students Sayed
Maleck and Sami Mohamed for many stimulating discussions we have had.

Thanks and wishes are extended to all my colleagues and "Brothers" at the
Islamic Center of Greater Lansing for their encouragement and prayers.

Thanks for King Fahad University of Petroleum and Minerals (KFUPM) for
supporting me throughout my studies at Michigan State University.

Special appreciation also is expressed to Engineer Mohammed Hasan Al-
Hazmi from KFUPM who helped me in distributing and collecting the questionnaire
forms. Without his help, this research might have taken a longer time.

Finally I would like to thank my mother, and may father for providing me
with my early education. Also, my heartfelt appreciation is extended to all the
members of my family for their constant encouragement and their moral support
while I was studying in the United States. My special gratitude goes to my wife
Ebtisam who has walked every step with me for her patience, care, and
encouragement in each step I made toward the completion of the research. I would
also express my deep appreciation to my son Basam and my daughter Haneen, whose
smiles and childish looks gave me the courage to accomplish my goals. May Allah

bless all of us and make us among the righteous (Ameen)

HMH’AIAA._

Re:

 

Reg

 

TABLE OF CONTENTS

Page
CHAPTER I INTRODUCTION .................................. 1
Background: Study Area ................................... 1
Behavior of Intercity Tripmaker in Saudi Arabia ................. 4
Statement of the Problem .................................. 5
ScOpe of the Study ...................................... 6
Deﬁnition of Terms ...................................... 9
Plan of Presentation ..................................... 10
Limitations of the Study ................................... 10
CHAPTER II LITERATURE REVIEW .......................... 11
Intercity Modal-Sth Model Development ...................... 11
Background: Intercity Modal-Split Model Development ...... 11
Disaggregate Model Structure ......................... 15
Independence from Irrelevant Alternatives Property (IIA) . . . . 19
Measurements of Level-of-Service Variables .............. 20
Review of Intercity Disaggregate Models ................. 22
Critique of Previous Models .......................... 29
Transferability Issues ...................................... 32
Previous Research on Transferability of Mode Choice Models . 32
CHAPTER III METHODOLOGY ............................... 38
Model Development ...................................... 38
Data Required ..................................... 38
Sampling Strategy ................................... 42
Sample Requirements ................................ 42
Model Calibration ................................... 43
Model Validation ................................... 44
Recommended Methodology for Transferring the Models ........... 44
Hypotheses to be Tested .............................. 47
Statistics to Test the Hypotheses ........................ 48

CHAPTER IV DATA COLLECTION
Research Questions ....................................... 53
Sample Size ....................................... 64

vii

TABLE OF CONTENTS, CONT’D.

Page
CHAPTERV THE CALIBRATION PROCESS 65
The Theoretical Model .................................... 65
Model Speciﬁcation ....................................... 66
Test of Independence from Irrelevant Alternatives Assumption ....... 84
Model Validation ......................................... 87
Aggregate Elasticities of the Estimated Models .................. 89
CHAPTER VI TRANSFERABILITY ANALYSIS .................... 95
Evaluation of the Transferability of the Models .................. 98
CHAPTER VII CONCLUSION AND RECOMMENDATIONS ........ 128
Recommendations for Further Study ......................... 131
APPENDICES .............................................. 135
APPENDIX A DISAGGREGATE MODELS ................. 135
APPENDIX B QUESTIONNAIRES ....................... 141
APPENDIX C CODING MANUAL FOR INTERCI'TY MODE
CHOICE MODELS IN SAUDI ARABIA ........ 192
APPENDIX D FORTRAN PROGRAM ..................... 201
REFERENCES .............................................. 207
viii

 

 

LIST OF TABLES

Table Page
2.1 Comparison Between Aggregate and Disaggregate Model Predictions . . 14
2.2 Watson Intercity Mode-Choice Disaggregate Model ................ 23
2.3 Stopher Intercity Mode-Choice Disaggregate Model for Business Trip . . 24
2.4 Stopher Intercity Mode-Choice Disaggregate Model for Non-Business Trip 24
2.5 Grayson Intercity Mode-Choice Disaggregate Model ............... 27
2.6 Stephanedes Et al. Intercity Travel Mode-Choice Disaggregate Models . 28
4.1 Description of the Abbreviated Variables ........................ 55
4.2 Basic Statistics for Plane Tripmakers in Dhahran

in Dhahran-Riyadh Corridor .................................. 57
4.3 Basic Statistics for Train Tripmakers in Dhahran-Riyadh Corridor ...... 58
4.4 Basic Statistics for Bus Tripmakers in Dhahran-Riyadh Corridor ....... 59
4.5 Basic Statistics for Car Tripmakers in Dhahran-Riyadh Corridor ....... 60
4.6 Basic Statistics for Plane Tripmakers in Jeddah-Riyadh Corridor ....... 61
4.7 Basic Statistics for Bus Tripmakers in Jeddah-Riyadh Corridor ........ 62
4.8 Basic Statistics for Car Tripmakers in Jeddah-Riyadh Corridor ........ 63
4.9 Sample Size Based on Income ................................. 64

5.1

5.2

 

Model Results for Mode Choice Models for the Dhahran-Riyadh
Corridor (Non-Business Trips; Train is Not Included) ............... 67

Model Results for Mode Choice Models for the Jeddah-Riyadh
Corridor (Non-Business Trips) ................................ 70

 

 

 

Tab]
53

5.4

 

LIST OF TABLES, CONT’D.

Table Page

5.3 Dhahran-Riyadh Corridor Mode-Choice Model for Non-Business
Trips (Train Included) ...................................... 76

5.4 Dhahran-Riyadh Corridor Mode-Choice Model for Non-Business
Trips (Train is not Included) .................................. 77

5.5 Jeddah-Riyadh Corridor Mode-Choice Model for Non-Business Trips . . . 78
5.6 Prediction Success Table for the Jeddah-Riyadh Corridor Model

-- The Calibration Process .................................... 82
5.7 Prediction Success Table for the Dhahran-Riyadh Corridor Model

(with Train) - The Calibration Process .......................... 82
5.8 Prediction Success Table for the Dhahran-Riyadh Corridor Model

(without Train) - The Calibration Process ....................... 83
5.9 IIA Test for the Jeddah-Riyadh Corridor Model ................... 85
5.10 IIA Test for the Dhahran-Riyadh Corridor Model .................. 86

5.11 Prediction Success Table for the Jeddah-Riyadh Corridor Model
-- The Validation Process .................................... 88

5.12 Prediction Success Table for the Dhahran-Riyadh Corridor Model
- The Validation Process .................................... 88

5.13 Direct Elasticities for Variables in the Jeddah-Riyadh Corridor Model . . 91
5.14 Direct Elasticities for Variables in the Jeddah-Riyadh Corridor Model . . 91

5.15 Cross Elasticities for Variables in the Jeddah-Riyadh Corridor
Model for Air Mode with Respect to Bus and Car Attributes ......... 92

5.16 Cross Elasticities for Variables in the Jeddah-Riyadh Corridor
Model for BUS Mode with Respect to AIR and CAR Attributes ....... 92

5.17 Cross Elasticities for Variables in the Jeddah-Riyadh Corridor
Model for CAR Mode with Respect to AIR and BUS Attributes ....... 93

5.18 Cross Elasticities for Variables in the Dhahran-Riyadh Corridor
Model for AIR Mode with Respect to BUS and CAR Attributes ....... 93

X

 

Tabl

5.194

 

 

LIST or TABLES, CONT’D.

Table Page
5.19 Cross Elasticities for Variables in the Dhahran-Riyadh Corridor

Model for BUS Mode with Respect to AIR and CAR Attributes ....... 94
5.20 Cross Elasticities for Variables in the Dhahran-Riyadh Corridor

Model for CAR Mode with Respect to AIR and BUS Attributes ....... 94 '
6.1 Transferability of the Jeddah-Riyadh Model Before and

After Updating the Coefﬁcients .............................. 100
6.2 Transferability of the Dhahran-Riyadh Model Before and

After Updating the Coefﬁcients .............................. 101
6.3 Comparison Between the Calibrated Jeddah-Riyadh Model and

the Updated Dhahran-Riyadh Model .......................... 104
6.4 Comparison Between the Dhahran-Riyadh Model and the Updated

J eddah-Riyadh Model ...................................... 105
6.5 J eddah-Riyadh Versus Dhahran-Riyadh Coefficients ............... 108
6.6 Comparison Between the Variables Used in Calibrating Dhahran-

Riyadh Model and Jeddah-Riyadh Model ....................... 109
6.7 The Ratio of the Objective Level-of-Service Variable .............. 110
6.8 Transferability Test of the Modiﬁed Jeddah-Riyadh Model Before

6.9

and After Updating Coefficients; (the Speciﬁc LOS Ratio Case) ...... 113

Transferability Test of the Modiﬁed Dhahran-Riyadh Model Before
and After Updating Coefﬁcients; (the Speciﬁc LOS Ratio Case) ...... 114

6.10 Transferability Test of the Modiﬁed Jeddah-Riyadh Model Before

and After Updating Coefficients; (the distance case) ............... 117

6.11 Transferability Test of the Modiﬁed Dhahran-Riyadh Corridor

and After Updating Coefﬁcients; (the distance case) ............... 118

6.12 Comparison Between the Calibrated Dhahran-Riyadh Model and

the Updated Modiﬁed Jeddah-Riyadh Model (Distance Case) ........ 119

6.13 Comparison Between the Calibrated J eddah-Riyadh Model and

the Updated Modiﬁed Dhahran-Riyadh Model (Distance Case) ....... 120

Table
6.14 'l
6.15 I
6.16 T
6.17 C

6.18 Cc

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LIST OF TABLES, CONT’D.

Table Page
6.14 Test of the General Model for the Two Corridors ................. 123
6.15 The General Model Versus the Speciﬁc Jeddah-Riyadh Model ....... 124
6.16 The General Model Versus the Speciﬁc Dhahran-Riyadh Model ...... 125

6.17 Comparison Between the Dhahran-Riyadh Model and the
General Model ........................................... 126

6.18 Comparison Between the Jeddah-Riyadh Model and the
General Model ........................................... 127

7.1 Results Of Different Approaches Used to Transfer Dhahran-Riyadh Model
to Jeddah-Riyadh Corridor .................................. 132

7.2 Results Of Different Approaches Used to Transfer Jeddah-Riyadh Model
to Dhahran-Riyadh Corridor ................................. 132

xii

LIST OF FIGURES

Figure Page
1.1 Map of Saudi Arabia ....................................... 3
1.2 Diagram of the Research .................................... 8

xiii

 

CHAPTER I
INTRODUCTION

.Baﬂmundnﬁmdxma.

Saudi Arabia is located in the southwestern part of Asia. It occupies most of
the Arabian Peninsula. The estimated land area for Saudi Arabia is 2,240,000 square
kilometers, which is approximately one-third the size of the USA. Saudi Arabia is
bounded by the United Arab Emirates, Qatar, Oman, and the Arabian Gulf on the
east; the Red Sea on the west; South and North Yemen on the South; and Kuwait,
Iraq, and Jordan on the north.

According to. the World Almanac and Book of Facts (1987), the population
of Saudi Arabia is estimated to be 11,152,000 inhabitants, the birth rate is estimated
to be 43.7 per 1,000 population, and the death rate is 15.4 per 1,000 inhabitants.

The temperature in Saudi Arabia varies between the coastal lands and interior
land. In the interior, the average mean temperatures in the summer and the winter
are around 35°C, and 17°C, respectively. In the coastal region, the average mean
temperatures in the summer and the winter are about 30°C, and 24°C, respectively.

Saudi Arabia is one of the rich developing countries. Its wealth comes
primarily from oil revenues. The discovery of oil in Saudi Arabia changed the
Kingdom of Saudi Arabia from a pre-industrial country to a modern industrial
country. This brisk change placed a burden on all public utilities and facilities,

especially the transportation system.

 

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Riyadh is the capital of Saudi Arabia, and Dammam and Jeddah are industrial
and commercial cities on the Arabian Gulf and the Red Sea, respectively (see Figure
1.1). The distance between Riyadh and hahran is 467 kilometers, while the distance
between Riyadh and Jeddah is 1061 kilometers.

Five modes of transportation serve Riyadh and Dhahran: railroad,airway,
bus, taxi, and private car. Four modes serve Riyadh and Jeddah: airways, bus, taxi,
and private car. The passenger railway is operated by the Saudi-Arabian
Government Railways Organization (SAGRO). The bus mode is operated by the
Saudi Arabian Public Transport Company (SAPTCO). SAPTCO is the only bus
company allowed to operate buses along these corridors. The taxi mode has been
eliminated from this research because very few passengers in Saudi Arabia use the
taxi for intercity trips.

Three airports serve the two corridors. King Khaled International Airport
serves the Riyadh area, Dhahran International Airport serves the eastern province
(Dammam, Khobar, Abgaig, and Dhahran), and King Abdulaziz International Airport
serves the Jeddah area. The only air carrier allowed to operate between these
airports is the Saudi Arabian Airline (Saudia). Hence, the fare does not change with
respect to the day of reservation. The fare is constant within each class and each

corridor. However, students receive a 50% discount off the economy fare.

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Understanding the behavior of the tripmaker will provide the model builder
with the most likely variables for inclusion in the model. The deﬁnition of a
tripmaker in this research is a man who is traveling between cities by himself or with
his family. The following paragraphs discuss the characteristics of Saudi behavior
when a person makes an intercity trip. These characteristics may not be applicable
to Western culture.

In Saudi Arabia, the percentage of females traveling alone from one city to
another is very low. This is because the Islam religion forbids women to travel
alone. In addition, women are not allowed to drive in Saudi Arabia. They may use
an airplane to travel alone, but only under special circumstances, and relatives must
meet them at the airport.

Another factor affecting the tripmaker in choosing an intercity mode is the
weather. In Saudi Arabia the weather, especially in summer, does not encourage the
tripmaker to use ground transportation.

Saudi tripmakers are very concerned with safety, because the risk of becoming
involved in an automobile accident is very high. This perception of risk may cause
the tripmaker to hesitate to drive his car or use ground transportation for an intercity
trip.

Another characteristic of Saudi tripmakers is that they prefer to travel as
families (the average family size is around six) for non-business trips. Finally, in
Saudi Arabia a unique intercity trip purpose exists. This trip purpose is religious and
is called the "Aumra trip". This is not a trip purpose commonly associated with

intercity travel in the West.

 

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The ﬁrst step in any engineering work is planning. In transportation, planning
is especially important because transportation systems are among the most expensive
investments to build or modify. The investment in transportation improvements
should be based on the understanding of future demand. To achieve this, an
understanding of tripmaker behavior is essential.

Understanding the behavior of tripmakers in selecting a travel mode is
necessary for public transportation agencies or private carriers to make managerial
decisions, and to prevent underdesign or overdesign. For instance, underestimation
of future travel demand may lead to congestion, delay, high accident rates on many
major roads, and excessive stand-by at major airport terminals. These problems may
waste valuable manpower and time, and may impede the economic development of
the Kingdom. At the other extreme, if future travel demand is overestimated, too
much capital will be tied up in transportation facilities and not used for other more
needed aspects of development.

An intercity model must exist to predict the future modal split. The results
of this study will provide the transportation agencies with a tool to maximize their
revenue and better allocate their resources. In addition, if intercity mode choice
models can be transferred directly or through a small effort, such as updating, the
beneﬁts would be enormous in that it would signiﬁcantly reduce the data
requirements, calibration time, cost, and detailed analytical expertise required by

planners to perform modal split analysis.

 

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There has been signiﬁcant work done in testing the transferability of intracity
mode choice models in the United States. Yet, no research was found that tested
the ability of intercity mode choice models to predict the behavior of the tripmaker
in corridors other than those where the models were originally calibrated and tested.
In this research, the methodology used for intracity mode choice model transferability
has been extended to intercity mode choice models.

The primary focus of this study was to evaluate the ability of intercity mode
choice models to be transferred across corridors within Saudi Arabia. To test this
capability, intercity mode choice models were calibrated for the Dhahran-Riyadh
corridor and the Jeddah-Riyadh corridor, and an evaluation was constructed on the
transferability of the intercity disaggregate behavioral mode choice models within
Saudi Arabia.

A survey was conducted to collect the data required to construct the models.
Those data were randomly divided into two data sets. One data set was used for
specifying and calibrating the models; the other data set was used for validation
purposes.

The term ”model” is used to denote an abstraction of reality. In other words,
it is an abstract representation of a real-world system that behaves like the real-
world system. In constructing any model a hierarchy should be considered. This
hierarchy depends on the model’s objectives. In this research, the objective of the
model is to accurately predict the mode choice of a traveller in selected Saudi Arabia

intercity corridors. Given this objective, the steps in intercity mode choice model

 

 

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construction are: develop the theoretical concept of the model (for example, utility
maximization); specify the functional form of the model (that is, linear or product
form); determine the speciﬁcation of the model; and, ﬁnally, calibrate the model and
estimate the values of the variables.

This hierarchy of model construction was used as a guideline to test model
transferability. The potential for model transferability decreases as one moves down
the hierarchy. For instance, the theoretical concept of the model and the functional
form of the model have more potential to transfer than the speciﬁcation of the
model. Furthermore, the estimated parameters have the lowest potential for
transferability (27). The theoretical concept and the functional forms are very
general and can be extended and adopted to different behavioral contexts (27).

The ﬁrst step in testing model transferability is to determine if the
speciﬁcation of the variables are transferable. For instance, if the transferable model
has some variables that are not applicable in the new context, the model cannot be
used to predict the behavior of the tripmaker. If the same speciﬁcation of variable
can be used in both contexts, the speciﬁcation of the transferable model (the form
of the variables only) can be used to calibrate an intercity mode choice model for the
new corridor. Statistical testing can then be used to determine if the parameters of
the transferable model and the parameters of the new models are equal. A second
option is to transfer the model unchanged. A third option is to re-estimate the
parameters of the transferable model with a smaller data set than would be used to
calibrate a model for the corridor in which the transferability test is being conducted.
Each of these approaches was used in this study. A diagram summarizing this

research can be seen in Figure 1.2.

l .IIIIIIII

 

 

 

 

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Dhahran-Riyadh (D-R)

 

 

 

 

 

 

 

 

 

 

 

Data Collected from
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l

 

Data required
to calibrate
the model

 

 

 

 

Model
Development

 

 

 

 

 

Used to predict
mode choice in
R~J corridor

 

 

 

 

 

Compare between the local
and the transferred model

 

 

 

 

 

 

Compare between the local and the
transferred model after updating

 

 

 

 

 

 

General model calibrated with data
pooled from the two corridors

 

 

 

 

 

 

 

Compare between the general
Model and the specific models

 

 

Figure 1.2 Diagram of the Research

 

I856

 

 

Different hypotheses were used to test the different approaches in this

research. These hypotheses are as follows:

1.

Aumra

Islam

Local model

There is no difference in the prediction accuracy between a local
model and a transferred model.

There is no difference in the prediction accuracy between a local
model and a transferred model after updating the coefﬁcients.
There is no difference in the model speciﬁcation between Saudi Arabia
corridors.

The parameters of the speciﬁcation variables for the transferred and
local models are equal.

Coefﬁcients for level-of-service variables (e.g. time or cost) for the
Jeddah-Riyadh model and the Dhahran-Riyadh model are equal.
Coefficients for level-of-service variables (e.g. time or cost) for a

transferred model after updating and a local model are equal.

Deﬁlﬁtionnflcrms

A non-obligatory act of worship occurs in Mecca, which can
performed at any time of the year.

The third major religion that had been revealed to the Prophet
Mohammed, the messenger of "Allah" 610-632 AD.

The calibrated model for the corridor under study.

Transferred model The local model transferred to another corridor.

Zoning procedure A method of dividing the survey area into spatial units (zones)

suitable for data collection. The designation of zone boundaries
is based on selecting units that will be as nearly homogeneous
as possible.

 

oft

inter
the ]

trans

Chaplt
Uansfc
presen
for em
tfansfer

COHCIUSI'

 

10

ﬂanﬂresentatien

Chapter I contains the background of the study area, issues in the behavior
of the intercity tripmaker in Saudi Arabia, and an introduction to the problem. In
Chapter II, a review of the literature is presented. It covers the background of
intercity modal-split model development, disaggregate model structure, a review of
the previous intercity disaggregate models and their critiques, and past work on
transferability.

Chapter III presents the methodology used in conducting this study. In this
chapter the recommended approach for data collection, model calibration, and model
transferability testing is identiﬁed. Statistical analysis of the collected data is
presented in Chapter IV. Chapter V includes the development of a calibrated model
for each corridor, and the general model. In Chapter VI the results of the
transferability study are presented. Chapter VII is a summary of the study, and

conclusions and recommendations for further study are presented.

imi i

This study has the following limitations:

1. This study includes an analysis of tripmakers in the Jeddah-Riyadh
corridor and the Dhahran-Riyadh corridor only.

2. Due to limited funds this study was conducted in the spring and early
summer (March, April, and May) of 1988 and may not represent the
behavior of the tripmaker the rest of the year. For instance, the
behavior of the tripmaker in selecting an intercity mode may be

different in the winter.

 

coun
on 1‘“
Issues
Devel.
Develc
Variabl
rIIOdeIs.

0f mode

Mam
St

to deVCIC

 

Predjq p:
C0m'dor q
aggregate
model

saf‘

researChC .

CHAPTER II
LITERATURE REVIEW

There is no literature concerning mode choice model calibration or
transferability speciﬁcally for Saudi Arabia. However, several articles related to the
goal of this study exist for the United State Of America (USA) and other developed
countries. For the purpose of this study, the major emphasis of this review will be
on two major areas Intercity Model-Split Model Development and Transferability
Issues. After a discussion the background of the Intercity Modal-Split Model
Development, the emphasis of the review on the Intercity Modal-Sth Model
Development will be on: (a) model structure, (b) measurement of level of service
variables, (c) review of intercity disaggregate models and (d) critiques of. the previous
models. Transferability Issues will emphasize previous research on transferability

of mode choice models.

° I r ' - Ii 1 v 1 m
Several research efforts were undertaken from the mid-19605 to the present
to develop intercity mode choice models. Much of this research was performed to
predict patronage of potential new modes as well as existing modes for the Northeast
corridor (1). These intercity mode choice models were based on the analysis of
aggregate data. These models include the Kraft-Sarc model, Quandt and Baumol
model, and the Walmsley model (1). Development of aggregate models provided

researchers with knowledge of the various relationships between zone characteristics

11

 

and 1
tripm
time).

(busin

have p
Aggret
a decre
the ass
were r

several

Within

 

 

12

and mode choice. For example, aggregate models showed which variables the
tripmaker was sensitive to (such as out-of-pocket cost, income, and out-of-vehicle
time). Moreover, aggregate models showed that segmentation by trip purpose
(business and non-business) is important for intercity mode choice analysis.

However, studies of aggregate models demonstrated that these models may
have produced biased estimates of model coefﬁcients due to data aggregation (2, 3).
Aggregation before the model was calibrated resulted in a loss of information and
a decrease in the explanatory power of the model. These conditions occurred because
the assumption behind using aggregate data was that the tripmaker characteristics
were relatively more homogeneous within zones than between zones. However,
several studies showed that the opposite was true, that more variation occurred
within zones than between zones (3, 4).

Model coefﬁcients were determined to explain the variations in observed
travel behavior. In a purely statistical analysis, the more variation that was explained
by the model the more reliable the model was thought to be. But, as previously
mentioned, often more variation occurred within zones than between zones. Thus,
a model based on aggregate data was less likely to explain the behavior of the
individual, and is thus likely to be a poor prediction model.

Another problem with aggregate models was the risk of ’ecological fallacy’ (5)
in which correlation among aggregate variables does not necessarily reﬂect actual
individual behavior. In other words, an aggregate model based on average
observations of socioeconomic variables in a speciﬁc zone does not necessarily

represent an individual tripmaker’s behavior in that zone or the average behavior of

A |

 

the t
befor
behai

thatir

non-tr.
genera
deman

may nc

expkuua

 

 

13

the tripmaker in that zone. This condition may occur because data aggregation
before the model construction phase of the analysis may cloud the underlying
behavioral relationships and result in a loss of information. Several studies showed
that intracity aggregate models produce biased estimates of model parameters (2, 3).

Another limitation of an aggregate model is that it is expected to be
non-transferable between contexts because the bias resulting from aggregation is
generally different between contexts (6). In other words, the reason that. aggregate
demand models may not be transferable is that a group of individuals, on average,
may not behave the same as an individual who possesses average values of the
explanatory variables. These phenomena associated with aggregate models made
them questionable for transferability and prediction purposes.

The disaggregate approach was the second generation in modeling methods.
The development of disaggregate models provided a more effective tool for
predicting an individual’s behavior in selecting one mode from among different
modes available. The decrease in explanatory power of the aggregate models due to
data aggregation was avoided with the disaggregate models. This advantage greatly
improved the predictive power of disaggregate models. For example, Watson (7, 8)
developed and evaluated aggregate and disaggregate binary (rail versus car) mode
choice models in the Edinburgh-Glasgow corridor. His results indicated an error in
mode choice prediction for this city pair 12 to 15 times higher for an aggregate
model than those for a disaggregate model for the same speciﬁcation. The result of
this study is shown in Table 2.1. The disaggregate model was preferred over the best

aggregate model for intercity travel prediction.

 

 

 

14

Table 2.1

Comparison Between Aggregate and
Disaggregate Model Predictions

 

 

Actual train Aggregate Disaggregate
tripmakers Prediction Prediction
1,183 1,029 1,184
% prediction error 13.02 0.08

 

The development of disaggregate models was extensively documented (9, 10,
11, 12, 13, 14, 15, 16) and is widely used in urban travel analysis.

The use of disaggregate models is supported by their representation of the
individual tripmaker’s decision, data efﬁciency, and superior estimation results. Most
disaggregate models are based on the theory of ”utility maximization." They assume
that a person makes a particular choice from a set of different alternatives depending
on the maximum beneﬁt he receives. For example, a person may wish to minimize
travel time and cost of the trip, and maximize comfort and convenience in selecting
a mode from the available modes.

The primary model form for intercity mode choice utilizing disaggregate data

is in a probabilistic form, as seen in the following example:

 

EXP V“
P‘,=
2: EXP V,
1
Where:
P', = probability of tripmaker i choosing mode k out of j alternatives
the utility of alternative k to trip maker i

5
II II

(X. S)

 

par

inco

mod

 

15

a row vector of characteristics of alternative k

X.
Si

a row vector of socioeconomic characteristics of a tripmaker i
From this example, we see that the probability of a tripmaker choosing a

particular alternative is a function of the characteristics of the tripmaker; such as,

income, age, and sex and of the characteristics of the mode relative to alternative

modes.

WM

Model structure is the central theoretical concern for modal-split analysis.
Multinomial logit (MNL), nested logit (NL), and multinomial probit (MNP) are the
popular types of demand functions tested to date (17,18) (logit and probit models are
described in Appendix A). The choice of the types of demand functions depends on
the similarity among transport modes and the underlying behavior of travelers (19).
When travelers evaluate air, rail, and roadway modes simultaneously, MNL models
are usually speciﬁed. When travelers evaluate roadway and railway as one composite
alternative against air, then MNP or N L models are usually used. The assumption
in the simultaneous approach is that the tripmaker considers all attributes of the
available alternatives at the same time. For instance, the tripmaker will consider
airplane, train, car, and bus at simultaneously. On the other hand, for the sequenced
or nested model one assumes a certain hierarchy exists among the choices. For
example, the tripmaker compares the air mode and ground mode, then compares the

train, bus, and car within the ground mode.

 

does

incon
in the
to spe
is prei

decisic

are wit
SimUIIaj

Ilumber

Used [0
the IDost

log: "10

 

altemalii

based 0n

 

16

Unfortunately, software capable of estimating efﬁcient nested logit models
does not exist (20). A further problem is that simple computer programs give
incorrect results for the nested models with respect to the accuracy of the estimates
in the upper levels of the model. Moreover, the nested model is quite complicated
to specify and utilize. Hensher and Johnson (15) stated that a simultaneous structure
is preferable from theoretical considerations to the nested structure. In a study of
decision making Ben-Akiva and Koppelman (18) stated that:

The problem with decisions is that we cannot ﬁnd a unique ’natural’

sequence of partitions that will be generally applicable. Therefore a

simultaneous structure is superior to a recursive structure.

Moreover, the number of alternatives available to the tripmaker in this study
are within the realistic limit of the simultaneous approach. Furthermore, the
simultaneous model is calibrated one time, whereas with the sequential model a
number of models have to be calibrated depending on how they are postulated.

Based on the ﬁnding of these authors, the simultaneous logit approach will be
used to calibrate the models for the corridors under study. The logit model has been
the most prominent methodology used in disaggregate travel demand models. The
logit model assumes that a person chooses a particular mode from different
alternative modes depending on maximum beneﬁt. The multinomial logit model is
based on the following assumptions about the random terms of the utilities:

1. they are independent,

2. identically distributed, and

3. Gumbel distributed

 

In 2
Mor

actu.

idios
impo
Varial
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behav

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17

The logit model has been widely used in intracity modal split analysis (21).
In addition, the properties of the logit model have been identiﬁed and tested.
Moreover, because logit models are stochastic they are more likely to simulate the
actual decision process as can be seen from the following paragraph.

First, the tripmaker does not always make rational decisions, and consumer
idiosyncrasies cannot be anticipated in a deterministic model. Second, it is usually
impossible to include all the variables which inﬂuence the choice function. If all the
variables inﬂuencing the choice function are considered, the model will become a
complicated one. There may be essential random elements in the consumer’s
behavior since it varies from day to day (22). Finally, consumers may not have
correct information about the attributes of the alternatives.

Several studies compared probit and logit models. The result of these studies
show that the same prediction capability can be obtained by both techniques (17).

In summary, the reasons for the choice of the logit form for the structure of
the proposed models are as follows:

1. The logit approach has been widely used and tested in several studies

(21).

2. The logit form has a more straightforward estimation procedure than the

probit model which requires a complex computational procedure.

3. Many statistics packages have this model, while the others are under

development or have not been used.

 

are I“
and 2'
ooefﬁ.
The Ct
to and

Service

mode 1
Utility 1

Choice

 

 

Charam

numbe:

better it

18

Model speciﬁcation is another important issue in model calibration. There
are two speciﬁcation measures to calibrate the required models: generic speciﬁcation
and alternative speciﬁc speciﬁcation. In a generic speciﬁcation, the estimated
coefﬁcient for any variable is restricted to the same value across the alternatives.
The coefﬁcient in an alternative-speciﬁc speciﬁcation can vary from one alternative
to another. In other words, a separate coefﬁcient is estimated for each level-of-
service (LOS) attribute of each alternative.

There are two major advantages to using generic LOS data in disaggregate
mode choice models. First, generic LOS variables are consistent with the economic
utility theory. Second, the use of a generic LOS facilitates demand forecasts of new
choice alternatives. Moreover, the abstract model attempts to quantify mode
characteristics affecting their likelihood of being chosen. It also requires fewer
numbers of parameters than the mode-speciﬁc model.

A mode-speciﬁc constant may be introduced in the abstract choice function
to capture mode effects that are not captured by the variables common to all
alternatives. However, the best type of speciﬁcation cannot be known until an
empirical study is done.

The previous paragraphs can be summarized by noting that the disaggregate
simultaneous abstract logit form has been recommended for the structure of the
proposed models unless the empirical study shows that a different form is much

better in explaining the behavior of the intercity tripmaker.

 

ava
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pro;
of a
exam
and t
probl
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19

v rv

One of the most important issues about the logit model is independence from
irrelevant alternatives property (IIA). This property states that if two modes are
available and a new mode is introduced, the ratio of the probabilities of the two old
modes have been unchanged regardless of the choice for the new mode. The IIA
property is both one of the strengths of the logit model and its major weakness. The
property is advantageous in that the model can be calibrated based on one choice set
of alternatives and then used to predict choices from a modiﬁed choice set. For
example, a mode split model can be calibrated based on currently available modes
and then used to explore the impact of introducing a new mode into the system. The
problem with the IIA property is that the alternatives included in the choice set are
independent of each other. To describe this weakness, due to the IIA property, the
classic case of red and blue buses has been used. For instance, assume that both the
auto and red bus modes capture 50% of the travel market. Then a new blue bus is
introduced which has exactly the same service attributes as the red bus but has a
different color. The actual market share now becomes 50, 25, and 25 percent for
auto, blue bus, and red bus, respectively. The car share remains the same but the
share of the red bus is reduced to 25%. However, the multinomial logit model
(MNL) will predict that each of three modes capture 1/3 of the market. This
condition increases because IIA requires that the ratio of the red bus share to the

auto mode should not be affected by the introduction of the new mode.

feasibli
compa
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likelihc
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estimat

ICSI Sla‘
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CSIImati

 

 

20

McFadden, Tye, and Train (13) investigated a wide range of computational
feasible tests to detect a violation of the IIA assumption. The test involved
comparison of logit models estimated with a subset of alternatives from the universal
choice set. This test involves a comparison of two likelihood values. One is the
likelihood resulting from estimating the restricted sample by using the parameters of
the universal set, while the other likelihood value is the one resulting from
estimating the restricted sample but without restricting the parameters.

The likelihood ratio test statistic was used to test the IIA assumption. This
test statistic is chi-square distributed with degrees of freedom equal to the number
of restricted parameters. This test will be used to test the null hypothesis that the
IIA model structure holds

HATST= -2(LL.(B')- LL.(B'))

Where LL,(B') is the likelihood from estimating the restricted sample by using
the parameters of the universal set, and LL,(£‘) is the likelihood resulting from

estimating the restricted sample without restricting the parameters.

v - ' V ' 1
There are two major measures of the level-of-service (LOS) attributes:
perceived and objective values. Perceived LOS data are those values the individual
reports when answering a questionnaire. Objective DOS data are the reported values
by the carrier, such as the fare and the published train, bus, and airplane schedules.
For auto users, the objective LOS values are the averaged ones. For example, total
in-vehicle time is the distance between the two centers of the cities divided by the

average travel speed.

DOS or
from th
on the e
LOS va
I
perceive
Other a1
exists w}
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used for
I

data (26
the med
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data f0r

21

Considerable debate has been found in the literature over whether perceived
LOS or objective IDS values should be used in model calibration. This debate stems
from the fact that travel decisions are not based on actual time and cost but rather
on the expected or perceived values. Thus, for a better behavioral model, perceived
LOS values should be used in model calibration.

In practice, this method presents major problems. One problem with
perceived data is that the traveler’s perception of IDS on the chosen alternative to '
other alternatives is likely to be in favor of the chosen alternative. This condition
exists when a tripmaker is questioned about the attributes of his chosen alternative.
He tends to justify his choice by making it seem more attractive than it really is
compared to the alternatives rejected. Furthermore, for predicting future modal
split, the manner in which IDS values are estimated in the base year would have to
be used in estimating the future values. Only objective or engineering values can be
used for estimating future IDS values.

There is an. argument that perceived data is actually weighted engineering
data (26). If models are to be transferred, objective LOS values should be used in
the model. Whether perceived or objective values are used in the model, objective
values are needed for the base year to estimate future values of the variables
included in the model. In this research, perceived data for the chosen mode were
collected from the tripmaker. Moreover, objective IDS data for the modes under
consideration were collected from the agencies operating those modes. In other
words, a model having the two types of measures will be calibrated; the perceived

data for the chosen and the objective data for the unchosen modes.

22

B . E I . D' I l i l
The ﬁrst disaggregate intercity mode choice model was developed by Watson

(7). He developed a disaggregate binary (rail versus car) mode choice model in the
Edinburgh-Glasgow corridor. The disaggregate speciﬁcation he used was very simple
(see Table 2.2). He used four variables to explain the tripmaker’s behavior:
out-of-pocket cost (C), total travel time (T), waiting time (W), and number of modes
used in a one-way trip (N). The expression of "utility" used to calibrate the
disaggregate model may be seen in Table 2.2.

Stopher and Prashker (23) developed multinomial logit models to forecast
intercity modal split among car, rail, bus, and air. They used 2085 observations from
the 1972 National Travel Survey (NTS) to formulate various intercity choice models.
The formulation which best explained the tripmaker behavior was segmented for
business and non-business trips, as shown in Tables 2.3 and 2.4. The linear additive
utility used to cah'brate the model was:

G(X,) = a‘,+a,T,+a,C,+a,F,+a.D,+a,E,

Where

G(X,) = The utility function describing alternative k

T, = Line-haul travel time for alternative k

C, = Line-haul travel cost for alternative k

F, = Service frequency of alternative k

D, = Line-haul distance for alternative k

E, = Access-egress travel time for alternative k
a,k = Model constant for alternative k

a,, a2, ..... , a,= coefﬁcients

V

 

Relative
Relative
Differeni I
Different
journey

 

23

Table 2.2

Watson Intercity Mode-Choice Disaggregate Model

 

 

Variable ' Coefﬁcient t-Value
Relative time difference (T d) -1.05 -6.48
Relative cost difference (Cd) -0.667 -8.95
Difference in waiting time (Wd) -0.002 -9.45
Difference in number of ‘
journey segments (Ns) -0.132 -5.95

P... = {1 + EXP [T‘d(T,,-T,,,) + Cd(C,_,- ....) + Wd(w,,-w,,,) + Ns(N,,-N_,,]}

 

Variable

 

Line-haui
line-haul
&Muh
Line-hau'
ACCESS~e1
Bus cons
hﬂmm
Air cons

X“ (do
%Pmm

24

Table 2.3

Stopher Intercity Mode-Choice Disaggregate Model
for Business Trip

 

 

Variable Coefﬁcient t-statistics
Line-haul travel time -0.62 -2.1
Line-haul travel cost -3.96 -9.79
Service frequency 0.01 -3.44
Iine-haul distance -10.64 -5.78
Access-egress travel time -0.52 -3.13
Bus constant -1.65 -4.31
Rail constant -0.40 -0.93
Air constant 3.13 -5.10
X’ (d.f) 1016 (8)

% Predicted Correctly 63.1

 

Table 2.4

Stopher Intercity Mode-Choice Disaggregate Model
for Non-Business Trip

 

 

Variable Coefﬁcient t-statistics
Line-haul travel time -1.69 -5 .65
Line-haul travel cost -4.25 -7.95
Service frequency 0.012 -4.48
Line-haul distance -0.523 -0.29
Access-egress travel time -0.196 -1.59
Bus constant -1.41 -4.42
Rail constant 0365 -0.96
Air constant 2.476 -4.08
X2 (d.f) 1561 (8)

% Predicted correctly 77.8

 

T1
for travel.
mode in
replicate
elasticitie

predictec

”.11 uh} I g0 r: g r:

 

25

The Stopher models are not truly disaggregate since they used average values
for travel time, travel cost, service frequencies, and access-egress times for each trip
mode in each corridor. Even though the model ﬁt was quite good, it was unable to
replicate mode shares in other selected corridors. Furthermore, many computed
elasticities were counter-intuitive. For example, a 25% reduction in rail fare was
predicted to reduce rail, bus, and auto shares. The authors attributed the
unsatisfactory results to the quality of the data used.

Grayson (24) used the same NTS data to calibrate another multinomial (car,
rail, bus, and air)intercity logit choice model. His formulation differs from the
earlier model by the replacement of access time by access distance to terminal and
the inclusion of a variable formed by the product of travel time and family income.
This variable follows the hypothesis that the value of time varied linearly with
income. The model speciﬁcation was:

UII = aC_+bYT_+cY/2F_+dYA_+e,

Where

U,I = utility of mode M

C. = travel cost of mode M

T, = travel time of mode M

F, = frequency of mode M

A. = access of mode M

Y = family income /2000

a, b, c, d, e. = Coefﬁcients to be estimated

W
behavior
Grayson
to the in.
road mileI
variable

M
for busin
auto moc
Choice tr.
Havel tirij
travel tin
time), ho
Plane.
A,
the airpla
Percent.
bUS team
ahalysisi.

 

26

With this approach, Grayson obtained a good ﬁt and explanation of the
behavior of the tripmaker for all trip purposes (see Table 2.5). Improved results of
Grayson’s effort relative to those of Stopher and Prashker were probably due in part
to the inclusion of access distance in the 1977 NTS data, the use of more accurate
road mileage estimates, and improved model speciﬁcation (inclusion of the income
variable and elimination of relative values for attributes).

More recently, Stephanedes et. al (25) calibrated multinomial choice models
for business travel in the Twin Cities-Duluth, Minnesota corridor for bus, plane, and
auto modes (See Table 2.6). Variables used to build these different intercity mode
choice models were out—of-pocket cost (OPTC), household income (HINC), total
travel time (TIT), out-of-vehicle travel time (OVTT), distance (DIST), in-vehicle
travel time (WIT), and waiting time (WT) for bus only (other modes had 0 waiting
time), household income for auto (HINC), and mode-speciﬁc constants for bus and
plane.

All the variables in these models were signiﬁcant with 90% conﬁdence except
the airplane mode-speciﬁc constant, which showed a conﬁdence limit around seventy
percent. Three-hundred people were randomly contacted at the Twin Cities air and
bus terminals and outlying gas stations to ensure completely disaggregate data in the

analysis.

 

Variable

 

    

Travel c

 

27

Table 2.5

Grayson Intercity Mode-Choice Disaggregate Model

 

 

Variable ' - Coefﬁcient t-statistics
Travel cost - 0.0161 - 5.65
Travel time - 0.024 -12.66
Service frequency - 0.0055 - 1.81
Access time - 0.0007 - 1.66
Bus constant - 2.552 -14.32
Rail constant -_ 3.027 -16.89
Air constant - 2.7 ' -14.6

p’ .303

% Predicted correctly 82.7

 

p’ = Goodness of ﬁt measure.

28

Table 2.6

Stephanedes Et al. Intercity Travel Mode-Choice
Disaggregate Models

 

Minnesota 1

 

 

Variable Minnesota 2 Minnesota 3
OPTC/HINC - 3.43 (-2.74) -- - 7.75 (~5.07)
OPTC - - .69 (-5.10) --
OVTT/DIST -- -30.90 (-3.50) -23.20 (-3.13
IVTT - 0.01 (-2.03) - 0.08 (-1.41) - 0.08 (~1.81)
T'TT - 0.06 (-4.38) -- --

WT -- -- - 0.20 (-1.90)
HINC, -- 0.24 ( 2.13) --

C, 4.80 ( 2.10) 4.68 ( 2.65) 3.82 ( 2.95)
C, -12.13 24.80 ( 2.56) 7.62 ( 1.20)
2 0.61 0.64 0.50

% predicted correctly 73 78 69

 

(‘ ‘) t-statistic

OPTC One-way out-of-pocket cost.

'I'I'I' One-way total travel time,min;

TIT = IV'I'I'+ OVTT

OVTT One-way out-of-vehicle time,min;

OVTT = AT+ WT+ ET
IVTT One-way in-vehicle travel time,min.
WT One-way wait time,min.
HINC Household income,000$

HINC, Household income for auto,000$

C, 1 for bus, 0 else
C! 1 for plane, 0 else
p A goodness of ﬁt measure.

IQ

8°.

speciﬁ:
becaus

trade-o

provide
two C0.
represei
0f the c.
1[lllltttion
fllIlt‘tion
the COCf
Constant

T
Choice if
culture’ (

inﬂueHCe

riti

 

29

From this literature review it can be seen that although these models were
disaggregate and were developed for a speciﬁc trip purpose, they showed different
speciﬁcations and different coefﬁcients. This diﬁerence between coefﬁcients exists
because different variables were used in calibrating the model, leading to different
trade-offs between variables.

The ratio of any two coefﬁcients appearing in the same utility function
provides an estimate of the trade-off or a marginal rate of substitution between the
two corresponding variables. In other words, the ratio of these coefﬁcients
represents the relative importance of one variable to another. However, the value
of the coefﬁcient for each variable depends on the utility function. Different utility
functions will produce a different coefficient value for each variable because in each
function the tripmaker weighs the variables differently. However, the ratio between
the coefﬁcients of any two variables having the same unit in any utility should be
constant (17).

This literature review only indicates the variables that inﬂuence the mode
choice in Western countries. N 0 mode choice model calibrated in the Arabic
culture, or in Saudi Arabia, was found in the literature. Therefore, variables that

inﬂuence mode choice cannot be known until the empirical study is done.

2.. ElE' III]

From the previous observations of available intercity mode choice models,
several conclusions may be reached. First, all models assume the tripmaker will
choose a particular mode from among different alternative modes available to

maximize some measure of beneﬁt. Second, these models use the same functional

linear lo
indepent
model (2
to differe

T
case. M:
use to ra
a model
Variables
ill-Vehicle
triPmake
between

imPOYIan

spedﬁcai

 

30

linear logit form. This is because the speciﬁcation variables are assumed to be
independent, and due to the utility theory, the linear additive form is an appropriate
model (26). Third, these models differ in terms of their speciﬁcation and this leads
to different coefﬁcients, as explained in the previous section.

The Watson model was developed for a binary (rail versus car) mode choice
case. Moreover the model was calibrated using mode speciﬁc constants, limiting its
use to rail-versus-car modes. This model is not appropriate for this study because
a model for choosing a mode among several modes is required. Furthermore, the
variables in the Watson model are not satisfactory since they do not include
in-vehicle travel time, egress time, and income. The value of waiting time to a rich
tripmaker is not the same as to a poor traveler. While the difference in waiting time
between the bus mode and the rail mode may not be great, this factor will be
important as additional modes are considered.

The absence of trip length or its related measures from the model
speciﬁcation represents a deﬁciency for this study. Other studies have indicated
that intercity travel mode choice depends heavily on trip length and purpose.
Different characteristics exist in the choice of mode for an intercity tripmaker as trip
length increases (22), and different elasticities in the mode choice model will result
as the trip length increases signiﬁcantly. Some researchers stratiﬁed trips by trip
length in conducting their intercity mode choice analysis (22). They divided intercity
trip length into "long-haul” and "short-haul." If the trip length was more than one
thousand kilometers, it was considered a long-haul trip. If the trip length was less

than one thousand kilometers, it was considered short-haul (22). Since this study

will cons

T
partially
frequenc
In additi

therefore

 

31

will consider only two corridors, this technique is not applicable.

The major drawback of the Stopher model is that it was calibrated with
partially aggregated data. Average values for travel time, travel cost, service
frequencies, and access-egress times for each trip mode in each corridor were used.
In addition, the model was unable to replicate the mode share in selected corridors;
therefore the model could not be used effectively in policy analysis.

The Grayson model is also a pseudo-disaggregate model because it was
calibrated with partially aggregated data. Moreover, it did not include some of the
important speciﬁcations explaining the tripmaker-’5 behavior. For example it did not
include in-vehicle time, length of trip, or a measure of income (such as out-of-pocket
costs related to income).

The Minnesota models were calibrated for the business trip only. The models
were calibrated with disaggregate data and were used effectively in policy analysis.
The major drawback for the Minnesota models is that they were calibrated with a
small sample (only 90 observations were found to be suitable for analysis out of the
300 people interviewed). If the Minnesota models had been calibrated with a large
sample size, they might be the best candidate models to test transferability. None
of the known intercity models is believed to be a candidate for use in a
transferability test conducted in Saudi Arabia. However, it is believed the
speciﬁcation of the variables used to calibrate the Minnesota models is likely to be
the most explanatory measures of tripmaker behavior in the Riyadh-Jeddah and the

Dhahran-Riyadh corridors.

Pretigt

mode c
models
models

 

32

I E l .1. I
3‘0- {"1 10, 1.!_,‘1'§. turrﬁlio- Hf,

In recent years much work has been undertaken in developing disaggregate
mode choice models. Yet little work has been done in evaluating the ability of these
models to predict the tripmaker’s behavior in contexts other than those where the
models have been calibrated. There are no examples of intercity mode choice models
in the literature that have been tested for transferability. This may be due to the
fact that there are only four known intercity mode choice models, and each of these
models has weaknesses which have been discussed.

Additional intercity mode choice models may exist, but they have not been
published and were developed for private operators. However, some work has been
done in evaluating the ability to transfer intracity models. These studies provide
insight into the ability to transfer and test intercity mode choice models.

The actual comprehensive conceptual studies on transferability of intracity
mode choice began in the late 1970’s (27, 28, 29, 30, 31, 32). Atherton and
Ben-Akiva (33) tested the ability of transferring a work-trip modal split model,
estimated on Washington DC. data, to New Bedford and Los Angeles. The model
predicted the probability of a traveler choosing to drive alone, share a ride, or use
mass transit for a work trip. The independent variables included mode-speciﬁc
constants, in-vehicle times, out-of-vehicle times, and out-of-pocket costs for the three
modes: income, auto availability, and a dummy variable indicating whether the
tripmaker was the head of household. The test they performed was based on using

the variables of the original (Washington) model to calibrate new models with New

Bedfo
model

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model
and Ne

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the Wa

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33

Bedford and Los Angeles data and then comparing the coefﬁcients of the new
models with those of the old model.

The comparison of the coefﬁcients consisted of a statistical test of the null
hypothesis that the individual coefﬁcients of the Los Angeles and New Bedford
model were equal to their Washington model counterparts. For both the Los Angeles
and New Bedford models, only the coefﬁcients on the auto availability variables were
signiﬁcantly different from their Washington counterparts.

Four approaches were used by Atherton and Ben-Akiva to test the ability of
the Washington model to explain travel behavior in Los Angeles and New Bedford.

The ﬁrst approach was transferring the original model. The second approach
used the aggregate population share of various modes to adjust the mode-speciﬁc
constants. The logic behind this approach was that since mode-speciﬁc constants
capture the mean effects of the unobserved factors, and since these factors cannot
be measured or controlled, they were most likely to vary from one city to another.
This approach could not be used to forecast analyses because the resulting model
was only replicating the existing data and did not explain the behavior of the
tripmaker in the new context.

The third and fourth updating approaches assumed the presence of a small,
disaggregate sample (44, 89, 177 observations). The third approach ignored the
original coefﬁcients and transferred only the model variables. The disaggregate data
set was used to calibrate a new model (as speciﬁed in the Washington model). Thus
all of the model coefficients were recalibrated. The major drawback of this approach

was that for a small sample the coefﬁcients could be seriously biased, and if a larger

sample
Further]
sample '
'I
as prior
to updai
with prit

the forrr

 

HQ
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34

sample was required it meant the advantage from model transferability was lost.
Furthermore, it was better to calibrate a new model for the new context if a larger
sample was required.

The fourth approach was to consider the coefﬁcients of the original model
as prior information for the true coefﬁcients and use the small sample coefﬁcients
to update this prior information. This approach for combining sample information
with prior information is known as Bayesian updating (34). The form they used, and

the form to be used in this research to update the constants, is as follows:

 

a: =(or/ar’)+(o./a.’)
(l/ar’)+(1/a.‘)
and

a: = ((1/01’)+(1/a.’))“'
Where

a, = original coefﬁcient

a, = sample coefﬁcient

a, = updated coefﬁcient

a, = standard deviation of the original coefﬁcient

standard deviation of the sample coefficient

.9
II

standard deviation of the updated coefﬁcient

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35

The most signiﬁcant result of their research was the ability of the original
Washington model to explain the behavior of the tripmaker in New Bedford.
Furthermore, they found the Baysian updating method gave the best performance.
The results of their research veriﬁed the ability to transfer disaggregate mode choice
models.

Koppehnan and Wilmot (35) discussed issues that inﬂuenced transferability
and methods to evaluate the process. These methods were demonstrated by dividing
the Washington, DC. region into three sectors. Socioeconomic data such as
round-trip total travel time, round-trip out-of-vehicle travel time divided by trip
distance, number of cars per driver (used as an alternative-speciﬁc constant for travel
alone), and other dummy variables for government worker (as an example) were
collected from each sector. The summation of data from the three sectors was used
to build four models: one model for each sector, and a model for the Washington,
DC region. These models described the choice among drive-alone, shared-ride, and
transit alternatives for "breadwinners" working in the central business district (CBD).
They then analyzed intraregional transferability of these models. The results of
their study indicated that at the 0.01 level the observed choice frequencies differed
signiﬁcantly from those generated by transferable models in ﬁve of the six cases.
They also found that a model that transferred from sector A to sector B could not
necessarily be transferred from sector B to sector A. However, the level of

signiﬁcance used to reach this conclusion was not mentioned in their paper.

updat
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36

Another study by Koppelman et al. (36) examined the effectiveness of
updating procedures to enhance model transferability. This study was concerned with
the effect of updating alternative speciﬁc constants and the scale of the model
parameters, representing the variance of the distribution of the error terms, on the
transferability of a disaggregate mode choice model. This study used a disaggregate
sample to recalibrate the mode-speciﬁc constants and to calibrate a sealer used to
scale all of the other coefﬁcients (to keep the ratios between them unchanged). The
logic behind recalibrating mode-speciﬁc constants was the assumption that the mean
effect of unobserved factors was likely to vary from one city to another, and this was
reﬂected in the adjustment of the mode-speciﬁc constants. The logic behind
adjusting the scale of the other coefficients was that travelers in different cities did
not differ in the level of importance they attached to the variables in the mode
choice utility. Maintaining the scale of the coefﬁcients assumed constant tradeoffs
between measured attributes. This approach was demonstrated and evaluated for
both intraregional and interregional transfer of disaggregate models of mode choice
for the work trip. One-ﬁfth of the size of sample required to calibrate the full model
was recommended for updating.

The results of this study indicated that full-model transfer is better than using
only market-share information to adjust the transfer model. Furthermore, the use
of updating procedures substantially improved the expected level of model
effectiveness. Adjustment of alternative speciﬁc constants explained half of the
deﬁciency with respect to local models, while adjustment of the parameter scale

provided only a small incremental increase in model effectiveness. In summary, this

study

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by ado

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37

study indicated that one-half of the difference between full transfer and local
estimation was obtained by updating mode speciﬁc constants. An additional small
increment in model effectiveness could be obtained by updating both the speciﬁc
constants and parameter scale. In conclusion, the results of their study indicated that
model transfer using the previous updating method was better than full-model
transfer or the development of a new model estimated with a small sample.
Furthermore, the effectiveness of the transfer model could be substantially improved
by adoption of the updating procedures.

From the previous work it can be seen that evidence of the transferability of
logit mode choice models from one location to another is encouraging. Yet, it also
appears that models are not perfectly transferable and a procedure for updating is
required. However, the updating procedures are minor efforts compared to the

initial model development.

cons
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51 mod

the foli

CHAPTER III
METHODOLOGY

This chapter describes the methodology used in conducting this study, which
consist of two major parts: model development and model transferability. The
methodology of model development is directed toward data required, sampling
strategy, sample size, model calibration, and model testing. The methodology of
model transferability is directed toward the recommended approaches for transferring '

a model.

Modelmxelonmem

W

Based on the literature, the data needed for specifying, calibrating and testing
transferability consist of three categories: socioeconomic variables, level-of-service
or supply variables, and data regarding the trip. Some of these variables are
qualitative and others are quantitative. In model calibration it cannot be
predetermined which variables best explain the tripmaker’s behavior unless the
impact of the other variables is tested in the preliminary modeling stage. For this
reason, the following variables have been collected and used to determine the best
ﬁt model for each corridor under study.

For the level-of-service variables which may inﬂuence the tripmaker’s choice,

the following variables have been collected:

38

39

W. This is the time in minutes spent in the mode
for a one-way trip.

Me. This is the time in minutes that the tripmaker spends
after leaving the origin until he gets into the mode of choice.
mm. This is the time in minutes the tripmaker spends after
leaving the mode terminal until he reaches the destination.
mm. This variable is the time in minutes between the time
the tripmaker arrives at the terminal and departure of the trip.
W. This variable is the summation of access time, egress
time, waiting time, and in-vehicle travel time.

Wat. Travel cost is the total cost perceived by the tripmaker,
such as airplane fare or gas for the, auto user. This is mainly
out-of-pocket cost. Perceived cost has been found to be more
important than actual cost in mode choice decision-making from the
traveler’s point of view (37). Trip cost has been estimated in Saudi
riyals. This total cost for travel consists of two parts. One is in-vehicle
cost, which includes fare paid for the major carriers, e.g., airplane or
train, and the perceived operation cost for a private car. The other
component is the out-of-vehicle cost, which includes costs such as
access, egress, and parking costs.

Conﬁrm, Brim ﬁafeﬂ, and Expense are qualitative and attitudinal
variables which are used to explain the behavior of the tripmaker in

choosing a mode.

4

Socioec
ll
5 do t.
choice I
such as
variable

I
l

0.4

LIL.

 

40

Another category of data collected consisted of socioeconomic variables.

Socioeconomic characteristics for a given tripmaker do not vary across alternatives

as do the level of service variables. Socioeconomic characteristics enter into the

choice function as mode-speciﬁc, or as a function of the level-of-service variables,

such as out-of-pocket cost divided by income. The following are the socioeconomic

variables collected for use in explaining mode choice behavior:

1.

IneQme. This variable is commonly used as an indicator of a trade-off
between expense, convenience, and other qualitative variables.
Furthermore, it is also used as a proxy for other quantitative variables,
such as the number of autos in the household. Income has been
considered in the Saudi monetary unit, the Saudi riyal (SR).
We. This variable is used to determine whether the
tripmaker owns a car or is captive to other modes. In other words,
does the tripmaker have a complete set of choices? Furthermore, the
number of autos available to a household may affect the mode choice
behavior.

License. This variable has been used to determine if the tripmaker
actually has a choice between an auto and other modes.

QLQQILSiZS- This variable has been used to determine the impact of
the size of a group traveling together in the tripmaker’s mode choice.
13am. This variable has been used to determine if the group traveling
together is related. The size of the family traveling between cities

often reﬂects the actual cost of the trip.

41

6. Age. This variables has been used to determine if age has an impact
on intercity mode choice.

7. Nationality. To determine if there is a difference in travel behavior
for intercity mode choice between Saudi citizens and non-Saudis, this
variable has been introduced into the questionnaire.

8. Wore This variable
will distinguish between tripmakers from outside the country and
tripmakers from Saudi Arabia.

Data regarding the trip were collected and are summarized as follows:

1. Mae. The distinction among trip purposes is an important
step in mode choice analysis because different tripmaker behaviors
are expected in selecting a mode for different trip purposes (22). In
order to distinguish between trip purposes, this information should be
available to the model builder. Trip purposes include business,
personal business, aumra, social, recreational, and work.

2. W. The length of time a tripmaker is planning to stay
at the destination city has been collected. The categories for this
variable are one day, 2-7 days, and more than 7 days.

Moreover, objective LOS data for the modes under consideration have been
collected from the agencies operating those modes. In other words, a model having
the two types of measures will be calibrated: perceived data for the chosen and

objective data for the modes not chosen, except the perceived value will be used for

comfort, privacy, expense and safety for all modes.

prc

use

sann
ouux
idenr

frOrn

 

42

mummy

Data collection is the preliminary step in any travel demand study. Random
sampling, stratiﬁed sampling, and choice-based sampling are the three possible
procedures for data collection. Random sampling and stratiﬁed sampling are usually
used when users in the transportation market are evenly distributed. Choice based
sampling, which samples passengers on the roadside, trains or planes, is
recommended when the demand in the transportation market is unevenly distributed
(38). Consequently, choice based sampling has been used to collect the required
data.

The choice based sampling technique is the least expensive method for
sampling. With the choice based method, observations are drawn based on the
outcome of the decision maker process. Choice-based sampling is conducted by
identifying the decision group of interest and then randomly choosing individuals

from this group.

Warrants

Sample size determination is an important decision in the planning phase of
any research. The sample size required in any statistical analysis is dependent upon
the desired level of conﬁdence and the size of the interval.

Snedecor and Cochran (39) stated that the sample size depends on the
allowable error (L) in the sample mean, the speciﬁed degree of conﬁdence that the
error will not exceed L, ((1-a)‘100%), and the standard deviation. Mathematically

it can be represented as follows:

43

[2(1-0/2)]’a

11:
L2

 

Where:

n= sample size.

a= standard deviation.

L= allowable error.

z= normal random variable.

I-a = conﬁdence level.

I! l l C 1'] r .

Calibration is the process of estimating model parameters using collected
data. Based on the literature review, a simultaneous logit approach is recommended
to be the structure of the models for the corridors under study. The superior method
for calibrating a logit model is the maximum-likelihood procedure. The maximum-
likelihood procedure is usually used by transportation planners to estimate model
parameters. The maximum-likelihood estimation of the model produces
goodness-of—ﬁt statistics, such as t-statistics for coefﬁcients and a X2 statistic for
assessing the entire model.

Several statistical packages are available to calibrate logit models. Among
these are the Statistical Packages for the Social Science (SPSS), the Statistical
Analysis System (SAS), ULOGIT, BLOGIT, and SIDGIT. The Statistical Analysis
System (SAS) package was used to perform the preliminary statistics procedure, such
as the mean and the standard deviation of the collected data. The BLOGIT package

was used to calibrate the model using different model speciﬁcations. In this package

eqi
esti
con

esn

data
coHe

Inod

depe
Signs
9051 .

traVe

the v;

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44

the maximum likelihood approach iteratively solves for the coefﬁcients in the utility
equation. The estimation package will iterate through the problem until the
estimated coefﬁcients reach a speciﬁc convergence criterion or the estimation
completes a speciﬁed number of iterations. After iteration has been completed, the
estimated model will provide the best ﬁt to the observed pattern of choices in the

calibration sample.

I I l l V 1'! .

The validation process is an integral aspect of the model development process.
The model’s validation should be tested by using the model to predict modal-split for
data other than that used for model calibration (40). Validation data have been
collected for use in comparing the predicted and observed modal split to test the
model’s validation.

A test of reasonableness validation process was also used. This process
depends on the reasonableness of the model in terms of the expected coefficient
signs, and the reasonableness of the parameters. For example, travel time and travel
cost always have negative impacts on travel demand; no model which has a positive

travel time or cost coefﬁcient would be considered a reasonable or valid model.

R l nfrrin h 1

After a model has been constructed for one corridor in Saudi Arabia, and
the variables which explain the behavior of the tripmaker have been determined,

several approaches will be used to transfer the model. Transfer models are those

I110

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45

models calibrated with one data set (for example, a different area, or a different
time) and used to explain the variation in the new data set.

The ﬁrst approach accepts the model as it is. For instance, the calibrated
model for the Riyadh-Jeddah corridor is used to explain the behavior of the
tripmaker in the Dhahran-Riyadh corridor, and vice-versa. This approach depends
on the assumption that disaggregate models have the potential to transfer, because
they are based on the behavior of the tripmaker, and this behavior is constant over
space. Another assumption required in using the model in its original form is that
the factors relevant to the choice process are embodied in the model. However, this
assumption is never completely justiﬁed because most disaggregate models are not
perfectly speciﬁed in order to decrease the complexity of the model. The
speciﬁcation of most known models contain constant terms. These constant terms
represent all other factors affecting the behavior of the tripmaker not explicitly
considered in the model (e.g. comfort, convenience, safety, etc.). Thus the presence
of these constants indicates that the model has not captured all factors affecting the
tripmaker’s choice. Those factors not explicitly explained by the model may vary
from one area to another. Thus the value of such constants estimated for one
context may not be appropriate for another context. A ﬁnal assumption is that the
relationships estimated between time, cost, income, etc., are transferable.

The second approach is to update the transferable model. In other words
the, constant terms as well as the coefficients of the variables in the transfer model
are re-estimated using a part of the sample required to calibrate a new model. The

size of the sample is about one-ﬁfth the sample required to calibrate the proposed

mo<
for
the
com

upda

Jedd:
coefﬁ
(Dhal

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46

model (36). Then coefficients of the transfer model are considered prior information
for the true coefﬁcients. The coefﬁcients resulting from calibrating the model with
the small sample are used to update this prior information. This approach for
combining sample information with prior information is known as "Bayesian
updating" (40).

In this case, the constant terms and the coefﬁcients of the variables in the
Jeddah-Riyadh model are considered prior information and the constant and the
coefﬁcients of the variables are re-estimated with small data from the other corridor -
(Dhahran-Riyadh corridor). Then the re-estimated coefﬁcient is used to update the
transfer model.

The third approach is to transfer the model speciﬁcation only. Then the
model is calibrated with the new data. This approach has been introduced in order
to determine the universal set of speciﬁcations required to calibrate the mode choice
model, and to determine if the parameters estimated for the two corridors are equal.

In summary, the three approaches tested for the transferability of models
are:

1. transferring the unchanged model.

2. using the Bayesian updating method to combine the original and small

sample coefﬁcients.

3. transferring the speciﬁcation of the variables of the model only, and

recalibrating the model.

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47

W

Several sets of hypotheses will be tested in this research. The ﬁrst set of
hypotheses tests whether the disaggregate models are transferable. In other words,
a disaggregate model can be calibrated and tested in one area and used to explain
the variation in mode choice in another area. In order to perform this test the
calibrated model for each corridor will be used to predict the behavior of the
tripmaker in the other corridor for the same trip purpose. For example, the original
model for the Dhahran-Riyadh corridor will be used to predict tripmaker behavior
in the Riyadh-Jeddah corridor.

The second set of hypotheses tests whether the updating method improves
the prediction power of the transfer models signiﬁcantly. In other words, can the
prediction power of the transfer model for each corridor be improved signiﬁcantly
if the updating method is used?

The third hypothesis to be tested is whether the speciﬁcation of the model
in the transfer model replicates the data as well as the original speciﬁcation. The
fourth hypothesis is whether the parameters in the transfer model and the parameters
after recalibrating the model for the same speciﬁcation are equal. For instance, are
the parameters estimated for Riyadh-Jeddah and Dhahran-Riyadh for the same
speciﬁcation equal?

A ﬁfth hypothesis is whether the coefﬁcient for level-of-service variables (e.g.
time or cost) in the transfer model and the original model are equal (assuming both
models have the same speciﬁcation). For example, for the models calibrated for the

two corridors under study, are the coefﬁcients for the level-of-service variable equal?

lfdus
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ofser

shnuﬁ

Inode

behav

 

evahu

 

 

 

48

If this is the case, there is no need to collect level-of-service data for calibrating new

models.

The last hypothesis is related to the ﬁfth one. Does the coefﬁcient of level-

of-service in the transfer model (e.g. time or cost) before and after updating differ

signiﬁcantly from the original model?

In summary, the following hypotheses will be tested when transferring intercity

mode choice model from one area to another:

1. There is no difference in prediction power between the calibrated
model for each corridor and the transfer model.

2. There is no difference in prediction power between the original model
and the transfer model after updating the coefﬁcients.

3. The goodness of ﬁt produced by the transfer speciﬁcation and the
calibrated speciﬁcation is the same.

4. The parameters in the transfer model and the estimated parameters
in the recalibrated model are equal for the same speciﬁcation.

5. Coefﬁcients for level-of-service variables (e.g. time or cost) for the
two corridor speciﬁc models are equal.

6. Coefﬁcients for level-of-service variables (e.g. time or cost) for the
original and the transfer model after updating are equal.

5 . . I l H 1

Two measures of how the transfer model explains the variation in the

behavior of the tripmaker in the new context were used by Ben-Akiva (17) in

evaluating the ability of intercity disaggregate model transferability. The ﬁrst

mea:
ObSCl

OVC IE

test, a
mode

produ

linpro‘

 

We.

 

 

49

measure is the X2 statistic (41). In this test, a comparison is made between the
observed value and the predicted choice value for each mode. Larger values of the
overall discrepancy between the proposed model and the transfer model indicate
disagreement between the nvo models.

The second measure is the percent of correct estimates for each mode. In this
test, a comparison is made in each cell between the predicted value from the transfer
model and the observed value. This measure is analogous to the X’ test, yet it
produces additional insight into the differences between the distribution of observed
and predicted values. These approaches will also be used to determine the
improvement in model prediction before and after updating the transfer model.

The asymptotic "t" statistic test of equality of individual coefﬁcient between
two models is used to test the hypotheses that the coefﬁcients for the level-of-service
variable (e.g. time or cost) for the proposed models are equal, and the coefﬁcient for
the level-of-service variable (e.g. time or cost) for the transfer models before and
after updating are equal.

The t-test statistic for the null hypothesis 3,, =3, is as follows:

 

5u°3a
t =
[var (3:1) 7' var(5a)]§
Where:
3,, = is the coefﬁcient of the variable under consideration e.g. cost in model
1.
8,, = is the coefﬁcient of the variable under consideration e.g. cost in model
2.
var(3,,) = the variance of the coefﬁcient of the variable under consideration in

model 1.

var(B

 

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that t
($01116
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50

var(£,,) = the variance of the coefﬁcient of the variable under consideration in
model 2.

Another statistical measure of the transferability of the disaggregate mode
choice model estimated in context j and used to predict mode choice in context i for
the same speciﬁcation is the Likelihood ratio test statistic,

"l‘ISt(£,-)=-2(LL(B.)- use.»

where TTS,(£,) is the transferability test statistic, LL(B,) is the log likelihood
that the behavior observed in context i was generated by the model estimated in
context j, and LL,(&)) is the log likelihood for the model estimated in the same
context i. The Likelihood ratio test statistic is chi-square distributed with degrees
of freedom equal to the number of model parameters under the assumption that
the number of parameters is ﬁxed. This test has been used by Atherton and
Ben-Akiva (33) in their test of transferability between Washington, DC and New
Bedford, Massachusetts, and by Koppelman and Wilmot (42) in their test of
transferability between sectors in the Washington, DC. area. This test has been
used to test the null hypothesis that the parameters in the transfer model and the
parameters in the recalibrated model for the same speciﬁcation are equal.

A goodness of ﬁt measure is used in determining which speciﬁcation is better
in replicating the data. This measure is somewhat analogous to the R’ used in
regression. Since the logit model is asymptotic to 0 and 1 probabilities in its tails,
one can never precisely achieve a value equal to 1. At the other extreme, if all the
parameters in a logit model are 0, the model predicts that all the choices for any

given individual are equally likely. In this case, the model does not explain choice

variati

the ne

transit

identic
for ex
achiev
new sii
mOdel

Preclic:

 

 

 

51

variation. In order to compare alternative models used to explain the variation of

the new data, the rho-square (p’) goodness of ﬁt measure has been used:

L(s)
transfer p’ = 1- ——
L(0)
in which:
L(B.) = Log likelihood for the vector of estimated coefﬁcients
L(0) = The value of the log likelihood function when all the

parameters are zero
This measure is most useful in comparing two speciﬁcations developed from
identical data. The model which has the higher goodness of ﬁt is the better model
for explaining the behavior of the tripmaker in the new context. This measure
achieves an upper limit of one when the transferred model predicts perfectly in the
new situation, has a zero value when the model predicts as well as the market share
model (L(s) = L(0)), and it may attain a negative value when the transferred model
predicts worse than the market share model.
In summary the following methods are used to test the proposed hypotheses:
1. the chi-square teSt and the percentage right method will be used to test
if there is a difference in prediction accuracy between the original model
for each corridor and the transfer model. In addition, they will be used
to test if there is a difference in prediction accuracy before and after
updating the coefﬁcients for the transfer model.
2. "t” test statistics will be used to test if the coefficients for the level-of-
service variable (e.g. time or cost) for the calibrated models are equal,

and if coefﬁcients for the level-of-service variable (e.g. time or cost) for

52

the transfer model before and after updating are equal.

transferability test statistics (TTS) will be used to test if the parameters
in the transfer model and the estimated parameters in the local model
are equal, assuming both have the same speciﬁcation.

goodness of ﬁt will be used to determine which speciﬁcation is better in
explaining the tripmaker behavior in the new context. For instance, does
the transfer speciﬁcation or the original one produce a. better goodness

.of ﬁt?

mod
choi.
and

W215

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resea

ofPe

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in A

Conn:

0n.b(_

Were

 

 

CHAPTER IV
DATA COLLECTION

The main purpose of this study was to determine the feasibility of intercity
mode choice model transferability within Saudi Arabia. Since no intercity mode -
choice model has been developed to predict the behavior of the Saudi tripmaker,
and the data required to achieve this purpose did not exist, data for this research
was collected as part of this research study. The researcher contacted the
Government Railways Organization, Saudi Arabian Public Transport Company, and
the Ministry of Civil Aviation to get permission to distribute the questionnaires. The
researcher personally with the help of a graduate student from King Fahd University

of Petroleum and Minerals located in Dhahran, distributed the questionnaire forms.

W

Appendix B shows the questionnaire form distributed for each mode under
consideration. While the formats used to code the questionnaire forms are presented
in Appendix C. Because many tripmakers in Saudi Arabia are from different
countries, and the most prevalent languages among tripmakers are Arabic and
English, the questionnaire forms were written in both Arabic and English. These
forms were distributed at the airplane terminal, bus terminal, and train station for
tripmakers traveling in the corridors under study. Questionnaires were distributed
on—board while the subjects waited for the departure. The completed questionnaires

were collected at the destination of each trip.

53

mid'
forn
retu;

ICILll

(by 1:
of b
char;
safer}
the q'

train,

 

 

 

 

54

Tripmakers traveling by car were interviewed at the gas stations located
midway between the cities under study. In addition, one-hundred questionnaire
forms were placed at the gas stations. However, none of these questionnaires were
returned, even though the recipients were asked to complete the questionnaire and
return it by mail.

This questionnaire included a wide range of variables characterizing the trip
(by mode, trip purpose, origin destination, duration, etc.), the service characteristics
of both the chosen mode (travel time, cost, frequency, etc.) and perceived
characteristics of other available but unchosen modes (comfort, privacy, expense, and
safety), and the tripmaker’s characteristics (age, income, occupation, etc.). Moreover,
the questionnaires were coded by the name of the four different modes under study:
train, airplane, private car, and bus.

Table 4.1 shows the description of the abbreviated variables used throughout
this research. Tables 4.2, 4.3, 4.4, and 4.5 show the number of responses, minimum,
maximum, mean, and standard deviation values obtained for each variable for plane,
bus, train and car serving the Dammam-Riyadh Corridor.

Tables 4.6, 4.7, and 4.8 show the number of responses, minimum, maximum,
mean, and standard deviation values obtained for each variable for plane, bus, and

car serving the Jeddah-Riyadh Corridor. There is no train service in this corridor.

_V I.

NTTTTTTTTTTTTTTVVVVTTTTUUHWﬂ

55

Table 4.1

Description of the abbreviated variables

 

eraser g2;

3.5

-l

Variable deﬁnition

 

Number of observations

One-way total travel time by AIR ,hrs.

One-way total travel time by BUS ,hrs.

One-way total travel time by CAR ,hrs.

One-way total travel time by TRAIN, hrs.
One-way access time for AIR tripmakers, hrs.
One-way access time for BUS tripmakers, hrs.
One-way access time for TRAIN tripmakers, hrs.
One-way egress time for AIR tripmakers, hrs.
One-way egress time for BUS tripmakers, hrs.
One-way egress time for TRAIN tripmakers, hrs.
One-way waiting time for AIR tripmakers, hrs.
One-way waiting time for BUS tripmakers, hrs.
One-way waiting time for TRAIN tripmakers, hrs.
One-way waiting time for CAR tripmakers, hrs.
One-way in-vehicle travel time by AIR, hrs.
One-way in-vehicle travel time by BUS, hrs.
One-way in-vehicle travel time by TRAIN, hrs.
One-way in-vehicle travel time by CAR, hrs.
One-way total out-of-pocket cost by AIR, SR.
One-way total out-of-pocket cost by BUS, SR.
One-way total out-of-pocket cost by TRAIN, SR.
One-way total out-of-pocket cost by CAR, SR.
One-way ticket cost by AIR, SR.

One-way ticket cost by BUS, SR.

One-way ticket cost by TRAIN, SR.

One-way oil cost by CAR, SR.

Monthly personal income,SR.

Monthly household income,SR.

Group size.

Number of cars the tripmaker owns.

Student.

License.

Tripmaker age.

Relative comfort for AIR , Scaled from 5 to 1".
Relative comfort for BUS , Scaled from 5 to 1.
Relative comfort for CAR , Scaled from 5 to 1.
Relative comfort for TRAIN,Scaled from 5 to 1.

 

56

Table 4.1 continued

 

 

Variable Vaﬁable deﬁnition

.liame'

PRIV, Relative privacy for AIR, Scaled from 5 to 1.
PRIV, Relative privacy for BUS, Scaled from 5 to 1.
PRIVC Relative privacy for CAR, Scaled from 5 to 1.
PRIVT Relative privacy for TRAIN,Scaled from 5 to 1.
SAFA Relative safety by AIR, Scaled from 5 to 1.
SAP. Relative safety by BUS, Scaled from 5 to 1.
SAFC Relative safety by CAR, Scaled from 5 to 1.
SAFT Relative safety by TRAIN, Scaled from 5 to 1.
EXP, Relative expense by AIR, Scaled from 5 to 1.
EXP. Relative expense by BUS, Scaled from 5 to 1.
EXPC Relative expense by CAR, Scaled from 5 to 1.
EXP, Relative expense by TRAIN, Scaled from 5 to 1.
DUR Duration of stay.

DIS Distance in 1000 KM

ASC-AIR Mode-speciﬁc constant for air.

ASC-BUS Mode-speciﬁc constant for bus.

ASC-CAR Mode-speciﬁc constant for car.

IVTT One-way in-Vehicle time in hours.

OPTC One-way Out-of-pocket cost

OVTT One-way out-of-vehicle time,hrs.

WT One-way wait time,hrs.

TIT One-way total travel time,hrs.

COMFORT Relative comfort, Scaled from 5 to 1.
PRIVACY Relative privacy, Scaled from 5 to 1.

SAFETY Relative safety, Scaled from 5 to 1.
EXPENSE Relative expense, Scaled from 5 to 1.

 

' Variables with subscript/s are speciﬁc to a mode(s) (A for air, B for bus, C,
for car)

” 1 is best, 5 is worst.

Ndv 07.5.5

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is 4,
met
witl
hou
with
size

inl

coll

moc

 

 

 

Samplem

Sample size was based on the income variable because it contained the
highest variation among the variables. The average monthly income in Saudi Arabia
is 4,500 SR, with a standard deviation of 1,250 SR (43). From the survey, the sample
mean for household income for the Dhahran-Riyadh corridor was 4,233 SR / month,
with a standard deviation of 1,959 SR. For the Riyadh-Jeddah corridor, the mean
household income was 3,868 SR/month, with a standard deviation of 1,830 SR. 80,
with a 5% risk, the error will exceed 10% of the mean [z(.975)= 1.96], the sample
size required by the sample size equation for each mode ineach corridor is shown
in Table 4.9.

From Tables 4.2, 4.3, ..., 4.9 it can be seen that the number of observations
collected are greater than the size of the sample required to calibrate the intercity

mode choice model for each corridor.

Table 4.9

Sample Size Based on Income

 

 

Monthly Standard Sample
Corridor Name Mean Income Deviation Size
(SR) Required
Dammam Riyadh Corridor 4,233 1,959 83

Jeddah Riyadh Corridor 3,868 1,830 86

 

 

 

 

 

 

preser
frame
calibr:
transfc
presen
BLOC
study V

also be

has the

CHAPTER V
THE CALIBRATION PROCESS

In the previous chapter the results of the data collection process were
presented. In Chapter II and Chapter III, the theoretical considerations and the
framework for the empirical work were described. Using that framework, model
calibration procedures were illustrated, 0 and the recommended approach for
transferring intercity mode choice models from one corridor to another were
presented. In this chapter, the intercity mode choice models generated by the
BLOGIT computerized statistical estimation package for the two corridors under
study will be presented. The result of testing the transferability of these models will

also be presented.

W11
The intercity mode choice model for the non-business trip within each corridor

has the following form:

EXP v,
P‘, =

 

ZEXP v,
1'

Where:
P‘, = probability of a tripmaker i choosing mode k out of j alternatives

V,, = the utility of alternative k to trip maker i
= (xx: Si)

X, = a row vector of characteristics of alternative k

65

functior
the char
only in

assumes
function

values a.

66

S, = a row vector of socioeconomic characteristics of a tripmaker i

The probability of a tripmaker choosing a particular mode alternative is a
function of the characteristics of the tripmaker, such as income, age, and sex and of
the characteristics of that mode relative to alternatives modes. If a variable appears
only in the utility function of mode K, then it is a mode-speciﬁc variable which
assumes a value of zero in all jfk model utilities. If a variable appears in the utility
function of all modes, it is considered a generic variable, which takes on different

values across the utilities for different modes.

Medel Speeiﬁeetien

Different speciﬁcations for the models have been evaluated to determine
which speciﬁcation best replicates the data for each corridor. These speciﬁcations
include the variables that have been found in the literature review to inﬂuence the
tripmaker choice (such as out-of pocket cost (OPTC), egress travel time (EGTI'),
access travel time (AT'I‘), household income (HINC), total travel time (TIT),
out-of-vehicle travel time (OVTT), distance (DIST), in—vehicle travel time (IVTI‘),
and waiting time (WTXIIomposite variables such as OPTC/HINC and
OVTT/DIST are used to modify the impact of the pure level-of-service variables
OPTC and OVTT. It is hypothesized that tripmakers with different levels of income
perceive travel cost differently. Similarly, out-of-vehicle time is hypothesized as
becoming less important as the length of the trip increases.

Different model speciﬁcations were tested, as can be seen in Tables 5.1, and
5.2. Each model estimate is based on a different modal utility function. Modal

speciﬁcations were formulated based on prior experience in intercity mode

 

‘ﬁ—
V arrat
Nam:

ABC-A
ASC-B
OPTC
OPTC
OVT/1
IV'IT

5553

EGRC}

§

IN
MHIN

(“)

67

Table 5.1

Model Results for Mode Choice Models for the Dhahran-Riyadh Corridor
(Non-Business Trips; Train is Not Included)

 

 

 

 

 

 

 

Variable Wan“
Me 4 M l
ASC-AIR -6.75 (-5.60) -5.90 (6.14) -3.98 (-3.51) 2.79 ( 5.20) 2.52 ( 4.69)
ASC-BUS 0.94 ( 1.95) 3.21 ( 6.94) 2.68 ( 5.51) 3.83 ( 8.82) 3.97 ( 8.94)
OPTC-MHINC -0.06 (-8.15) - -0.06 (-8.77) - -
OPTC - -0.02 (-8.61) - -0.02 (-8.76) -0.02 (-8.71)
OV‘T/DIS - 0.06'( 0.38) 0.22'( 1.02) - -
NW 482 (-8.27) -2.64 (-6.76) -2.40 (-6.24) - -
T'TT 2.63 ( 6.27) - .- .. ..
WT -- - -0.75'(-l.15) - -
TTI"MHINC -- -— -- -0.ll (-6.l4) -
IV'I'I‘*MHINC - - - - -0.22 (-7.43)
EGR‘MHINC - - - 0.36 ( 5.64) 0.72'( 0.70)
MHINC/FREQ — - - 0.18( 1.94) 0.34 ( 5.25)
MHINCA - 0.43 (5.75) - - .-

p‘ W3 0.30 036 0.33 0.36

 

‘ The estimated coefficient is not significantly different from zero at the 0.05 level.

(”) t-statistic.

 

_wi_mmmmowwnww( w(HMummwum \2p\.,..t

 

 

68

 

 

 

 

 

 

Table 5.1, Cont’d.
Variablc W‘
M MOEU—MﬂﬂL—MﬂdL—M 9 MQELISL
ASC-AIR 41.17 ( 4.30) 38.52 ( 4.29) 2.33 ( 3.33) 40.16 ( 4.00) 0.96'( 1.04)
ASC-BUS 2.82 ( 3.75) 0.50'( 0.77) 5.17 ( 7.88) -1.58'(-1.64) -0.13°(-0.14)
OPTC-MHINC -0.08 (-6.36) -0.09 (-332) - -0.08 (-5.89) -.
OPTC - - -0.02 (-7.67) - -0.03 (-6.13)
OVT/DIS -0.28'(-0.69) - .. .. ..
IVT'I‘M 0.01'( 0.01) -3.53 (4.00) - -0.08°(-0.16) -
IVT'I‘A 40.10 (4.30) 45.90 (-5.06) -- 40.23 (4.09) --
TIT - 3.29 (4.90) -- -- --
wr 152033) -- .. .. --
IVTPMHINC -- -. -0.80 (-8.99) -- 037 (-3.70)
(sp. bus, car)
IVTT'MHINC - - -3.04 (-8.16) - -10.07 (4.69)
(sp. air)
EGR‘MHINC - - 0.09°(0.59) -- --
MHINC/FREQ —- -- 0.06' (0.72) -- --
COMFORT 0.73 (6.10) 0.75 (5.75) 0.75 (5.86) 0.79 (5.73) 0.70 (4.86)
PRIVACY 0.29 (2.81) 0.30 (2.59) 0.09°(0.86) 0.30 (2.47) -
SAFETY 0220.86) 032 (2.60) 0.42 (3.69) 031 (2.48) 0.48 (332)
MHINCA -- - - - 8.91 (4.05)
no, .- -- -- 3.73 (4.80) 3.02 (3.94)
DURA - - -- 2.20 (3.42) --
p3 0.65 0.69 0.62 0.71 0.73

 

3 The estimated coefﬁcient is not sigmf’rcantly different from zero at the 0.05 levef

(u) t-statistic.

 

2

at

CC

M]

M]

DI

GF

p2

D

69

Table 5.1, Cont’d.

 

 

 

 

 

Variable ' ' ' 4
Jim M0421 11 MudﬂJz—MSEIQILMLIL
ASC-AIR '22; ( 3.04) 0.06‘( 0.05) 0.87‘( 1.13) 4034 ( 3.88)
ASC-BUS 0.06°( 0.07) -137'(- 133) 3.09 ( 3.63) 533 ( 6.45)
one 0.03 (420) 0.03 (-5.69) 4101 (-229) 0.03 (45.17)
rvr'rM - - .- -0.56°(-1.04)
rvr'rA .- .. -. 43.46 (.421)
(rv'r'rrrvrrrIrIC),c 0.78 (-790) 032 (3.02) 0.90 (-8.46) --
(IVTT'MHINC), 3.01 (-771) -971 (4.18) .350 (807) .-
COMFORT 0.75 ( 5.01) 0.73'( 4.47) 0.94 ( 5.82) 0.67 ( 450)
my 050 (3.44) 0.47 ( 2.86) 0.63 (4.40) 050 (330)
MHINC, .- 8.77 (3.66) .- 039 ( 2.05)
WC, -- .. .. -0.72 (-554)
11c, 3.11 ( 434) 325 ( 3.92) 253 ( 4.02) -.

DUR, 219 (4.11) 295 ( 3.91) 1.82 ( 3.67) 2.08 ( 3.10)
SAUD, 2.60 (531) 2.17 (4.40) ... .-

(mopc .. .- 4.71 ( 5.71) --

p2 0.71 0.78 0.73 0.75

 

3 The estimated coefﬁcient is not signiﬁcantly different from zero at the 0.05 level.

(") t-statistic.

\Aaruahdc:

.AHSCJuALII
ASC-BU:
()l’fIZ-IVi
()r'rrz

' OVT/DIS

(u)

l-st

70

Table 5.2

Model Results for Mode Choice Models for the Jeddah-Riyadh corridor
(Non-Business Trips)

 

 

 

 

 

 

Variable ' r ' n "

Jim MadsLL_Mm:LL_Mndsl 3 MOW
ASC-AIR 027‘(-030) -3.71(-3.16) -1.42°(-1.69) 080‘(130) 0.77'( 124)
ASC-BUS 201 ( 5.90) 1.96 ( 4.66) 1.48 ( 269) 636 ( 8.78) 636 ( 8.85)
OPTC-MHINC -0.04 (-9.99) - .004 (-9.99) -. -

one -. 00109.04) .. -0.01 (-299) -0.01 (-779)
OVT/DIS .- 0.06'( 020) 0.75’( 1.86) - --

Ivrr 0.08’( 0.47) -031 (-2.86) -0.41 (-3.83) - ..

m -0.53 (-3.01) -- - .- --

WT -- -- -0.94'(-189) -- --
mmnmc - .- - -0.16 (-8.76) .-
WTF‘MHINC -- -- -. - -0.26 (-8.49)
EGR’MHINC .- .. .- 027 ( 2.55) 0.74 ( 6.76)
MHINC/FREQ -- - - 0.80 ( 6.98) 0.16'( 1.45)
MHINCA .- 1.13 (9.12) .- — --
MHINC, .- .. .- .. ..

p’ 036 0.42 035 0.58 057
T—The estimated coefﬁcient is not signiﬁcantly different from zero at the 0.05 level.

(”)

 

t-statistic.

 

PR

M}

LIc

\ZDNHMI

71

 

 

 

 

 

 

Table 5.2, Cont’d.

Variable :' ' ' "
m MW 8 M03151 9 MstLm.
ASC-AIR 3.60’( 1.14) 023'( 032) -132 (225) 263'( 080) 0.19'( 027)
ASC-BUS 1.76 ( 2.83) 633 ( 786) 1.34 ( 1.96) 1.69 ( 2.12) 6.41 ( 7.91)
OPTC-MHINC 0.04 (-8.82) - .- 0.02 (.465) --
OPTC - 0.01 (.244) 0.01(-7.43) -- 0.01 (-7.63)
OVT/DIS 039°( 0.84) -- -- -- --
IV'I'rm 029 (-249) .- .. 033 (-273) -.
Ivm -3.54’(-1.88) - - -235 (0.10) --
WT -0.82°(-1.45) -- .. .. --
m‘MHINC -- -- -. -- 0.16 (-7.93)
IV'IT‘MHINC -- 0.17 (-5.03) 020 (-5.81) -- --

(89- bus. at)
IV'IT‘MHINC -- 037‘(-1.22) -1.00‘(-1.76) -- --

(59- air)
EGR‘MHINC -- 021'( 1.59) - -- 0.26 (2.21)
MHINC/FREQ - 0.67 ( 5.26) -- -- 0.74 ( 5.77)
COMFORT 0.48 (536) 038 (3.58) 0.40 ( 386) 0.44 ( 432) 039 ( 3.68)
PRIVACY 0.18‘( 1.94) 023'( 020) - 0.13'( 122) 0.02'( 0.02)
SAFETY 037 ( 3.94) 038 (335) 0.44 ( 3.98) 0.51 ( 4.76) 038 ( 331)
MHINCA -- -- 0.14‘( 0.16) - --
LIC, -- - 132 ( 274) 212 (4.56) --
DURA -- -- - 3.06 ( 263) --
p2 0.47 053 059 0.58 0.64

 

‘ The estimated coefﬁcientis not signiﬁcantly different from zero at the 0.05 level.

(”) t-statistic.

COMFORT

 

 

 

 

72

Table 5.2, Cont’d.

 

 

 

 

 

 

Variable V ' l f "

M ’MEELLMLILJMQLLMQM—
ASC-AIR 0.49'(0.66) -1.36 (-225) 0.70'(0.99) 055'(0.15)
ASC-BUS 1.61‘( 1.76) 0.10‘( 0.13) 282 ( 3.43) 7.69 (7.80)
OPTC/MHINC 0.00 (-3.72 - — ..

OPTC - 0.01 (-727) 0.00 (4.18) 0.01 (-244)
Ivrrw -- - -- 0.43 (-305)
IV'I'I'A -- .- .. -279’(-1.14)
(IVTT‘MHINChc 0.16 (.466) 0.17 (-5.06) 0.18 (-5.58) --
(IVI'IWItiHINC)A 0.91‘(-133) 0.67 (-254) 0.78 (-299) .-
COMFORT 032 ( 274) 037 ( 3.43) 0.38 ( 335) 0.42 ( 388)
SAFETY 0.49 ( 4.15) 0.46 ( 3.99) 0.50 ( 431) 0.43 (3.77)
MHINCA -- .- - 053 (3.36)
MHINC, .- .. .. -1.64 (0.77)
no, 0.95‘(1.77) 0.93‘( 1.90) 131 (245) .-

DURA 240°( 1.91) 297 (240) 275 ( 264) 330 ( 269)
SAUD. 211 ( 4.19) 1.94 (4.16) -- -

(mopc 3.57 ( 5.94) - 339 ( 5.86) --

p2 0.69 0.63 0.66 0.65
7——The estimated coefﬁcient is not signiﬁcantly different from zero at the 0.05 level.

(n) t-statistic.

choice 10:
For instal
and 3 m0
and 5 are
the mode
models 1
model cal

Sor
counter-in
produced:
time (Tn
but is not .
used as an
Variable I\
goodness-0
the Size of
mOdeL 13

PIC)

Variable. F

 

 

73

choice modelling, and the impact of introducing additional explanatory variables.
For instance, models 1, 2 and 3 have the same speciﬁcation as the Minnesota 1, 2,
and 3 models, respectively, described in Chapter II. The speciﬁcation of Models 4
and 5 are analogous to that used by Grayson (discussed in Chapter II). The rest of
the models consist of modal utilities that have additional variables than the ones in
models 1 to 6. These different specifications of modal utility have been used in
model calibration. .

Some of these models exhibited poor statistical goodness-of-ﬁt and/ or
counter-intuitive signs and were rejected. For example, model 7 in Table 5 .1
produced a very good ﬁt but it has a counter-intuitive Sign in the variable total travel
time (TIT). Model 12 for the Dhahran-Riyadh corridor produced a very good ﬁt,
but is not selected because the monthly household income variable (MI-IINC) was
used as an airplane mode-speciﬁc variable, which is highly correlated with the
variable IV'IT'MHINC. Furthermore, trial model 11 (Table 5.2) has the highest
goodness-of-ﬁt measure but it has not been selected because the variable indicating
the size of the group (GROP) is highly correlated with the total trip cost. Finally
model, 13 for the same corridor was not selected for the same reason.

Previous intercity mode choice models used in-vehicle travel time as a generic
variable. For this study, this practice is not justiﬁed because models with generic in-
vehicle travel time (IVTI') show lower goodness of ﬁt than those with a generic
IVTI‘ variable for bus and car, and a mode-speciﬁc in-vehicle travel time for air.
This means that the traveller views the in-vehicle travel time for the bus or car

similarly but differently from that for the airplane.

74

Of all the model speciﬁcations tested, the most satisfactory model for the
Dhahran-Riyadh corridor with and without the train mode, and the Riyadh-Jeddah
corridor are given in Tables 5.3, 5.4, and 5.5 respectively, which is the same
speciﬁcation as model 14 in'Tables 5.1 and 5.2.

The following model speciﬁcation was determined to be the best in explaining the
behavior of the tripmaker for the two corridors under study:
Utility for air mode (p) for tripmaker k =

a,’ + a,OPTC, + a,IVIT, + a,MHINC,‘ + mSAFETY, + a,COMFORT, + a,DUR

Utility for bus mode (b) for tripmaker k =

a,” + a,OPTC. + a,IV'IT, + a.MHINCK+ aSAFETY, + a,COMFORT.

Utility for train mode (t) for tripmaker k =

3.," + a,OPTC,+ a.,IV'I'1‘T + aSAFETY, + a,COMFORTT

Utility for car mode (c) for tripmaker k =

anOPTCc + a,IV'IT, + a.SAFETYc + a,COMFORTC

The deﬁnition of these terms are:

OPTC W. This is total out-of-pocket cost perceived by the
tripmaker (such as airplane fare, parking cost and gas for the auto).
Trip cost is expressed in Saudi riyals (SR). This total cost for travel
consists of two parts. One is in-vehicle cost, which includes fare paid
for the major carriers, e.g. airplane, or train, and the perceived
operation cost for a private car. The other component is the
out-of-vehicle cost which includes costs such as access, egress, and

parking costs.

MHINC

DUR

COMFOR

SAFE”

 

 

MHINC

DUR

COMFORT

SAFETY

75

W This is the time in hours spent in the mode for
a one-way trip.

W. This variable is the monthly household
income for the tripmaker. Income is expressed in Saudi riyals (SR).
W. This is a mode-speciﬁc socioeconomic variable to
air only and is deﬁned as 1 if duration of stay is one day or less, 0
otherwise. This variable divides the population into two subgroups,
and its coefﬁcients measure a difference between the subgroups.
Comfort is a qualitative and attitudinal variable used to explain the
behavior of the tripmaker in choosing a mode. This variable is scaled
from 5 to 1 in the questionnaire form, where 1 represent a perception
of very good comfort of the mode, and 5 represent very poor comfort.
In the calibration process a reversed scale was used to be more
meaningful. For instance, 5 represent a perception of very good
comfort for the mode, and 1 is very poor.

Safety is a qualitative and attitudinal variable used to explain the
behavior of the tripmaker in choosing a mode. This variable is scaled
from 5 to 1 in the questionnaire form, where 1 represent a perception
of very good safety of the mode, and 5 represent very poor safety. In
the calibration process a reversed scale was used to be more
meaningful. For instance, 5 represent a perception of very good

safety for the mode, and 1 is very poor.

76

Table 5.3

Dhahran-Riyadh Corridor Mode-Choice Model
for Non-Business Trips (Train Included)

 

 

 

 

 

 

 

INDEPENDENT COEFFICIENT t-STAT STANDARD

VARIABLES ERROR
ASC-AIR 42.00 3.26 12.9
ASC-BUS 4.08 9.50 0.42
ASC-TRAIN 0.44 1.80 0.25
IVTT (specific to Train

CAR, and BUS) -.84 -2.44 0.34

IVTT (specific to AIR) -47.79 -3.70 12.92
OPTC (generic) -.013 -5.94 0.0022
HINC (specific to AIR) 0.236 1.65 0.142
HINC (specific to BUS) -.58 -6.33 0.092
COMFORT (generic) 0.61 8.00 0.076
SAFETY (generic) 0.39 4.82 0.082
DUR (specific to air) 1.88 3.45 0.55

LOG LIKELIHOOD L(B) =-307.2

LOG LIKELIHOOD L(0) =-665.4

-2(L(0)-L(B)) = 716.2

LOCAL RHO SQUARED =I-0.538

LOCAL RHO-BAR SQUARED =0.535

ASC-AIR
ASC-BUS

ASC-TRAIN

IVTT
OPTC
HINC
COMFORT
SAFETY
DUR

In-vehicle time in hours
Out-of-pocket cost
Monthly household income
Qualitative variable
Qualitative variable
Duration of stay

Mode-specific constant for air
Mode-specific constant for bus
Mode-specific constant for train

 

 

T

— AAIflIOHHCSDN

DI

77

TabkLi4

Dhahran-Riyadh Corridor Mode-Choice Model for
Non-Business Trips (Train is not Included)

 

 

INDEPENDENT COEFFICIENT t-STAT STANDARD

VARIABLES ESTIMATE ERROR
ASC-AIR 40.34 3.88 10.4
ASC-BUS 5.33 6.45 0.83
IVTT '
(specific to CAR and BUS) -0.56 -1.04 0.539
IVTT (specific to AIR) -43.45 -4.21 10:33
OPTC (generic) -0.031 -6.17 0.0052
HINC (specific to AIR) 0.39 2.0 0.191
HINC (specific to BUS) -0.716 -5.54 0.129
COMFORT (generic) 0.670 4.5 0.147
SAFETY (generic) 0.492 3.3 0.149
DUR (specific to air) 2.1 3.1 0.68

 

 

 

 

 

LOG LIKELIHOOD L(B) --100.2
LOG LIKELIHOOD L(0) =-395.5
-2(L(0)-L(B)) = 590.6
LOCAL RHO SQUARED =0.746

LOCAL RHO-BAR SQUARED =0.743

ASC-AIR = Mode-specific constant for air
ASC-BUS a Mode-specific constant for bus
IVTT/DIS = In-vehicle time in hours
OPTC/DIST = Out-Of-pocket cost

HINC - Monthly household income
COMFORT = Qualitative variable

SAFETY = Qualitative variable

DUR - Duration Of stay

 

 

78

Table 5.5

Jeddah-Riyadh Corridor Mode-Choice Model
for Non-Business Trips

 

 

INDEPENDENT COEFFICIENT t-STAT STANDARD

VARIABLES ERROR
ASC-AIR -0 . 5486 -0 . 15 3 . 754
ASC-BUS 7.6891 7.797 0.986
IVTT ’
(specific to CAR and BUS) -.4263 -3.05 0.1398
IVTT (specific to AIR) -2.795 -1.14 2.439
OPTC (generic) -.0088 -7.43 0.0012
HINC (specific to AIR) 0.530 3.36 0.158
HINC (specific to BUS) -1.646 -6.79 0.242
COMFORT (generic) 0.416 3.88 0.107
SAFETY (generic) 0.430 3.77 0.114
DUR (specific to air) 3.30 2.69 1.225

 

 

 

 

 

LOG LIKELIHOOD L(B) --140.3
LOG LIKELIHOOD L(0) --395.5
-2(L(0)-L(B)) - 510.4
LOCAL RHO SQUARED =0.645
LOCAL RHO-BAR SQUARED 20.641

ASC-AIR = Mode-specific constant for air
ASC-BUS = Mode-specific constant for bus
IVTT a In-vehicle time in hours

OPTC = Out-of—pocket cost

HINC = Monthly household income
COMFORT = Qualitative variable

SAFETY = Qualitative variable

DUR = Duration Of stay

 

 

Sign

and]

0.746

COm'd

0531,

tested

EQUa] t

79

The coefﬁcients of the parameters all have the expected signs in the selected
models. The coefﬁcients of in-vehicle travel time, total out-of-pocket cost, and
household income speciﬁc to bus are negative, as expected, while household income
Speciﬁc to air, comfort, and Safety are positive, as expected. The cost, comfort, and
safety variables are generic. However, the in-vehicle travel time variable is generic
for bus and car, and mode-speciﬁc for air. This assumes that out-of-pocket cost has
the same marginal effect on each alternative’s utility, but a minute in a bus or a car
has a different marginal effect on mode choice than a minute on the plane.

It is clear from the t-stat values in Tables 5.3, 5.4 and 5.5 that the null
hypothesis that the true value of each coefﬁcient is zero can be rejected at the 0.05
signiﬁcance levels except for in-vehicle travel time (IVTT) speciﬁc to bus and car
in the Dhahran-Riyadh corridor model (without train), and in-vehicle travel time
(IVTT) speciﬁc to air in the Jeddah-Riyadh corridor model. However, these
variables are kept for transferability testing.

The goodness-of-ﬁt measure rho-square (p’) for the J eddah-Riyadh corridor
and Dhahran-Riyadh corridor models with and without train, are 0.645, 0.534, and
0.746, respectively. The p statistics for these models represent a very good ﬁt.

The adjusted likelihood ratio index (rho-squared bar) for the J eddah-Riyadh
corridor and Dhahran-Riyadh corridor models with and without train are 0.641,
0.531, and 0.743, respectively.

The null hypothesis that all the parameters are zero (Is,=3,=s,...s.=0) is
tested by the X (chi-square) test (-2(L(0)-L(B)), which has a degree of freedom

equal to the number of model parameters. The critical X’ value with degrees of

CXC!

with
para.
the ln

follow

L(C) .
Where
From

null 11)
is -2(-3
-2(-395
-2(-665.

(X?

45.8) l:

authec

and Win

5.6. 5.7

80

freedom equal to the model parameters, and a 0.05 level of Signiﬁcance (e.g. X’m),
is 16.92, while the calculated X’ test statistic for the Jeddah-Riyadh corridor model
is 510. In other words, the null hypothesis that all the parameters are jointly zero
is rejected at the 95% level. Moreover, the null hypothesis that all the coefﬁcients,
except, the mode-speciﬁc constants, are zero is tested by

-2(L(C)-L(B))
with degree of freedom equal to K-J +1, where K is the number of model
parameters, J is the number of alternatives in the universal choice set, and L(C) is
the log likelihood for a model with only constants. This statistic is calculated as
follows:

N 1

L(C)=2:'..l N, In ——
where Ni is the nliimber of travelers selecting mode i and N is the total sample size.
From Tables 5.3, 5.4 and 5.5, the X’ test statistic with 8 degrees of freedom for the
null hypothesis B,=3,=B,...&,=O
is -2(-395.5+ 145.4) =500.2 for the Jeddah-Riyadh model;
-2(-395.5 + 100.200) =590.6 for the Dhahran-Riyadh model (without train); and
-2(-665.4+309.740) =711.2 for the Dhahran-Riyadh model (with train).

The critical value with 8 degrees of freedom for a .05 level of signiﬁcance
(X’m) is 15.51, which is lower than the calculated X’. Hence, the null hypothesis that
all the coefﬁcients, except the mode-speciﬁc constants, are zero is rejected.

The overall prediction ratios for the Jeddah model and Dhahran model with

and without trains are 84%, 74%, and 89%, respectively, as can be seen in Tables

5.6, 5.7 and 5.8. In other words, 89% of tripmakers in the Dhahran-Riyadh corridor

sar
pre
the
pre

the

Jedd
these

Alten

0f 01) t.

(HINC
Comfor

81

sample are correctly predicted by the model. A comparison of observed and
predicted cell frequencies in Table 5.6 shows that the correctly predicted value for
the car mode is larger than the other modes. While, a comparison of observed and
predicted cell frequencies in Table 5.8 shows that the correctly predicted value for
the air and bus mode is larger than the car mode.

In order to test models for transferability, the same type of modes must exist
in each corridor. The Dhahran-Riyadh corridor model (without train) and the
J eddah-Riyadh corridor model were tested for model transferability. Furthermore,
these two models were also tested for the "Independence from Irrelevant
Alternatives" assumption.

In summary, model speciﬁcation for both corridors is the same, and consists
of out-of-pocket cost (OPT C), household income speciﬁc to air and bus tripmakers
(HINC),, HINC.) respectively, in-vehicle travel time (IVTT), safety (SAFETY) and
comfort (COMFORT), and mode speciﬁc-constants for bus and plane.

82

Tabkhi6

Prediction Success Table for the Jeddah-Riyadh
Corridor Model - The Calibration Process

 

ALTERNATIVES

 

AIR BUS CAR

 

Number of tripmakers choosing 120 120 120
this alternative

 

Number Of tripmakers correctly 96 102 104
predicted by the model

 

PREDICTION RATIO 0.80 .85 .87

 

 

 

 

OVERALL PREDICTION RATIO = 0.84

'x’ .. 9.63

 

 

 

Table 5.7

Prediction Success Table for the Dhahran-Riyadh Corridor Model
(with Train) - The Calibration Process

 

ALTERNATIVES

 

TRAIN AIR BUS CAR

 

Number Of tripmakers 120 120 120 120
choosing this alternative

 

Number of tripmakers

 

correctly predicted by 78 107 91 80
the model
PREDICTION RATIO 0.65 0.89 .76 .67

 

 

 

 

 

OVERALL PREDICTION RATIO = 0.74

f = 36.45

 

 

 

83

Table 5.8

Prediction Success Table for the Dhahran-Riyadh Corridor
Model (without Train) -- The Calibration Process

 

ALTERNATIVES

 

AIR BUS CAR

 

Number Of tripmakers choosing 120 120 120
chose this alternative

 

Number Of tripmakers correctly 108 108 104
predicted by the model

 

PREDICTION RATIO 0.90 .90 .87

 

 

 

 

 

OVERALL PREDICTION RATIO = 0.89

2’ = 4.53

 

 

W
E] .v E .

An "Independence from Irrelevant Alternatives (IIA)" Test was performed to
determine if this assumption has been violated. This test involves a comparison of
two likelihood values. One is the likelihood resulting from estimating the restricted
sample by using the parameters of the universal set, while the other likelihood value
is the one resulting from estimating the restricted sample but without restricting the
parameters.

The Likelihood ratio test statistic is used to test the HA assumption. This
' test statistic is chi-square distributed with degrees of freedom equal to the number
of restricted parameters. This test was used to test the null hypothesis that the IIA
model structure holds:

IIATSO!)=-2(I-L.(13)- 114(3)).
where LL,(B) is the likelihood from estimating the restricted sample by using the
parameters of the universal set, and LL,(B) is the likelihood resulting from estimating
the restricted sample without restricting the parameters.

It can be seen from Tables 5.9, and 5.10 that the null hypothesis of a logit
model structure cannot be rejected. In other words, the HA assumption is not

violated.

85

Table 5.9
IIA Test for the J eddah-Riyadh Corridor Model

 

 

BUS. CAR‘ AIR‘
1.1.,(3) -56.9 -61.7 -37.9
LL,,(B) -55.0 -58.6 -31.4
-2(LL,(E)- LL,(E)) 3.8 6.2 13.0
Degrees Of freedom 8 8 5
x’ statistic x’amzo. 09 x’,,o,20.09 {5,0,15. 09

 

 

 

‘ Alternative excluded from the available modes

LL,(B) = The likelihood of the restricted sample by using the parameters of the
universal set.
LL,(B) = The restricted likelihood resulting from estimating the restricted sample

without restricting the parameters.

86

Table 5 .10
IIA Test for the Dhahran-Riyadh Corridor Model

 

 

 

BUS. CAR' AIR‘
LL,(B) -32.8 -35.1 -53.6
1.11,,(B) -28.1 -24.3 -48.6
-2(LL,(E)- LL,,(B) 9.4 21.6 10.0
Degrees Of freedom 8 8 5
x1 statistic {3.0052136 {$0,521.96 185.0046.”

 

 

' Alternative excluded from the available modes

LL,(B) = The likelihood of the restricted sample by using the parameters of the
universal set.

LL.(B) = The restricted likelihood resulting from estimating the restricted sample
without restricting the parameters.

87

M l l I! ll .
Model validation was conducted by using the calibrated model to predict
modal-sth for data other than that used for model calibration. Two-hundred forty-
four observations from the Jeddah-Riyadh corridor and one-hundred eighty-nine
observations from the Dhahran-Riyadh corridor not used in model calibration were
used to test model validity. A FORTRAN computer program was written to
calculate the model prediction of each mode from the validation data (Appendix D).
The prediction result of the model validation is presented in Tables 5.11, and 5.12.
Validation tests were conducted by comparing the estimated and observed
ridership modal split using the X’ statistics. Since there is no evidence at the 2.5%
level of signiﬁcance for the Dhahran-Riyadh corridor case and at the 5% level of
signiﬁcance for the Jeddah-Riyadh corridor case that there is a difference between
the observed and the predicted modal split, the null hypothesis that there is no
signiﬁcant difference between the predicted values from the model and the observed
ones cannot be rejected. Hence, there is no signiﬁcant difference between the
observed and predicted mode choice for the validation sample, and each model

adequately ﬁts the observed validation data for its corridor.

88

Table 5.11

Prediction Success Table for the Jeddah-Riyadh
Corridor Model - The Validation Process

 

 

 

 

 

ALTERNATIVES
AIR BUS CAR
Number Of tripmakers in validation 108 103 33
sample choosing this alternative
Number Of tripmakers correctly 88 83 32
predicted by the model
PREDICTION RATIO 0.81 .80 .97

 

 

 

 

 

OVERALL PREDICTION RATIO I 0.83

f = 7.6

 

Table 5.12

Prediction Success Table for the Dhahran-Riyadh Corridor

Model - The Validation Process

 

 

 

 

 

ALTERNATIVES
AIR BUS CAR
Number Of tripmaker in validation 50 84 55
sample choosing this alternative
Number Of tripmakers correctly 46 72 44
predicted by the model
PREDICTION RATIO 0.92 .86 .80

 

 

 

 

 

OVERALL PREDICTION RATIO = 0.86

x’ .. 4.2

 

 

 

89

E El ElE' lllll
Aggregate point elasticities for the Jeddah-Riyadh corridor model (J eddah

model) and for the DhahranfRiyadh corridor model (Dhahran model) are presented
in Tables 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, 5.19, and 5.20. A direct elasticity is the
percentage change in market share caused by a 1 percent change in the attribute of
that mode. Cross elasticity is the percent change in market share for alternative i
caused by a 1 percent change in an attribute of another alternative j. Interpreting
the estimated elasticities is as follows: the direct elasticity for in-vehicle travel time
speciﬁc to air in the Jeddah-Riyadh corridor is -1.01. This means that a one percent
increase in the in-vehicle travel time by air, all else remaining constant, causes a
1.01% decrease in the overall probability of air choice. The variables OPTC and
MHINC. can be interpreted similarly, while COMFORT, and SAFETY HINCA have
an opposite interpretation because they have an opposite sign. For instance, the
direct elasticity for the air mode variable "comfort” in the Jeddah-Riyadh corridor
model is 0.42; this means that a one-percent increase in the comfort in the air mode,
all else remaining constant, causes a 0.42% increase in the overall probability of air
choice.

The elasticity of the air-mode choice probability in the Jeddah-Riyadh corridor
model with respect to in-vehicle travel time (IVTT) is -1.01, which is much lower
than that in the Dhahran-Riyadh corridor model (-3.98). This result is expected
because tripmakers on longer trips are usually less elastic with respect to level-of-
service variables than on short trip. The opposite relationship was found for the out-

of-pocket cost (OPTC) elasticity for the Jeddah-Riyadh corridor model and the

90

Dhahran-Riyadh corridor model. However, the trend of direct elasticities for bus
and car are opposite to that for the air mode, and this may be due to the different
perception of level of service between air and bus or car.

From the estimation .of the elasticities of the in-vehicle travel time (IVTT)
variable it can be expected that the Saudi Arabian Airlines can beneﬁt more by
decreasing in-vehicle travel time (IVTT) than by decreasing the cost especially in the
Dhahran-Riyadh corridor. For example, the direct elasticities for in-vehicle travel
time (IVTT) and total-out-of-pocket cost (OPTC) speciﬁc to air in the Dhahran-
Riyadh corridor are -3.98 and -0.5 respectively. This means that a one-percent
decrease in in-vehicle travel time (IVTT), or out-of-pocket cost (OPTC), all else
remaining constant, causes a 3.98% or 0.5% increase in the overall probability of air
choice.

The bus tripmakers are more sensitive to out-of-pocket cost (OPTC) than in-
vehicle travel time (IVTT) in the Dhahran-Riyadh corridor. This indicates that
tripmakers selecting bus in this corridor are more sensitive to cost than time.
However, for bus tripmakers in the J eddah-Riyadh corridor the opposite relationship
exists.

The HINC elasticity in the Jeddah-Riyadh corridor is approximately twice that
in the Dhahran-Riyadh corridor.

The elasticity associated with the DUR variable is relatively low, indicating
that the choice probabilities can be expected to be relatively insensitive to the

duration of the trip.

91

 

 

 

 

 

 

 

 

 

 

Table 5. 13
Direct Elasticities for Variables in the
Jeddah-Riyadh Corridor Model
AIR BUS CAR
IVTT (specific to a) -1.01 0.00 0.00
IVTT (specific tO c and b) 0.00 -1.14 -1.0
OPTC -0.86 -0.415 -.36
COMFORT 0.42 0.217 0.349
SAFETY 0.44 0.298 0.333
HINC (specific to a) 0.467 0.00 0.000
HINC (specific to b) 0.00 -1.0 0.000
DUR 0.02 0.00 0.000
Table 5. 14
Direct Elasticities for Variables in the
Dhahran-Riyadh corridor Model
AIR BUS CAR

IVTT (specific to a) -3.98 0.00 0.00
IVTT (specific to c and b) 0.00 -0.48 -0.39
OPTC -0.50 -.56 -0.431
COMFORT 0.29 0.33 0.53
SAFETY 0.20 0.31 0.31
HINC (specific to a) 0.18 0.00 0.00
HINC (specific to b) 0.00 -0.52 0.00
DUR 0.08 0.00 0.00

 

 

 

 

 

 

 

92

Table 5.15

Cross Elasticities for Variables in the J eddah-Riyadh Corridor
Model for Air Mode with Respect to Bus and Car Attributes

 

 

 

 

 

 

 

 

 

BUS CAR
IVTT (specific to a) 0.00 0.000
IVTT (specific to c and b) 0.589 0.553
OTPC 0.159 0.190
COMFORT -0.109 -0.195
SAFETY -0.150 -0.186
HINC (specific to a) 0.000 0.000
HINC (specific to b) 0.476 0.000
DUR 0.000 0.000
Table 5. 16
Cross Elasticities for Variables in the J eddah-Riyadh Corridor
Model for BUS Mode with Respect to AIR
and CAR Attributes
AIR CAR

IVTT (specific to a) 0.458 0.000
IVTT (specific to c and b) 0.000 0.444
OPTC 0.318 0.166
COMFORT -0.191 -0.154
SAFETY -0.206 -0.147
HINC (specific tO a) -0.15 0.000
HINC (specific to b) 0.000 0.000
DUR -0.014 0.000

 

 

 

 

 

 

93

Table 5. 17
Cross Elasticities for Variables in the J eddah-Riyadh Corridor Model

for CAR Mode with Respect to AIR and BUS Attributes

 

 

 

AIR BUS
IVTT (specific to a) 0.553 0.000
IVTT (specific to c and b) 0.000 0.554
OPTC 0.555 0.256
COMFORT -0.230 -0.108
SAFETY -0.231 -0.147
HINC (specific tO a) -0.314 0.000
HINC (specific to b) 0.000 0.522
DUR -0.006 0.000

 

 

 

 

Table 5.18

Cross Elasticities for Variables in the Dhahran-Riyadh Corridor
Model for AIR Mode with Respect to BUS and CAR Attributes

 

 

 

BUS CAR
ASC-AIR 0.000 0.000
ASC-BUS -.225 0.000
IVTT (specific to a) 0.00 0.000
IVTT (specific to c and b) 0.108 0.100
OPTC 0.103 0.109
COMFORT -0.757 -0.139
SAFETY -0.638 -0.833
HINC (specific to a) 0.000 0.000
HINC (specific to b) 0.116 0.000
DUR 0.000 0.000

 

 

 

 

94

Table 5.19

Cross Elasticities for Variables in the Dhahran-Riyadh
Corridor Model for BUS Mode with Respect to AIR and
CAR Attributes

 

 

 

 

 

AIR CAR
IVTT (specific to a) 1.82 0.000
IVTT (specific to c and b) 0.000 0.292
OPTC 0.216 0.322
COMFORT -0.137 -0.393
SAFETY -0.889 -0.231
HINC (specific to a) -0.063 0.000
MINC (specific to b) 0.000 0.000
DUR -0.047 0.000

 

Table 5 .20

Cross Elasticities for Variables in the Dhahran-Riyadh Corridor
Model for CAR Mode with Respect to AIR and BUS Attributes

 

 

 

AIR BUS
IVTT (specific to a) 2.16 0.000
IVTT (specific to c and b) 0.000 0.368
OPTC 0.286 0.460
COMFORT -0.152 -0.250
SAFETY -0.107 -0.246
HINC (specific tO a) -0.116 0.000
HINC (specific to b) 0.000 0.4043
DUR -0.035 0.000

 

 

 

 

 

CHAPTER VI
TRANSFERABILITY ANALYSIS

In the previous chapter, several intercity mode choice models were calibrated,
and one model for each corridor was selected as best explaining the behavior of the
tripmaker. In this chapter, the calibrated models for the two corridors under Study
will be tested for model transferability. These models are presented in Tables 5.4
and 5.5. These two models have the same speciﬁcation and both were calibrated with
an equal number of observations (360).

Several approaches were used to test model transferability. The ﬁrst approach
is to transfer these models without any modiﬁcation. For instance, the calibrated
model for the Riyadh-Jeddah corridor is used with data from the Dhahran-Riyadh
corridor to explain the behavior of the tripmaker in the Dhahran-Riyadh corridor,
and vice-versa. The second approach is to transfer the model speciﬁcations only and
develop new coefﬁcients. The constant terms as well as the coefﬁcients of the
variables are re-estimated using a part of the sample required to calibrate a new
model. The sample size used was one-ﬁfth of the sample required to calibrate the
models. The Bayesian updating method was used to update the coefﬁcients of the
models. The coefﬁcients of the models are used as prior information on the value
of the true coefﬁcients. The coefﬁcients resulting from calibrating the model with
the small sample are used to update this prior information. Updating the constants

was conducted as follows:

95

96

 

02: (ox/0.0+(0./a.’)
and (1/01’)+(1/a.’)

0. = ((l/a.’)+(1/a.’))“
Where

a, = original coefﬁcient

a, = sample coefﬁcient

a, = updated coefﬁcient

a, = standard deviation of the original coefﬁcient

a, = standard deviation of the sample coefﬁcient

a, = standard deviation of the updated coefﬁcient
In this case, the constant terms and the coefﬁcients of the variables for the
Jeddah-Riyadh corridor are considered prior information and the constant and the
coefﬁcients of the variables are re-estimated with data from the Dhahran-Riyadh
corridor. Then the re-estimated coefﬁcient is used to update the transfer model.

The third approach is to transfer the model speciﬁcation only, and calibrate
the model with new data. This approach has been introduced to determine the
universal set of speciﬁcations required to calibrate the mode choice model and to
determine if the parameters estimated for the two corridors are equal.

Several measures were used to evaluate how well the transfer model explains
the variation in the behavior of the tripmaker. The ﬁrst measure is the X2 test
statistic. In this test a comparison is made between the observed value and the

predicted value for each mode. large values of the overall discrepancy between the

97

model developed for a speciﬁc corridor and the transfer model indicate disagreement
between the two models.

The second measure is the percentage right estimate for each individual. In
this test a comparison is made between the predicted value from the transfer model
and the observed value. This measure is analogous to the X2 test, yet it produces
insight to the difference between the distribution of observed and predicted values.
These tests will also be used to determine the improvement in model prediction
before and after updating the transfer model.

The asymptotic t statistic test of equality of individual coefﬁcients between
the two models has been used to test the hypotheses that the coefﬁcients for level-
of-service variable (cg time or cost) for the proposed models are equal, and the
coefﬁcients for level-of-service variables (e.G. Time or cost) for the original and the
transfer model after updating are equal.

The following methods were used to test the proposed hypotheses:

1. The chi-square test and the percentage right method were used to test
if there is a difference in prediction accuracy between the original
model for each corridor and the transfer model. In addition, these tests
were used to test if there is a difference in prediction accuracy before
and after updating the coefﬁcients for the transfer model.

2. The t-test statistic was used to test if the coefﬁcients for level of service
variable (e.g. time or cost) for the calibrated models are equal, and if
coefﬁcients for level-of-service variable (e.g. time or cost) for the

transfer model after updating and the local model are equal.

98

3. The Transferability Test Statistic (TTS) was used to test if the
parameters in the transfer model and the estimated parameters in the
10%.] model are equal.

4. The goodness-Of-ﬁt test was used to determine which speciﬁcation is

better in explaining the tripmaker behavior in the new context.

El° EIlIEl'l'Elllll
The transfer approaches delineated in Chapter III will be evaluated using the

measures outlined. The following convention was used in these tests:

DHA- The local model for the Dhahran-Riyadh corridor using the entire
calibration data.

.JED- The local model for the Jeddah-Riyadh corridor using the entire
calibration data.

DHA-JED- The local model for the Dhahran-Riyadh corridor using the entire
calibration data, transferred as it is to the Jeddah-Riyadh corridor.

JED-DHA— The local model for the J eddah-Riyadh corridor using the entire
calibration data transferred as it is to the Dhahran-Riyadh corridor.

DHA-SM- The calibrated model for the Dhahran-Riyadh corridor using a small
sample to update the J eddah-Riyadh corridor model.

JED-SM- The calibrated model for the J eddah-Riyadh corridor using a small
sample to update the Dhahran-Riyadh corridor model.

JED-UP The updated J eddah-Riyadh model (using the Bayesian updating

method) to be transferred to the Dhahran-Riyadh corridor.

99

DHA-UP The updated Dhahran-Riyadh model (using the Bayesian updating
method) to be transferred to the Jeddah-Riyadh corridor.

The ﬁrst approach used was to transfer the Jeddah-Riyadh corridor model to
the Dhahran-Riyadh corridOr as it is, and vice-versa. The Likelihood Ratio Test
statistic measure of the transferability and transfer p2 resulting from this approach
are presented in Tables 6.1, and 6.2 for the Jeddah-Riyadh corridor and the
Dhahran-Riyadh corridor, respectively. The null hypothesis that the parameters in
the Jeddah-Riyadh model and the parameters in the Dhahran-Riyadh corridor model
are equal was rejected in both cases. Moreover, the comparison in goodness-of-ﬁt
measure (p’) between the original model (or the local model) and the transferred
model shows a very large difference (e.g., local p’ for the DHA model is 0.746 and
transfer p2 for the JED-DHA is 0.25, while local p’ for the JED model is 0.645 and
transfer p’ for the DHA-JED is -4.91).

The calibrated model for the Jeddah-Riyadh corridor yields a lower value in
the transferability test statistic (TTS) and the p2 difference between the original
model and the transferred model is less than that for the Dhahran-Riyadh corridor.
In other words, the calrhrated model for the Jeddah-Riyadh corridor in its original
form explains the variation of the Dhahran-Riyadh corridor data set better than the
Dhahran-Riyadh model explains the variation in the Jeddah-Riyadh corridor.

However, neither transferred model is acceptable.

100

Table 6.1

Transferability Test of the J eddah-Riyadh Model
Before and After Updating the Coefﬁcients

 

a

 

 

Variable
Name {512-1233 M0091 [21:18 Made] 1512-112 MQdQl
ASC-AIR -0.55 (-0.15) 40.34 ( 3.88) 2.15 ( 0.60)
ASC-BUS 7.69 ( 7.80) 5.33 ( 6.45) 6.69 ( 8.00)
OPTC -0.01 (-7.43) - 0.03 (-6.17) -0.01 (-7.64)
IVTT” -0.43 (-3.05) - 0.56 (-1.04) -0.41 (-2.90)
IVTTA -2.80 (-1.14) -43.46 (-4.21) -4.05 (-l.70)
COMFORT 0.42 ( 3.88) 0.67 ( 4.50) 0.46 ( 4.51)
SAFETY 0.43 ( 3.77) 0.49 ( 3.30) 0.43 ( 3.97)
MHINC, 0.53 ( 3.36) 0.39 ( 2.05) 0.54 ( 3.72)
MHINC. -l.65 (6.79) -0.72 (-5.54) -1.23 (6.69)
DUR).L 3.30 ( 2.69) 2.08 ( 3.10) 3.43 ( 3.84)
Local pz - 0,75 ..
Transfer p2 0.25 -- 0.09
L(0) -395.5 -395.5 -395.5
Liam) - -100.2 ...
LLD(3’,) -298.3 -- -339.7
T'I'SD(B',) 395.6 -- 519
Critical 3;“, 18.3 18.3 18.3
where:
(“) t-statistic
TI‘S,,(3',) Transferability test statistic
LLD(s',) The log likelihood of the behavior observed in Dhahran-Riyadh
corridor generated by the model estimated in Jeddah-Riyadh corridor
LLD(£',,) The log likelihood for the model estimated in Dhahran-Riyadh

corridor.
p’ Goodness of ﬁt measure.

101

Table 6.2

Transferability Test of the Dhahran-Riyadh Model
Before and After Updating the Coefficients

 

 

 

 

 

 

 

Variable WW

Name TED Mule] DHA-[ED M009] 121115-112 M000]
ASC-AIR -0.55 (015) 40.34 (3.88) 8.63 ( 1.51)
ASC-BUS 7.69 ( 7.80) 5.33 ( 6.45) 5.62 ( 7.20)
OPTC -0.01 (-7.43) - 0.03 (-6.17) -0.02 (-60.56)
IVTT},c -0.43 (-3.05) - 0.56 (-1.04) -0.56 (-1.99)
IVT'I‘A ~2.80 (-1.14) -43.46 (-4.21) -5.37 (-1.42)
COMFORT 0.42 ( 3.88) 0.67 ( 4.50) 0.50 ( 3.99)
SAFETY 0.43 ( 3.77) 0.49'( 3.30) 0.53 ( 3.98)
MHINC), 0.53 ( 3.36) 0.39 ( 2.05) 0.39 ( 2.31)
MHINC, -l.65 (-6.79) -0.72 (-5.54) -0.77 (-6.12)
DURA 3.30 ( 2.69) 2.08 ( 3.10) 2.09 (16.14)
Local p’ 0.65 - -
Transfer p2 -- -4.91 -0.24
L(0) -395 .5 -395 .5 -395 .5
LL,(s',) -140.3 .- ..
LL,(s‘.,) - -2339 -488.6
TTS,(3‘.,) -- 4398 696.5
Critical 2;”, 18.3 18.3 18.3
where
("’) t-statistic
T'I‘S,(s'.,) Transferability test statistic
1.1.,(5‘D) The log likelihood of the behavior observed in J eddah-Riyadh corridor

generated by the model estimated in Dhahran-Riyadh corridor
The log likelihood for the model estimated in J eddah-Riyadh corridor.
Goodness of ﬁt measure

1.21.0.)
P

102

In summary, transferring the J eddah—Riyadh model to the Dhahran-Riyadh
corridor, and vice-versa, does not work because this produces a very low goodness
of ﬁt, and a very large difference between the observed values and those predicted
by the transferred model. i

The second transfer approach is to use a Bayesian updating method. In this
approach the constant terms, as well as the coefﬁcients of the variables in the
transfer model, are re-estimated using a portion of the sample required to calibrate
a new model. The sample size recommended for this updating in reference (16) is
about one-ﬁfth the sample required to calibrate the model (75 observations were
used to estimate the small sample model). The coefﬁcients of the transferred model
are considered prior information of the true coefﬁcients, and the coefﬁcients
resulting from calibrating the model with the small sample are used to update this
prior information.

In this case the constant terms and the coefﬁcients of the variables in the
Jeddah-Riyadh model were considered prior information and the constant and the
coefﬁcients of the variables were re-estimated with small data from the Dhahran-
Riyadh corridor, and vice-versa.

Tables 6.1, and 6.2 Show the updated parameter values for each corridor as
well as the statistical test result. The result of the Likelihood Ratio Test statistic
shows a rejection of the null hypothesis that the parameters in the Jeddah-Riyadh
model and the parameters in the Dhahran-Riyadh model after updating are equal,

and vice-versa.

103

The comparison in goodness of ﬁt measure (p‘) between the original model
and the transferred model after updating shows a very large difference (e.g., p2 for
the DHA model (calibrated model) is 0.746 and p2 for the JED-DHA-UP (updated
transferred model) is 0.09). ’However, the calibrated model for the Jeddah-Riyadh
corridor yields a higher value of the TIS score and a lower p2 after updating than
transferring the model in its original form. This is the opposite result of the other
corridor, where updating the Dhahran-Riyadh model results in a lower value of the
ITS test and a higher p’ than transferring the model without any modiﬁcation.

From Tables 6.3, and 6.4 it can be seen that the hypothesis that the
coefﬁcients of IVTI‘ speciﬁc to bus and car, IVTT speciﬁc to air (JED model only),
COMFORT, SAFETY, DUR, and MHINC speciﬁc to air are equal in the original
model and the updated transferable one can not be rejected at the 95% signiﬁcance
level. The hypothesis of equal coefﬁcients for IV'I'I‘ speciﬁc to air (DHA model),
OPTC and MHINC speciﬁc to bus between the updated transferable model and the
original model is rejected at the 95% signiﬁcance level. This mix of results in the
level of signiﬁcance of service variables and socioeconomic variables led to the

conclusion that in performing another study both types of variables must be collected.

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106

The prediction power of the transferred model improved for the Dhahran-
Riyadh model after updating, and deteriorated for the Jeddah-Riyadh corridor.
Transferring the Jeddah-Riyadh model (after updating) to the Dhahran-Riyadh
corridor, and vice-versa, yields a very low goodness Of ﬁt, and a very large difference
between the estimated parameter for the local model and the transferred model.
In addition, the null hypothesis of equality of the parameters in the transfer model
after updating and the parameters of the original model was rejected. Hence these
models are not transferable after updating.

The third approach is to transfer the model speciﬁcation only, and to
determine if the parameters estimated for the two corridors are equal. As explained
in the model calibration section, both models have the same speciﬁcation. This
means that this speciﬁcation is a universal one required to calibrate an intercity
mode choice model in Saudi Arabia.

The asymptotic t statistic test of equality of individual coefficients between
the two models has been used to compare the individual coefﬁcients in the J eddah-
Riyadh model and the Dhahran-Riyadh model. Table 6.5 shows a comparison
between the individual coefﬁcients in the Jeddah-Riyadh model and in the Dhahran-
Riyadh model. The most signiﬁcant differences are between the coefficients for out-
Of-pocket cost (OPTC), in-vehicle travel time speciﬁc to air (IVTTA), monthly
household income speciﬁc to bus (MHINCB), and the mode-speciﬁc to air and bus.
The comfort variable, duration variable, in-vehicle travel time speciﬁc to bus, and car
(IVTI'BM), and the monthly household income variable speciﬁc to air (MHINCA),

are not signiﬁcantly different at the 90% level.

107

The difference between the individual coefﬁcients also supports the previous
conclusion that these two models are not transferable. These differences in the
individual estimated parameters, especially for the level-of-service variables, led to
a study of the difference in means between the independent variables used in
calibrating each model. Table 6.6 shows the mean value of the independent
variables for each mode, and the speciﬁc ratio between the J eddah-Riyadh variables
and the Dhahran-Riyadh variables. The same comparison is also applied to the
standard deviation of each variable. In comparing the means of each mode for each
variable, it can be seen that the level-of-service (LOS) variables contribute most to
the large difference between the estimated and the transferred parameters. The
speciﬁc ratio of each variable is approximately equal to one except for those related
to the level-of-service variables in-vehicle travel time (IVTI') and out of pocket cost
(OPTC). Moreover, these level-of-service variable ratios are approximately identical
to the objective ratio (obtained from the agency operating that mode), as can be

seen in Table 6.7.

108

Table 6.5

Jeddah-Riyadh Versus Dhahran-Riyadh Coefﬁcients

 

 

 

 

 

 

 

Variable Estimated Variable Coefficients1
Name Jeddah- Dhahran-
Riyadh Riyadh t-stat Ratioz
Model Model
ASC“AIR “0.55 40.34 “3.70 “0.01
(“0.15) (3.88)
ASC“BUS 7.69 5.33 1.83 1.44
(7.80) (6.45)
OPTC “0.0088 “0.032 4.34 0.28
(—7.43) (-6.17)
IVTTLC “0.426 0.56 0.24 0.76
(—3.05) (-1.04)
IVTTK “2.795 “43.45 3.83 0.06
(-1.14) (-4.21)
COMFORT 0.416 0.67 “1.39 0.62
(3.88) (4.50)
SAFETY 0.43 0.492 “0.331 0.87
(3.77) (3.30)
MHINCA 0.53 0.39 0.56 1.36
(3.36) (2.05)
MHINC; “1.646 “0.72 “3.37 2.29
(-6.79) (-5.54)
DURA 3.30 2.08 0.98 1.58
(2.69) (3.1)
p2 0.645 0.746
L(B) “140.3 “100.2
L(0) “395.5 “395.5

 

The estimated coefﬁcient is not signiﬁcantly different from zero at the 0.05

or greater value.

Ratio = Parameter in Jeddah-Riyadh model/ parameter in Dhahran-Riyadh

model

(“) t-Statistic

 

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111

Furthermore, the overall ratio is related to the ratio of the distance between
the cities under consideration. The distance between Jeddah and Riyadh is 1061 KM
while the distance between bhahran and Riyadh is 467 KM, so the ratio is 2.27, and
the overall average of the ratio of the level of service variable is 2.26
((2.45 + 2.06) / 2).
These two observations were used to recalibrate each model to improve
transferability. For instance, the in-vehicle travel time value and out-of-pocket cost
in each observation will be multiplied by its respective speciﬁc ratio. Thus to use
the Dhahran-Riyadh model to explain the variation of the data in the Jeddah-Riyadh
corridor, the in-vehicle travel time for air, bus, and car in the Dhahran-Riyadh
corridor was multiplied by 1.7, 3.1, and 2.5, respectively, and the out-of-pocket cost
value for air, bus, and car was multiplied by 2.0, 1.6, and 2.6, respectively. This
calibrated model was then used to test for transferability. In addition, IVTT and
OPTC in the Dhahran-Riyadh corridor data set were divided by the distance between
Dhahran and Riyadh (467 KM) to recalibrate another Dhahran-Riyadh corridor
model. The same procedure was applied to the Jeddah-Riyadh model. In these
tests, the following additional identiﬁcation conventions will be used:
JED-DHA-LOS The calibrated model for the J eddah-Riyadh corridor using the
entire modiﬁed calibrated data (LOS case) transferred as it is
to the Dhahran-Riyadh corridor.

DHA-JED-LOS The calibrated model for the Dhahran-Riyadh corridor using the
entire modiﬁed calibrated data (LOS case) transferred as it is

to the Jeddah-Riyadh corridor.

JED-LOS-UP

DHA-LOS-UP

JED-DHA-DIS

DHA-JED-DIS

JED-DIS-UP

DHA-DIS-UP

112

The updated modiﬁed J eddah-Riyadh model by Bayesian
updating method to be transferred to the Dhahran-Riyadh
corridor (LOS case).

The updated modiﬁed the Dhahran-Riyadh model by Bayesian
updating method to be transferred to the Jeddah-Riyadh
corridor (LOS case).

The calibrated model for the J eddah-Riyadh corridor using the
entire modiﬁed calibrated data (distance case) transferred as it
is to the Dhahran-Riyadh corridor.

The calibrated model for the Dhahran-Riyadh corridor using the
entire modiﬁed calibrated data (distance case) transferred as it
is to the J eddah-Riyadh corridor.

The updated modiﬁed Jeddah-Riyadh model to be transferred
to the Dhahran-Riyadh corridor (distance case).

The updated modiﬁed Dhahran-Riyadh model to be transferred
to the Jeddah-Riyadh corridor (distance case).

Tables 6.8, and 6.9 show the value of the modiﬁed parameter before and after

updating for each corridor, as well as the statistical test results. The result of the

likelihood ratio test statistic shows a rejection of the null hypothesis that the

parameters in the local model and the parameters in the modiﬁed transferred model

(LOS case) before or after updating are equal. However, in comparing the modiﬁed

approach and the non-modiﬁed approach, the modiﬁed approach provides a lower

value of the likelihood ratio test statistic. Hence, the modiﬁed approach is a better

method for transferring models.

113

Table 6.8

Transferability Test of the Modiﬁed J eddah-Riyadh
Model Before and After Updating Coefﬁcients;

 

 

 

 

 

(the Speciﬁc LOS Ratio Case)
VarTable WW
-._u' 1- D-M .0 m- 0.; mi LD-J - 1’ H6,
ASC-AIR 073 (-0.19) 40.34 (3.88) 2.13 ( 0.58)
ASC-BUS 6.56 ( 7.95) 5.33 ( 6.45) 6.04 ( 8.26)
OPTC -0.02 (-7.48) - 0.03 (-6.17) -0.02 (-8.00)
IVTT“ -1.09 (-2.97) - 0.56 (-1.04) -0.92 (-2.63)
IV'I'I‘A -4.29 (-1.16) 43.46 (-4.21) -6.87 (-1.96)
COMFORT 0.41 ( 3.81) 0.67 ( 4.50) 0.45 ( 4.44)
SAFETY 0.44 ( 3.79) 0.49 ( 3.30) 0.39 ( 1.25)
MHINCA 0.52 ( 3.30) 0.39 ( 2.05) 0.62 ( 1.62)
MHINC. -1.61 (-6.68) -0.72 (6.54) -1.21 (-6.64)
DURA 3.27 ( 2.72) 2.08 ( 3.10) 3.41 ( 3.86)
I 0.341 0.776 0.439

L(0) -395.5 -395.5 -395.5
1148'.) -- -1oo.2 ...
L14,(B‘,) -260.8 -- -221.8
1180(3)) 320.9 -- 243.3
Critical X’m, 18.3 18.3 18.3
where
(") t-statistic
TTSD(8‘.,) Transferability test statistic
LLD(B',) The log likelihood of the behavior observed in Dhahran-Riyadh

corridor generated by the model estimated in J eddah—Riyadh corridor
LL.,(B'D) The log likelihood for the model estimated in Dhahran-Riyadh

corridor
p Goodness of ﬁt measure

114

Table 6.9

Transferability Test of the Modiﬁed Dhahran-Riyadh
Model Before and After Updating Coefﬁcients;

 

 

 

 

 

 

(the Speciﬁc LOS Ratio Case)

Variable W

.__"- L D (1005 D.;,-] I- ,0 MH' .!_ﬁi;.l\ 1' gm;
ASC-AIR -0.55 (-0.15) 38.49 ( 3.47) 6.96 ( 1.19)
ASC-BUS 7.69 ( 7.80) 2.95 ( 2.89) 3.74 ( 3.99)
OPTC -0.01 (-7.43) - 0.01 (-4.17) -0.01 (-5.57)
IV'I'I'ch -0.43 (-3.05) - 0.12 (-0.72) -0.22 (-1.42)
IV'I'I‘A -2.80 (-1.14) -28.07 (-3.78) -6.06 (-1.70)
COMFORT 0.42 ( 3.88) 0.65 ( 5.65) 0.54 ( 5.20)
SAFETY 0.43 ( 3.77) 0.41 ( 3.54) 0.45 ( 4.11)
MHINC, 0.53 ( 3.36) 0.39 ( 2.26) 0.39 ( 2.50)
MHINC, -l.65 (-6.79) - 0.70 (629) —0.74 (-6.80)
DUR, 3.30 ( 2.69) 1.86 ( 2.97) 1.90 ( 3.09)
p1 0.645 0.392 0.558
L(0) -395.5 -395.5 -395.5
LL,(s',) -140.3 -- -
LL,(B'D) -- -240.4 -174.9
'1TS,(3',,) - 200.1 69.2
Critical X’m, 18.3 18.3 18.3
where
(”‘) t-statistic
'ITS,(£’,) Transferability test statistic
LL,(£'.,) The log likelihood of the behavior observed in J eddah-Riyadh corridor

generated by the model estimated in Dhahran-Riyadh corridor
The log likelihood for the model estimated in J eddah-Riyadh corridor.
Goodness of ﬁt measure

gm.)
P

115

The comparison in goodness of ﬁt measure (p’) between the original model
and the modiﬁed transfer model before and after updating shows a difference (e.g.,
p’ for the DHA model is 0.746 and p’ for the JED-DHA-IOS; JED-LOS-UP are
0.341, and 0.439, respectively). However, the calibrated model for the modiﬁed
Dhahran-Riyadh corridor data set after updating yields a lower value for the TTS
test and a higher p2 than transferring the model in its original form. In other words,
the updated modiﬁed approach provides a better model than either transferring the
original model as it is or updating it with a small sample.

The second modiﬁed approach was to divide IVTT and OPTC by the
respective distance in each corridor. Then the recalibrated models were tested for
transferability.

Tables 6.10, and 6.11 show the parameter before and after updating for each
corridor as well as the statistical result of the test. The result of the likelihood
Ratio Test statistic shows a rejection of the null hypothesis that the parameters in the
Jeddah-Riyadh distance model and the parameters in the Dhahran-Riyadh distance
model before or after updating are equal, and vice-versa.

The comparison in goodness of ﬁt measure (p’) between the original and the
transfer model (before or after updating) shows a very large difference (e.g., p2 for
the DHA model (calibrated model) is 0.746 and p2 for the JED-UP-DIS (updated
transferred model) is 0.146). The calibrated model for the J eddah—Riyadh corridor
yields a higher value of TI‘S and a lower p’ after updating than does transferring the
model in its original form. The Dhahran-Riyadh model exhibited just the opposite

effect.

116

The same observation of the mix of signiﬁcance and non-signiﬁcance using
the level-of-service variables and the socioeconomic variables can be seen in Tables
6.12 and 6.13. '

In summary, transferring the Jeddah-Riyadh model (after updating) to the
Dhahran-Riyadh corridor yields a very low goodness of ﬁt. The Dhahran-Riyadh
model (modiﬁed by distance), when transferred to the Jeddah-Riyadh corridor, yields
an acceptable goodness of ﬁt. Hence, the prediction power of the transfer model
improved for the Dhahran-Riyadh model after updating, and deteriorated for the
Jeddah-Riyadh corridor after updating. Hence, the DHA-DIS model is an acceptable
model after updating for transferability, while the JED-DIS model is not.

117

Table 6.10

Transferability Test of the Modiﬁed J eddah-Riyadh
Model Before and After Updating Coefﬁcients;
(the distance case)

 

 

 

 

 

Variable WW
-..u‘ 1..!i’ uon‘ D.;-D nor 1' P. l’un‘

ASC-AIR -0.55 (-0.15) 40.34 ( 3.88) 2.15 ( 0.60)

ASC-BUS 7.69 ( 7.80) 5.33 ( 6.45) 6.69 ( 8.00)

OPTC -0.01 (-7.43) - 0.02 (-6. 17) -0.01 (-7.80)

IVTT“: -0.45 (-3.05) - 0.26 (-1.04) -0.40 (-2.76)

IVTT, -2.96 (-1.14) -20.28 (-4.21) -5.20 (-2.28)

COMFORT 0.42 ( 3.88) 0.67 ( 4.50) 0.46 ( 4.50)

SAFETY 0.43 ( 3.77) 0.49 ( 3.30) 0.43 ( 3.97)

MHINCA 0.53 ( 3.36) 0.39 ( 2.05) 0.54 ( 3.72)

MHINC. -1.65 (-6.79) -0.72 (-5.54) -1.23 (-6.69)

DURA 3.30 ( 2.69) 2.09 ( 3.10) 3.43 ( 3.84)

p’ 0.25 0.7716 0.146

L(0) -395 .5 -395 .5 -395 .5

110(3'0) -- -100.2 --

LI..D(£',) -298.3 -- -338.0

TTSD(B',) 395.6 -- 476.1

Critical X’mo 18.3 18.3 18.3

where

(’ ') t-statistic

TI‘S,,(£',) Transferability test statistic

LLD(B',) The log likelihood of the behavior observed in Dhahran-Riyadh
corridor generated by the model estimated in J eddah-Riyadh corridor

LLD(£‘D) The log likelihood for the model estimated in Dhahran-Riyadh

corridor

’ Goodness of ﬁt measure

P

118

Table 6.11

Transferability Test of the Modiﬁed Dhahran-Riyadh
Corridor and After Updating Coefﬁcients;
(the distance case)

 

 

 

 

 

 

Variable W

.‘n’ 1.. “or I,;-] .-D “hr D,;-| J'uon'
ASC-AIR 0.55 (0.15) 4034 (3.88) 8.63 ( 151)
ASC-BUS 7.69 ( 7.80) 533 ( 6.45) 5.62 ( 720)
OPTC -0.01 (4.43) ‘- 0.02 (45.17) 0.02 (-721)
IVTT,c .043 (-3.05) - 0.26 (-1.04) -0.38 (-1.83)
IVTT, -2.96(-1.14) -20.28 (421) -8.71 (-2.71)
COMFORT 0.42 ( 3.88) 0.67 ( 450) 0.50 ( 3.99)
SAFETY 0.43 ( 3.77) 0.49 ( 330) 0.53 ( 3.98)
MHINCA 0.53 ( 3.36) 0.39 ( 2.05) 0.39 ( 2.31)
MHINC, -1.65 (45.79) -0.72 (.554) -0.77 (.012)
DUR, 330 ( 2.69) 2.09 ( 3.10) 2.09 (16.14)
p2 0_s’.64 4.91 0544
L(0) -395.5 -395.5 -395.5
LL,(s',) -1403 .. ..
L1,,(s-D) .— -2348 -180.5
TTS,(s‘.,) .- 4417 803
Critical rm, 183 18.3 183
where

(m) t-statistic

T1318.)
1145'.)

Transferability test statistic
The log likelihood of the behavior observed in J eddah-Riyadh corridor

generated by the model estimated in Dhahran-Riyadh corridor
LL,(B‘,) The log likelihood for the model estimated in J eddah-Riyadh corridor.
pz Goodness of ﬁt measure.

119

Table 6.12

Comparison Between the Calibrated Dhahran-Riyadh
Model and the Updated Modiﬁed J eddah-Riyadh Model

 

 

 

 

 

 

 

 

 

 

 

 

(Distance Case)
JED-IP-DIS Model DHA-DIS Model
Coefficients Standard Coefficients Standard t-Stat
Error Error
Ase-AIR 2.15 3.59 60.35 10.41 -3.47
Ase-nus 6.69 0.84 5.33 0.83 1.16
lVTTc, -0.39 0.14 -0.56 0.56 0.30
IVTTA -5.19 2.32 -43.46 10.33 3.61
OPTC -0.01 0.00 -0.03 0.01 4.19
MHINCA 0.54 0.15 0.39 0.19 0.64
nurse, -1.23 0.18 -0.72 0.13 -2.29
COMFORT 0.46 0.10 0.67 0.15 -1.19
SAFETY 0.43 0.11 0.49 0.15 -0.36
DURA 3.43 0.89 2.09 0.13 1.49
p’ 0.146 0.746
L(0) -395.5 -395.5
LLD(,D) "‘ '1 .2
LLD(03) -338 ---
IISD(FJ) ‘7601 "
Critical x’ 13.3 10.3
L ....
where
(' ') t-statistic

TTSD(B',) Transferability test statistic

LLD(B',) The log likelihood of the behavior observed in Dhahran-Riyadh
corridor generated by the model estimated in Jeddah-Riyadh corridor

11...,(8'D) The log likelihood for the model estimated in Dhahran-Riyadh
corridor

’ Goodness of ﬁt measure

P

120

Table 6.13

Comparison Between the Calibrated Jeddah-Riyadh Model
and the Updated Modiﬁed Dhahran-Riyadh Model

 

 

 

 

 

 

 

 

 

 

 

 

(Distance Case)
LJED-DIS Modol DllA-DIS-ll’ Model
ICoafficlanta) Standard Coefficients Standard' t-Stat
Error Error
ASE-AIR -0.55 3.75 0.03 5.73 -1.31.
ASE-BUS 7.09 0.99 5.02 0.70 1.05
M10” 015 0.15 -0.30 0.20 -0.30
1m, -2.90 2.59 -0.71 3.22 1.39
cm -0.01 0.00 -0.01 0.00 2.19
MHIMCA 0.53 0.10 0.39 0.17 0.03
munc, -1.05 0.21. -0.77 0.13 -3.21
001190111 0.1.2 0.11 0.50 0.13 -0.52
mm 0.1.3 0.11 0.53 0.13 -0.50
0011A 3.30 1.23 2.09 0.13 0.90
p‘ 0.01.5 0.51.1.
L(0) 395.5 -395.
LLJ([” ’1‘003 "'
LL’(’D’ "' 480.5
th’(’D, "' 80.3
! Critical x’m. 10.3 10.3 }
where
(”‘) t-statistic
TTS,(B‘.,) Transferability test statistic
L1,,(s'o) The log likelihood of the behavior observed in J eddah-Riyadh corridor
generated by the model estimated in Dhahran-Riyadh corridor
11,053) The log likelihood for the model estimated in J eddah-Riyadh

2

P

corridor.
Goodness of ﬁt measure

121

The last approach used was to calibrate general models by using both the
data set for the Dhahran-Riyadh corridor and the data set for the Jeddah-Riyadh
corridor. A second model, having the same speciﬁcation except the level-of-service
variable is divided by distance, was also tested. The following additional
identiﬁcation convention will be used:

GENERAL The calibrated model using both the Jeddah-Riyadh and
Dhahran-Riyadh data (without dividing IVTT and OPTC by the
distance).

GENERAL-DIS The calibrated model using both the Jeddah-Riyadh and
Dhahran-Riyadh data (dividing IVTT and OPTC by the
distance).

Table 6.14 shows the result of this approach. The general model with LOS
divided by the distance provided a slightly better ﬁt than the one where distance is
not considered. Yet the GENERAL-DIS model is not recommended to be the
general model for the two corridors because it has an unreasonable sign for the
IVTT variable speciﬁc to car and bus.

Tables 6.15, and 6.16 show the general parameters and the speciﬁc parameters
for each corridor as well as the statistical result. The result of the Likelihood Ratio
Test statistic is a rejection of the null hypothesis that the parameters in the general
model and the parameters in the speciﬁc Dhahran-Riyadh model or J eddah—Riyadh
model are equal. Yet, the comparison in goodness of ﬁt measure (p’) between the
original model and the general model shows a slight difference (e.g. p’, for the DHA
model (speciﬁc model) is 0.746 and p2 for the general model is 0.575).

122

The chi-square test was used to test if there is a difference in prediction
accuracy between the original model for each corridor and the general model.
Tables 6.17 and 6.18 show that the hypothesis that the number of tripmakers
correctly predicted by the speciﬁc model and the general one are equal cannot by
rejected at the 95 % signiﬁcance level. The percentage right for each mode in each
corridor for the general model and the speciﬁc model are approximately the same.

In summary, the most encouraging result of this phase of the study was the
ability of the general model to reasonably explain the behavior of the tripmaker in
both corridors. The different approaches used to transfer models between corridors
without modiﬁcation was not encouraging. Yet, the modiﬁed approach (LOS case)
gives an acceptable goodness of ﬁt. Furthermore, by using Bayesian updating
method the goodness of ﬁt measure improved in both corridors. In other words, the
transferred model after updating using the modiﬁed approach (LOS case) yields a
lower value for the 'ITS test and a higher p2 than transferring the model in its
original form. Hence, the prediction power of the transfer model improved after
updating. So, it is recommended to use the modiﬁed approach (LOS case) after
updating to transfer the speciﬁc model from one corridor to another. In other
words, the updated modiﬁed approach (LOS case) provides a better model than
either transferring the original model as it is or updating it with a small sample.

The ability to transfer the intercity mode choice model between the corridors
under study can signiﬁcantly reduce the data requirements, calibration time, cost,
and detailed analytical expertise required by planners to perform modal split analysis
in Saudi Arabia.

123

Table 6.14

Test of the General model for the Two Corridors.

 

 

 

 

 

Variable W

_N_ame Generalelel GenMngdeL
ASC-AIR 4.54( 5.08) 9.51 ( 6.02)
ASC-BUS 6.18 ( 13.63) _ 4.59 ( 13.63)
OPTC -0.01 (- 8.82) -0.01 (-11.27)
IVTT” -0.70 (-10.00) 0.25 ( 2.61)
IV'I'I‘A -8.24 (- 7.87) -4.34 (- 8.15)
COMFORT 0.65 ( 8.68) 0.66( 8.60)
SAFETY 0.36 ( 5.17) 0.42 ( 5.70)
MHINCA 0.27( 3.34) 0.44( 4.76)
MHINC, -1.01 (- 9.71) -0.95 (- 8.73)
DUR, 1.23( 3.75) 2.38( 6.33)

p2 0.568 0.536—
L(0) -790.9 -790.9

1143'.) -341.7 -319.9

where

(") t-statistic

LIQ(B‘G) The log likelihood for the general model estimated from the data set

for both corridors.
Goodness of ﬁt measure

124

Table 6.15
The General Model versus the Speciﬁc Jeddah-Riyadh Model

 

 

 

 

 

 

Variable WW

Jim 6902mm; Speciﬁc W
ASC-AIR 454( 5.00) 055 (015)
ASC-BUS 6.18 ( 13.63) 7.69 (7.00)
OPTC .001 (- 0.02) .001 (-743)
IVTT” -070 (-1000) 043 (3.05)
IVTT, -8.24 (- 7.87) -2.80 (-1.14)
COMFORT 0.65 ( 8.68) 0.42 (3.00)
SAFETY 0.36( 5.17) 0.43 ( 3.77)
Mimic, 0.27 ( 334) 0.53 ( 3.36)
MHINC, -1.01 (- 9.71) -1.65 (-6.79)
DURA 1.23( 3.75) 3.30 ( 2.69)
p1 036 0.645

L(0) -3955 -3955

110(3)) "" ’1403
1.140,) -173.0 -

TIS.(K.) ' 67.0 ..

Critical x’m, 103 10.3

where

(”) t-statistic

TIS,(KG) Transferability test statistic

1.1.,(3'0) The log likelihood of the behavior observed in J eddah-Riyadh corridor
generated by the general model

LL,(B'J,) The log likelihood for the speciﬁc model estimated in J eddah-Riyadh

p1 Goodness of ﬁt measure

125

Table 6.16

The General Model Versus the Speciﬁc Dhahran-Riyadh Model

 

 

 

 

 

 

 

 

Variable W
m GenﬂModel SW
ASC-AIR 4.54 ( 5.08) 40.34 ( 3.88)
ASC-BUS 6.18 ( 13.63) 5.33 ( 6.45)
OPTC -0.01 (- 8.82) - 0.03 (~6.17)
IVTT“ -0.70 (-10.00) - 0.56 (-1.04)
IVTT, -8.24 (- 7.87) 43.46 (-4.21)
COMFORT 0.65 ( 8.68) 0.65 ( 4.50)
SAFETY 0.36 ( 5.17) 0.50 ( 3.30)
MHINC, 0.27 ( 3.34) 039 ( 2.05)
MHINC. -1.01 (- 9.71) -0.72 (-5.54)
DURA 1.23 ( 3.75) 2.08 ( 3.10)
1 0.573 0.746
L(0) -395.5 -395.5
1.1.,(0'0) ... -1002
LLD(s'0) -167.9 ..
TI‘SD(B'G) 135.4 --
Critical X’mlo 18.3 18.3
where
(“) t-statistic

TS.,(B'G) Transferability test statistic

110(8‘0) The log likelihood of the behavior observed in Dhahran-Riyadh
corridor generated by the general model

11...,(B‘JD) The log likelihood for the speciﬁc model estimated in Dhahran-Riyadh
corridor.

p Goodness of ﬁt measure

126

 

 

 

 

 

 

 

 

 

 

Table 6.17
Comparison Between the Dhahran-Riyadh Model
. and the General Model
ALTERNATIVES
AIR BUS CAR
Number of tripmakers correctly 108 108 104
predicted by DHA-Model (90) (90) (87)
Number of tripmakers correctly 110 104 87
predicted by the General Model (92) (87) (72)
x’ = 2 . 9 6
where

(u‘) % predicted right of each mode

 

127

 

 

 

 

Table 6.18
Comparison Between the J eddah-Riyadh Model
and the General Model
ALTERNATIVES
AIR BUS CAR
Number of tripmakers correctly 96 102 104
predicted by JED-Model (80) (85) (87)
Number of tripmakers correctly 92 85 100
predicted by the General Model (77) (71) (83)

 

 

 

 

 

x’ = 3.15

 

“men:

("‘) % predicted right of each mode

 

CHAPTER VII
CONCLUSIONS AND RECOMMENDATIONS

The main purpose of this study was to develop intercity disaggregate
behavioral mode choice models for Saudi Arabia corridors and to test the
transferability of these models within Saudi Arabia.

Data required to calibrate the models were collected by a survey using a
questionnaire form. The collected data were divided into two data sets; one set was
used for calibrating the models while the other was used for validation.

Different model speciﬁcations were tested in this research. Each model
estimate is based on a different modal utility function. Three models were selected
to be most reliable in explaining the variation of mode choice of the tripmakers in
the corridors under study. Two of the models are speciﬁc to the J eddah-Riyadh
corridor and the Dhahran-Riyadh corridor, while the third one is a general model
which was calibrated with data from both corridors. The goodness of ﬁt measure
rho-square (p’) for the J eddah-Riyadh corridor, the Dhahran-Riyadh corridor, and
the general models is 0.645, 0.746, and 0.567, respectively. The p statistics for these
model represent a very good ﬁt.

The adjusted likelihood ratio index (rho-squared bar) for the J eddah-Riyadh
corridor and the Dhahran-Riyadh corridor models with and without the train mode

is 0.641, 0.743 and 0.556 respectively.

128

129

The overall prediction ratio for the Jeddah model and Dhahran model is
84% and 89%, respectively. In other words, the selected mode of eighty four percent
of tripmakers in the J eddah-Riyadh corridor sample were correctly predicted by the
model.

To determine the transferability of intercity mode choice models, several
approaches were tested. The ﬁrst approach was to use the calibrated model for the
Riyadh-Jeddah corridor to explain the behavior of the tripmaker in the Dhahran-
Riyadh corridor, and vice-versa. The second approach used a Bayesian method to
update the coefﬁcients and constants of the Jeddah-Riyadh model with sample data
from the Dhahran-Riyadh corridor. Third, the speciﬁcation of the J eddah-Riyadh
model and the Dhahran-Riyadh model was assumed to be similar, and new
coefﬁcients were determined for each corridor. Finally a modiﬁed approach was
used. This modiﬁed approach consisted of two forms. One form of the modiﬁed
approach was to use a separate scaling factor for each variable, while the other form
is to use the distance as the scaling factor.

Tables 7.1 and 7.2 show the results of the different approaches used to
transfer models between the two corridors under study. The criterion used to

compare alternative approaches is the rho-square (p’) goodness of ﬁt measure:

L(s)
transfer p2 = l- —-
L(0)
in which:
L(s) = Log likelihood for the vector of estimated coefﬁcients
L(0) = The value of the log likelihood function when all the

parameters are zero

130

The higher the goodness of ﬁt, the better the model explains the behavior of the
tripmaker in the new context. This measure achieves an upper limit of one when the
transferred model predicts perfectly in the new situation, has a zero value when the
model predicts as well as the market share model (L(s) = L(0)), and it may attain
a negative value when the transferred model predicts worse than a model in which
the alternatives are assumed to have equal probability of being chosen.

The results of the different approaches used to transfer models between
corridors without modiﬁcation was not encouraging. Yet, the modiﬁed approach
(LOS case) gives an acceptable goodness of ﬁt. Furthermore, by using the Bayesian
updating method, the goodness of ﬁt measure improved in both corridors. In other
words, the transferred model after updating using the modiﬁed approach (LOS case)
yields a higher p’ than transferring the model in its original form, which is an
indication that the prediction power of the transfer model improved after updating.

It is recommended that the modiﬁed approach (LOS case) after updating be
used to transfer the speciﬁc model from one corridor to another. The updated
modiﬁed approach (LOS case) provides a better model than either transferring the
original model as it is or updating it with a small sample. Moreover, the general
intercity disaggregate modal-sth model calibrated with data from both corridors
gives more accurate predictions than transferring a speciﬁc model from one corridor

to another.

131

The ability of the intercity mode choice model to be transferable between the
corridors under study using the recommended approach or by using the general
model will signiﬁcantly reduce the data requirements, calibration time, cost, and
detailed analytical expertise required by planners to perform modal split analysis in
Saudi Arabia.

Another conclusion of the study is that a universal speciﬁcation of utility for
modelling intercity mode choice in Saudi Arabia exists. This ﬁnding will help the
government concentrate their data collection efforts in an efﬁcient manner.

Knowledge of elasticities and cross-elasticities in Saudi Arabia intercity
corridors was gained through the research. For example, it was determined that the
elasticity of the air mode in the longer corridors is lower than that in the shorter
corridors. Moreover, from the estimation of the elasticities of the in-vehicle travel
time variable it can be expected that the Saudi Arabian Airlines can beneﬁt more
by decreasing in-vehicle travel time (IVTT) than by decreasing the cost, especially
in the Dhahran-Riyadh corridor. It was also found that bus tripmakers are more
sensitive to cost than in-vehicle travel time in the Dhahran-Riyadh corridor, while in
the Jeddah-Riyadh corridor the bus tripmaker is more sensitive to in-vehicle travel

time.

132

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133

In summary, the results of this study include the following:

1.

A modal utility speciﬁcation for intercity mode choice models in Saudi
Arabia was developed.

A general model for estimating the intercity modal split in Saudi Arabia
was developed.

A speciﬁc model for each of the two corridors under study was developed
and evaluated.

Knowledge of elasticities and cross elasticities in Saudi Arabia intercity
corridors was gained through the research.

Intercity disaggregate models without modiﬁcation are not transferable
within Saudi Arabia.

The modiﬁed (LOS case) updated intercity disaggregate model gives an
acceptable goodness of ﬁt measure.

Intercity disaggregate models after modiﬁcation (LOS case ) are
transferable within Saudi Arabia.

The general intercity disaggregate modal split model gives more accurate
predictions than transferring a speciﬁc model frOm one corridor to

another.

134

WWW

To complement and expand on the ﬁndings of this research, the following

recommendations for further study are presented:

1. This research focused only on the J eddah-Riyadh and the Dhahran-
Riyadh corridors. It would be desirable to survey other corridors to make
a comparison of the universal modal utility. Moreover, a comparison
between the estimated coefﬁcients of the variables in the J eddah-Riyadh
model and the Dhahran-Riyadh model and the estimated coefﬁcients
from another corridor is highly recommended.

2. Data should be collected for the same corridors over an entire year, and
should be categorized by the season when it was collected. A comparison
between these data should be performed to determine if the behavior of
the tripmaker changes from one season to another.

3. Research similar to this should be done using two corridors of
approximately the same length. This would help identify more common
factors which have a major eﬁect on selecting an intercity mode

independent of length.

APPENDICES

APPENDIX A

Disaggregate Models

135

DISAGGREGATE MODELS

Disaggregate models are probablistic in nature. In other words, the probability
of a tripmaker choosing a particular alternative is a function of the characteristics
of the tripmaker; such as, income, age, and sex-and of the characteristics of the
mode relative to alternative modes. So, the probability of choosing a mode among
other different modes depends upon the socioeconomic characteristics of the
individual and the level of service of the chosen mode and the unchosen modes.

Most disaggregate models are based on the theory of "utility maximization."
They assume that a person makes a particular choice from a set of different
alternatives depending on the maximum beneﬁt he receives. For example, a person
may wish to minimize travel time and cost of the trip, and maximize comfort and
convenience in selecting a mode from the available modes.

The utility of an alternative consists of two components, one systemic and the
other random:

U.= Vn+ a,

where:

U, = the utility of alternative k to trip maker i

Va. = the systematic component of U,

= (X... St)
X, = a row vector of characteristics of alternative k
Si = a row vector of socioeconomic characteristics of a tripmaker i

e, = the random component of Uill

\

136

The probability of a tripmaker choosing a speciﬁc alternative depends if the
utility of that alternative is greater than the utility of the other alternatives available
to him. Consequently the probability that a tripmaker (i) chose alternative k out of
N alternatives can be expressed as follows:

P(k:N,) = Pr(U,,>U,, vj in NJ/i)
= Pr(V,,+ ek>Vi+ e, vj in Nin)
= Pr(e,-e.<V.-V, vj in Nin)

Where:

P(k:N,) = the probability that tripmaker k will choose alternative i out of
N alternative.

'The most popular calibration techniques for the disaggregate models are
probit and logit. The difference between these two techniques is the assumptions
made concerning the distributions of the random elements of the utility function.
The logit model assumed that the random component (cm) of the choice utility
function (UQ is independent and identically distributed with a Gumbel (double
exponential) distribution function. The probit model is obtained by asSuming that
the random component (q) of the choice utility function (U. has a multivariate
normal distribution.

Predictions of modal split from the probit model are similar to those obtained
by the logit model. However, the probit model requires more complex computational
procedure than the logit model. Furthermore, the logit model is the most functional

form used in transportation demand model, and it is as follows:

137

 

EXP V”
P‘, =
x EXP V,
I
Where:
P‘, = probability of a tripmaker i choosing mode k out of j alternatives

the systematic utility of alternative k to tripmaker i
(X... Si)

X, = a row vector of characteristics of alternative k

.5
II n

Si = a row vector of socioeconomic characteristics of a tripmaker i

The superior method for calibrating a logit model is the maximum likelihood
procedure. The maximum likelihood procedure is usually used by transportation
planners to estimate model parameters. The estimation package will iterate through
the problem until the estimated coefﬁcients reach a speciﬁc convergence criterion
or the estimation completes a speciﬁed number of iterations. After iteration has
been completed, the estimated model will provide the best ﬁt to the observed
pattern of choices in the calibration sample.

The maximum-likelihood estimation of the model produces goodness-of-ﬁt
statistic (p’), t-statistics for coefﬁcients and a X‘ statistic for assessing the entire
model.

The goodness of ﬁt measure is used in determining which speciﬁcation is
better in replicating the data. This measure is somewhat analogous to R2 used in
regression. Since the logit model is asymptotic to 0 and 1 probabilities in its tails,
one can never precisely achieve a value equal to l. A model with p2 around 0.3 is

consider to have a good ﬁt. At the other extreme, if all the parameters in a logit

138

model are 0, the model predicts that all the choices for any given individual are
equally likely. In this case, the model does not explain choice variation. So in order
to compare alternative models used to explain the variation of the new data, the

rho-square (p’) goodness of ﬁt measure has been used:

L(B)
1f: 1.
L(0)
in which
ME.) = Log likelihood for the vector of estimated coefﬁcients
L(0) = The value of the log likelihood function when all the

parameters are zero
This measure is most useful in comparing two speciﬁcations developed from
the identical data. Another goodness of ﬁt measure is the adjusted rho-square. This
measure is also used similar to R’, and is as follows:

(lam-K)

 

p‘= 1-
L(0)
in which
K = Degrees of freedom; which is equal to the number of model parameters.
The model which has the higher goodness of ﬁt is the better model for explaining
the behavior of the tripmaker in the new context.
The likelihood ratio test statistic is used for assessing the entire model. This
test is a X (chi-square) test (-2(L(0)-L(B)), which has a degree of freedom equal
to the number of model parameters. This test is used to test the null hypothesis that

all the parameters are zero (s,=s,=s,...s,=0). Moreover the null hypothesis that

all the coefﬁcients, except the mode-speciﬁc constants, are zero is tested by

-2(L(C)-L(B))

139

with degree of freedom equal to K-J +1; where K is the number of model

parameters, J is the number of alternatives in the universal choice set, and L(C) is

the log likelihood for a model with only constants, and it is calculated as follows:
N .

L(C)=§i-I Ni 111 _
N

where N, is the number of travellers selecting mode i and N is the total sample size.

El |° . | . [I '|
Another property of the logit model is that it has uniform cross elasticities. That
is, the cross elasticity of the choice probability of alternative i with respect to
change in an attribute of alternative j is the same for all alternatives ifj.
This property can be considered a limitation of the logit model because equal

substitutability isn’t necessary logical in all cases.

W

In a simultaneous model it is assumed that the tripmaker will make a decision
considering all the travel choices at once. While a sequential (or nested) model
assumes that a tripmaker decomposes his travel choices according to an order or
hierarchy. It is more convenient to represent the nested logit as a tree. The choice
hierarchy by nested logit consists of higher level and lower level decisions. The lower
level decision (e.q. choice of travel mode) is conditional on the higher level decision
(choice of destination). In other words, the tripmaker chooses an alternative at level
one of the tree and then, conditional on this choice, chooses an alternative at level

2 from the alternatives connected to the level 1 choice by a branch of the tree. So

140

the probability that a tripmaker chose mode i, given that he select a destination ﬁrst,
can be expressed as a product of marginal and conditional choice probabilities.

More illustration of nested logit can be found in reference (8).

APPENDIX B

Questionnaires

141

Mmaﬂlghorﬁducaﬂon

hlﬂMdWmmétlﬂimlx

éLﬁ-d‘ Ml :Ju,

asulmqauag $1.1le

 

Questionnaire Form for Auto Tripmakers.

Dear Sir:

The Department of Civil Engineering at King Fahd University
of Petroleum and. Minerals is conducting a survey about
passenger travel from city to city by private car. Your
answers will help us determine how people choose one mode of
transportation over another. With a better idea of people's
travel habits and needs, we hope to be able to assist in
planning transportation systems which would be more
satisfactory and convenient for everyone. Your participation
is requested, and. your responses ‘will be kept strictly
confidential.

Please return the completed questionnaire to the person who
gave it to you. If you have any questions, please feel free

to ask the person who gave you the questionnaire. There are
no "rightﬁ or'" wrong" answers- just give your best estimate.

Your effort is very much appreciated. Thank you very much for
your cooperation.

Sincerely yours,

Hasan M. Al-Ahmadi

King Fahd University of Petroleum and Minerals

142

 

PART 1. The following general questions are about this
city-to-city trip by private car

 

 

1. Where did you begin this trip? City

 

2. What is your destination? City

 

3. What is your place of residence? City

For the following questions, please mark the one most
appropriate answer.

4. What is the purpose of your trip?
—- 1- work/ study
-- 2- personal business
-- 3- business, related to work
6- other (specify)

 

4- Aumra
5- social/recreation

 

 

5. How long are you planning to stay at your destination?
one day -—- 2-7 days more than 7 days

 

 

6. For this trip, about how long will it take you to reach
your destination (door-to-door)?
hours minutes

 

 

7. Please give jyour travel time in the following categories:

 

 

Total (door-to-door) travel time: --hours minutes
Total in-vehicle travel time: - 'hours minutes
Estimated time spend at the rest area:--hours :minutes

 

8. Please«give your travel costs in the following categories:
(only fill in those that are appropriate):

Costs are round-trip -—— or one way-—-

 

Total cost SR.
Gas, oil SR.
Other (specify) SR.

 

 

 

9. Who pay for this trip?

 

2. The Government
4. others (specify)

-- l. Yourself
--- 3. The company

 

143

 

2L3! II-

The questions below ask You to evaluate car, bus,
plane, and train with respect to different
characteristics.

Please circle one number in each row: in each
question 1' represent very good and 5 represent very
poor level.

You can select only one number from 1 to 5 in each
question to indicate how your feeling about
different characteristics of different means of

.transportation.

10. Evaluate the following means of transportation with
respect t0.£2!£2££a

BUS

PRIVATE CAR

PLANE

TRAIN

very very
good poor
1 2 3 4 5
1 2 3 4
1

5
2 3 4 5
5

ll. Evaluate the following means of transportation with

respect to prigagy

BUS

very no
private privacy

1 2 3 4 5

PRIVATE CAR 1 2 3 4 5

PLANE

TRAIN

1 2 3 4 5

1 2 3 4 5

144

12. Evaluate the following means of transportation with
respect 110.931.4313.

very not safe

safe at all
BUS 1 ' 2 3 4 5
PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5
TRAIN 1 2 3 4 5

13. Evaluate the following means of transportation with

 

respect to_g§pggggg;

very very
cheap expensive

BUS 1 2 3 4 5

PRIVATE CAR 1 2 3 .f4 5

PLANE 1 2 3 i 4 5

TRAIN 1 2 3 4 5

Por the following questions, please mark gm appropriate

“8"! e

 

14. What is your personal and household monthly income?
personal income household income
1- less than 1000 SR.

2- 1000-2000 SR.
3- 2000-4000 SR.

1- less than 1000 SR.
2- 1000-2000 SR.
3- 2000-4000 SR.

4000-5000 SR. 4- 4000-5000 SR.
5- 5000-7000 SR. -——— 5- 5000-7000 SR.
6- 7000-9000 SR. -——— 6- 7000-9000 SR.

9
l

7- more than 9000 SR. 7- more than 9000 SR.

15.

145

Did you consider other means of transportation for the
present trip?

-— yes -—- no

If your answer 18W.

11 your answer is ygg, what were your second and third
preferences? (please indicate your choices as 1, 2, etc.)

 

 

 

 

‘-—- plane train bus
--car(with others) ‘taxi other (specify) -—-
For this trip, are you traveling alone? -—yes -— no

16.

17.

11 your answer is ygg, go to question 12.

If your answer is 39, how many people are traveling with
you (please do not count your self)

--' people

18.

--yes

Are the people traveling with you from your household?

 

ITO

 

The next few questions will complete the questionnaires. Thank
you for your time and effort spent in answering our questions.

 

19.

20.

21.

22.

23.

24.

25.

26.

27.

 

What is your age?

 

How many cars are there in your household?

 

 

Do you have a driver's license? yes no
How many other people in your household have a driver's

license?

 

Are you employed?-——-—-— yes no

 

Are you a student? --- yes no

 

How many other people in your household are employed?

 

 

What is your nationality? Saudi non Saudi

If non Saudi specify

 

Do you have a permanent residence in Saudi Arabia?

-—- yes -- no

146

28. Why are you traveling by car?

 

 

Again, thank you for your cooperation.
Please return the questionnaire to the person who distributed
the questionnaire.

147

quzdw$;aﬂuﬁb
6:184" 4 Julie" =65 Ed." its-«Ls-

Ministry of Higher Education

hﬁmmuinl‘ﬁtlmlnmatﬂlimls

 

Questionnaire Form for Train Tripmakers.

Dear Sir:

The Department of Civil Engineering at King Fahd University
of Petroleum and. Minerals is conducting a survey about
passenger travel from city to city by train. Your answers will
help us determine how people choose one mode of transportation
over another. With a better idea of people's travel habits and
needs, we hope to be able to assist in planning transportation
systems which would be more satisfactory and convenient for
everyone. Your participation is requested, and your responses
will be kept strictly confidential.

Please return the completed questionnaire to the person who
gave it to you. If you have any questions, please feel free

to ask the person who gave you the questionnaire. There are
no "rightﬂ or'" wrong" answers- just give your best estimate.

Your effort is very much appreciated. Thank you very much for
your cooperation.

Sincerely yours,

Hasan M. Al-Ahmadi

King Fahd University of Petroleum and Minerals

148

 

2531_1; The following general questions are about this
city-to-city trip by Train

 

 

1. Where did you begin this trip? City

 

2. What is your destination? City

 

3. What is your place of residence? City

For the following questions, please mark the one most
appropriate answer.

4. What is the purpose of your trip?
-—--1- work/study
-- 2- personal business
-—- 3- business, related to work
6- other (specify)

 

4- Aumra
5- social/recreation

 

 

5. How long are you planning to stay at your destination?
one day -- 2-7 days more than 7 days

 

 

6. For this trip, about how long will it take you to reach
your destination (door-to-door)?
hours minutes

 

 

7. Please give your travel time in.the following'lcategories:

Total (door-to-door) travel time: --hou 5 -—-minutes
Time to get to the train station: - ’hours - 'minutes
Time spent waiting at the train station: --hou 3 -—-minutes
Total in-vehicle travel time: - 'hours -—— minutes
Estimated time from train station

to final destination: --hours -—- minutes

8. Please give your travel costs in the following categories:
(only fill in those that are appropriate):

 

Costs are round-trip -—— or one way

 

Total cost SR.
Ticket(fare) SR.

 

 

 

 

 

Taxi SR.
limousine SR.
Other (specify) SR.

9. Who pay for this trip?

 

2. The Government
4. others (specify)

-- l. Yourself
-- 3. The company

 

149

 

MB-

The questions below ask YOU to evaluate car, bus,
plane, and train with respect to different
characteristics.

Please circle one number in each row: in each
question I represent very good and 5 represent very
poor level.

You can select only one number from 1 to s in each
question to indicate how your feeling about
different characteristics of different means of

-transportation.

 

10. Evaluate the following means of transportation with
respect tom

very very

good poor
BUS 1 2 3 4 5
PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5
TRAIN 1 2 3 4 5

11. Evaluate the following means of transportation with

respect to 211142!

BUS

very no
private privacy
1 2 3 4 5

PRIVATE CAR 1 2 3 4 5

PLANE

TRAIN

150

12. Evaluate the following means of transportation with

respect t0.§§12&21

very

safe
BUS 1
PRIVATE CAR 1
PLANE 1
TRAIN 1

not safe
at all

2 3 4 5
5
2 3 4 5
5

2 3 4

l3. Evaluate the following means of transportation with
respect t0.2§223§2§1

very
cheap

BUS 1
PRIVATE CAR 1‘
PLANE 1

TRAIN 1

very
expensive
2 3 4 5
2 3 4 5
2 3 4 5
2 3 4 5

 

Por the following questions, please mark thg most appropriate

“8": e

 

14. What is your personal and household monthly income?

1- less than
2- 1000-2000
3- 2000-4000
4000-5000
5- 5000-7000

personal income household income
1000 SR. -- 1- less than 1000 SR.
SR. -- 2- 1000-2000 SR.
SR. - -’3- 2000-4000 SR.
SR. -—-— 4- 4000-5000 SR.
SR. '-- 5- 5000-7000 SR.
SR. -—- 6- 7000-9000 SR.

6- 7000-9000
7- more than

as
l

9000 SR. 7- more than 9000

SR.

151

15. Did you consider other means of transportation for the
present trip?

— yes — no
If your answer kW.

11 your answer is 15;, what were your second and third
preferences? (please indicate your choices as 1, 2, etc.)

 

 

 

 

-- plane train bus
- - car(with others) taxi other (specify) --
16. For this trip, are you traveling alone? -—yes -— no

If your answer 18W

17. If your answer is pg, how many people are traveling with
you (please do not count your self)

-—- people

18. Are the people traveling with you from your household?

 

-— yes no
19. How did you get to the train station?
walk bus car taxi
dropped off. -—-—other (specify)

 

 

 

 

 

 

20. If you had to leave your car at the train station, what
did it cost you to park? SR. For how long—

 

21. How long did it take you to reach the check-in counter
from the parking lot? minutes

 

22. How early or late did the train depart the train

station?
on time

 

minutes late

 

 

minutes early

23. How are you planning to get to your final destination
from the train station?

walk bus limousine

-- private car other (specify)

-- someone will pick you up

 

 

 

 

rental car

 

 

24. What class did you travel?
first class economy
other (specify)

 

 

 

reduced economy fare

 

 

152

 

The
you

next few questions will complete the questionnaires. Thank

 

25.

26.

27.

28.

29.

30.

31.

32.

33.

 

 

 

 

 

for your time and effort spent in answering our questions.
What is your age?

How many cars are there in your household?

Do you have a driver's license? yes no

How many other people in your household have a driver's
license? '

Are you employed? -—-—- yes no

Are you a student? ---— yes no

 

 

How many other people in your household are employed?

 

Saudi non Saudi

 

What is your nationality?
If non Saudi specify

 

Do you have a permanent residence in Saudi Arabia?

--yes -—- no

34.

Why are you traveling by train?

 

 

Again, thank you for your cooperation.
Please return the questionnaire to the person who distributed

the

questionnaire.

 

153

’4"

4‘!“ FILL—IT.“ ED)

deal-so" a denial] =44 Ed." ﬁnal-1:»

 

Questionnaire Form for Bus Tripmakers.

Dear Sir:

The Department of Civil Engineering at King Fahd University
of Petroleum and. Minerals is conducting a survey about
passenger travel from city to city by bus. Your answers will
help us determine how people choose one mode of transportation
over another. With.a better idea of people's travel habits and
needs, we hope to be able to assist in planning transportation
systems which would be more satisfactory and convenient for
everyone. Your participation is requested, and your responses
will be kept strictly confidential.

Please return the completed questionnaire to the person who
gave it to you. If you have any questions, please feel free

to ask the person who gave you the questionnaire. There are
no "right" or " wrong" answers- just.give your best estimate.

Your effort is very much appreciated. Thank you very much for
your cooperation.

Sincerely yours,

Hasan M. Al-Ahmadi

King Fahd University of Petroleum and Minerals

 

154

 

2331_1& The following general questions are about this

city-to-city trip by Bus

 

 

1. Where did you begin this trip? City

 

2. What is your destination? City

 

3. What is your place of residence? City

For the following questions, please mark the on; most

appropriate answer.

4. What is the purpose of your trip?
1- work/study

-—- 2- personal business
-- 3- business, related to work
6- other (specify)

 

4 - Aumra

 

 

 

5- social/recreation

5. How long are you planning to stay at your destination?

 

 

one day -- 2-7 days

more than 7 days

6. For this trip, about how long will it take you to reach

your destination (door-to-door)?
hours minutes

 

 

7. Please give your travel time in the following

Total (door-to-door) travel time: -—- hours
Time to get to the bus station: --hours
Time spent waiting at the bus station: — hours
Total in-vehicle travel time: --hours

categories:

-—-minutes
— minutes
--minutes
-——-minutes

Estimated time from bus station to final destination:

to final destination: -—-hours

8. Pleaselgive'your‘travel costs in the following
(only fill in those that are appropriate):

 

Costs are round-trip -—— or one way

 

Total cost SR.
Ticket(fare) SR.

 

 

 

— minutes

categories:

 

 

Taxi SR.
limousine SR.
Other (specify) SR.

9. Who pay for this trip?

2. The Government

 

-—- 1. Yourself
-- 3. The company

 

4. others (specify)

155

 

MH-

The questions below ask YOU to evaluate car, bus,
plane, and train with respect to different
characteristics.

Please circle one number in each row: in each
question I represent very good and 5 represent very
poor level.

You can select only one number from 1 to 5 in each
question to indicate how your feeling about
different characteristics of different means of
transportation.

 

10. Evaluate the following means of transportation with
respect t0.£2ﬂ12££1

very very

good poor
BUS 1 2 3 4 5
PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5
TRAIN 1 2 3 4 5

11. Evaluate the following means of transportation with
respect to pgiyagy

BUS

very no
private privacy
1 2 3 4 5

PRIVATE CAR 1 2 3 4

PLANE

TRAIN

5
1 2 3 4 5
5

1 2 3 4

156

12. Evaluate the following means of transportation with

respect to_§afgty;

very not safe
safe at all
BUS l ' 2 3 4 5

PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5

TRAIN 1 2 3 4 5

13. Evaluate the following means of transportation with
respect t0.££2§n§2£;

very very
cheap expensive
BUS 1 2 3 4 5
PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5
TRAIN 1 2 3 4 5

 

For the following questions, please mark M appropriate
answer.

 

14. What is your personal and household monthly income?
personal income household income

1- less than 1000 SR.
2- 1000-2000 SR.
3- 2000-4000 SR.

1- less than 1000 SR.
2- 1000-2000 SR.
3- 2000-4000 SR.

4000-5000 SR. 4- 4000-5000 SR.
5- 5000-7000 SR. -—-— 5- 5000-7000 SR.
6- 7000-9000 SR. -——— 6- 7000-9000 SR.

uh
I

7- more than 9000 SR. 7- more than 9000 SR.

157

15. Did you consider other means of transportation for the
present trip?

— yes — no
If.your answer is_asl_g2_;2_guestien__1§.

If your answer is 23;, what were your second and third
preferences? (please indicate your choices as 1, 2, etc.)

 

 

bus
other’(specify)---

train
taxi

-- plane
-—-car(with others)

 

 

16. For this trip, are you traveling alone? -—yes - no

If your answer is_!_si_ss_t2_guestign_12

17. If your answer is no, how many people are traveling with
you (please do not count your self)

-—- people
18. Are the people traveling with you from your household?

no

 

-- yes

19. How did you get to the bus station?
walk bus car taxi
dropped off. other (specify)

 

 

 

 

 

 

 

20. If you had to leave your car at the bus station, what did
it cost you to park?
SR. For how long---

 

21. How long did it take you to reach the check-in counter
from the parking lot? minutes

 

22. How early or late did the bus depart the bus station?
minutes early minutes late on time

 

 

 

23. How are you planning to get to your final destination
from the bus station?

walk bus limousine

private car other (specify)

someone will pick you up

 

rental car

 

 

 

 

 

 

 

158

 

The next few questions will complete the questionnaires. Thank
you for your time and effort spent in answering our questions.

 

24.
25.
26.

27.

28.
29.
30.

31.

32.

 

What is your age?

 

How many cars are there in your household?

 

 

Do you have a driver's license? yes no
How many other people in your household have a driver's

license?

 

Are you employed? -——-—- yes no

 

Are you a student? -—- - yes no

 

How many other people in your household are employed?

 

 

What is your nationality? Saudi non Saudi

If non Saudi specify

 

Do you have a permanent residence in Saudi Arabia?

— yes — no

33.

Why are you traveling by bus?

 

 

Again, thank you for your cooperation.
Please return the questionnaire to the person who distributed
the questionnaire.

159

 

CALL!“ Ml 3),},

6:43." a denial] ad 51." incl—7|

 

Questionnaire Form for Plane Tripmakers.

Dear Sir:

The Department of Civil Engineering at King Fahd University
of Petroleum and. Minerals is conducting a survey' about
passenger travel from city to city by plane. Your answers will
help us determine how people choose one mode of transportation
over another. With a better idea of people's travel habits and
needs, we hope to be able to assist in planning transportation
systems which would be more satisfactory and convenient for
everyone. Your participation is requested, and your responses
will be kept strictly confidential.

Please return the completed questionnaire to the person who
gave it to you. If you have any questions, please feel free

to ask the person who gave you the questionnaire. There are
no "right" or’" wrong“ answers- just give your best estimate.

Your effort is very much appreciated. Thank you very much for
your cooperation.

Sincerely yours,

Hasan M. Al-Ahmadi

King Fahd University of Petroleum and Minerals

160

 

PART_1& The following general questions are about this
city-to-city trip by plane

 

 

1. Where did you begin this trip? City

 

2. What is your destination? City

 

3. What is your place of residence? City

For the following questions, please mark the 93; most
appropriate answer.

4. What is the purpose of your trip?
-- 1- work/study 4- Aumra
-- 2- personal business 5- social/recreation
-—- 3- business, related to work .

6- other (specify)

 

 

 

5. How long are you planning to stay at your destination?
one day -—— 2-7 days more than 7 days

 

 

6. For this trip, about how long will it take you to reach
your destination (door-to-door)?
hours minutes

 

 

7. Please give your travel time in the following categories:

 

Total (door-to-door) travel time: hours -—-minutes

 

 

 

Time to get to the airport: hours minutes
Time spent waiting at the airport: hours -—-—minutes
Total in-vehicle travel time: hours minutes

 

 

Estimated time from plane terminal
to final destination:

 

hours --minutes

8. Please give your travel costs in the following categories:
(only fill in those that are appropriate):

Costs are round-trip --’ or one way--

 

Total cost SR.
Ticket(fare) SR.

 

 

 

 

 

Taxi SR.
limousine SR.
Other (specify) SR.

9. Who pay for this trip?

 

2. The Government
4. others (specify)

-- 1. Yourself
--— 3. The company

 

161

 

2331 II-

The questions below ask YOU to evaluate car, bus,
plane, and train with respect to different
characteristics.

Please circle one number in each row: in each
question 1' represent very good and 5 represent very
poor level.

You can select only one number from 1 to 5 in each
question to indicate how your feeling about
different characteristics of different means of
transportation.

 

10. Evaluate the following means of transportation with
respect t0_£2n£2££;

BUS

PRIVATE CAR

PLANE

TRAIN

very very
900d poor

1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1

2 3 4 5

11. Evaluate the following means of transportation with
respect to prizagy

BUS

very no
private privacy

1 2 3 4 5

PRIVATE CAR 1 2 3 4

PLANE

TRAIN

5
1 2 3 4 5
5

162

12. Evaluate the following means of transportation with

respect to_§afgty;

very not safe

safe at all
BUS 1 ' 2 3 4 5
PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5
TRAIN l 2 3 4 5

l3. Evaluate the following means of transportation with
respect t0_23222§2§x

very very
cheap expensive
BUS 1 2 3 4 5
PRIVATE CAR 1 2 3 4 5
PLANE 1 2 3 4 5
TRAIN 1 2 3 4 5

 

Por the following questions, please mark the most appropriate
answer.

 

14. What is your personal and household monthly income?
personal income household income
1- less than 1000 SR.

2- 1000-2000 SR.
3- 2000-4000 SR.

1- less than 1000 SR.
2- 1000-2000 SR.
3- 2000-4000 SR.

4000-5000 SR. 4- 4000-5000 SR.
5- 5000-7000 SR. -———'5- 5000-7000 SR.
6- 7000-9000 SR. ———- 6- 7000-9000 SR.

9
I

7- more than 9000 SR. 7- more than 9000 SR.

15.

163

Did you consider other means of transportation for the
present trip?

-- yes -- no

-- plane
--car(with others)

16.

17.

18.

19.

20.

21.

22.

23.

24.

 

If your answer 18W.

11 your answer is 11;, what were your second and third
preferences? (please indicate your choices as 1, 2, etc.)

 

 

bus
other (specify) -—-—

train
taxi

 

 

For this trip, are you traveling alone? -yes - no

11 your answer is yes, go to question 12.

If your answer is 39, how many people are traveling with

. you (please do not count your self)

-- people

Are the people traveling with you from your household?

 

-—— yes no
How did you get to the airport terminal?

walk bus car taxi
dropped off. --—other (specify)

 

 

 

 

 

 

If you had to leave your car at the airport, what did
it cost you to park? SR. For how long-————-

 

How long did it take you to reach the check-in counter
from the parking lot? minutes

 

How early or late did the plane depart the airport
terminal?
minutes early

 

 

minutes late on time

How are you planning to get to your final destination
from the airport?

 

 

 

walk bus limousine rental car
private car other (specify)

someone will pick you up

 

 

9

at class did you travel?
first class economy
-—-— other (specify)

 

 

 

reduced economy fare

 

164

 

The next few questions will complete the questionnaires. Thank
you for your time and effort spent in answering our questions.

 

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

 

What is your age?

 

How many cars are there in your household?

 

 

Do you have a driver's license? yes no
How many other people in your household have a driver's

license? -——- .

 

Are you employed? -——-- yes no

 

Are you a student? -—-- yes no

 

How many other people in your household are employed?

 

 

What is your nationality? Saudi non Saudi

If non Saudi specify

 

Do you have a permanent residence in Saudi Arabia?
‘-- yes -— no

Why are you traveling by plane?

 

 

Again, thank you for your cooperation.
Please return the questionnaire to the person who distributed
the questionnaire.

165

 

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APPENDIX C

Coding Manual for Intercity Mode Choice
Models in Saudi Arabia

 

192

CODING MANUAL FOR INTERCITY MODE CHOICE MODELS IN SAUDI ARABIA
(for Plane and Train Questionnaire Forms)

QUESTION
FIELD NUMBER

VARIABLE
81MB

INSTRUCTION

 

1-4

10-11

12-13

14-15
16-17

18-19
20-21

none

ID

city

city
name

city
name

trip
purpose

number
of days

time

coder assigned 4-digit number where
lst digit is mode of travel; 1=auto,
2=bus, 3=train, 4=plane

2nd-4th digits: start each sequence
at 001 for mode

e.g., first auto respondent 81001;
second auto respondent = 1002:...
first plane respondent a 4001:...

coder: write ID number on survey;
upper right-hand corner of first page

code a one-digit number for the name
origin city; coder set 1=1Riyadh, 2=
Jeddah, 3=eastern province

code a one-digit number for the
destination city; coder set 1=
Riyadh, 2- Jeddah, B-eastern province

code a one-digit number for the
residence city; coder set 1= Riyadh,
2= Jeddah, 3=eastern province

l=work/study; 2=personal

business; 3=business , related to
w o zrlc ; 4 = Atllln r a ;
5=socia1/recreationa1:

6=other; 7=other.

l=one day: 2=2—7days; 3=more
than 7days

code actual hours
code actual minutes

code actual # of hours.
code actual # of minutes

time to station, or airport # of hrs.

time to station, or airport # of min.

22-23
24-25

26-27
28-29

30-31

32-33

34

35-38
39-41
42-43
44-45
46-47

48

49
50
51
52

53
54
55
56

57
58
59
60

61
62
63
64

65

Q 8

Q 10

Q 11

Q 12

Q 13

Q 14

cost

comfort

privacy

safety

expenses

income
person

193

waiting time # of hrs.
waiting time # of min.

in-vehicle time # of hrs.
in-vehicle time # of min.
time from sta. to final
destination, # of hrs.
time from stat. to final

destination in minutes
l-one way; 2=round trip
total cost, code to the nearest SR.
ticket cost, code to the nearest SR.
taxi cost, code to the nearest SR.
limo. cost, code to the nearest SR.

other cost, code to the nearest SR.

l-yourself:
3-Company:

2=government:
=other

put the scale value; for bus

private car

plane

train

put the scale value; for bus

private car

plane

train

put the scale value: for bus

private car

plane

train

put the scale value; for bus

private car

plane

train

1=<10003
3=2000-4000:
5=5000-7000;
7=>9000

2= 1000-20003
4=4000-50003
6=7000-90007

66

67
68-71

72

73-74

75

76

77-78
78-80

81-82

83-84
85-86
87

88

88

90-91
92
93
94
95
96
97
98
99

Q

Q

14

15

(2 15

Q
Q

Q
Q

Q

16

17

18

19

20

Q 21

Q

Q 23

000000000

22

25
26
27
28
29
3O
31
32
33

income
hhld

early
late

one-time

1? mode

claes 24

age
cars

licen.
others

empl.
stud.

others

nat.
res.

194

1=<1000; 2= 1000-2000;
332000-4000; 434000-5000?
585000-7000; 687000-9000;
7=>9000

layes: 2=no

coder rank them as the tripmaker,
then write the hypothesized number
respectively, e.g. , tripmaker second
and third preference are plane, and
train respectively, so, in coding
planes 4 (see field 1-4) will be in
column 68 and train=3 will be in
column 69

layes; 2=no

code lsalone, or the actual number
if they are >1
l=yes: 2=no
l-walk; 2=bus; 3=car; 4a taxi:
5=dropped off: 6=other

cost of parking
period of parking

time in minutes to reach check-in
counter

code actual min. early

code actual min. late

zero minutes

l=wa1k3 2=bus; 3=limo; 4=rental car:
Esprivate car: 6=other:
7-someone will pick you up

1-first: 2=economy; 3=reduced
economy fare; 4=other

code #

code # (9=9 or more)

1=yes: 2=no

code #

l=yes: 2=no

layes; 2=no

code #

1-Saudi; 2=non Saudi
layes; 2=no

 

195

CODING MANUAL FOR INTERCI'I'Y MODE CHOICE MODELS IN SAUDI ARABIA
(for Bus Questionnaire Form)

QUESTION
rrsnn NUMBER

VARIABLE
NAME

INBTRDCTION

 

1-4

10-11
12-13

14-15
16-17

18-19
20-21

none

ID

city

city
name

city
name

trip
purpose

number
of days

time

coder assigned 4-digit number where
lat digit is mode of travel; 1=auto,
2=bus, 3=train, 4=plane

and-4th digits: start each sequence
at 001 for mode

e.g., first auto respondent 81001:
second auto respondent = 1002:...
first plane respondent = 4001:...

coder: write ID number on survey:
upper right-hand corner of first page

code a one-digit number for the name
origin city; coder set 1= Riyadh, 2=
Jeddah, 3=eastern province

code a one-digit number for the
destination city; coder set l=
Riyadh, 2- Jeddah, 3=eastern province

code a one-digit number for the
residence city; coder set 1= Riyadh,
2= Jeddah, 3=eastern province

1=work/study; 2=personal

business ; 3=bus iness , related to
‘w o r'lc ; 4 = A1111n r a ;
5-social/recreationa1:

6-other: 7=other.

1=one day; 2=2-7days; 3=more
than 7days

code actual hours
code actual minutes

code actual # of hours.
code actual # of minutes

time to station, or airport # of hrs.

time to station, or airport # of min.

22-23
24-25

26-27
28-29

30-31

32-33

34

35-38

39-41

42-43

44-45

46-47

48

49
50
51
52

53
54
55
56

57
58
59
6O

61
62
63
64

65

Q 8

Q 10

Q 11

Q 12

Q 13

Q 14

cost

comfort

privacy

safety

expenses

income
person

196

waiting time # of hrs.
waiting time # of min.

in-vehicle time # of hrs.
in-vehicle time # of min.
time from sta. to final
destination, # of hrs.
time from stat. to final

destination in minutes
1=one way; 2=round trip
total cost, code to the nearest SR.
ticket cost, code to the nearest SR.
taxi cost, code to the nearest SR.
limo. cost, code to the nearest SR.

other cost, code to the nearest SR.

1=yourself3
3-Company:

2=government:
4=other

put the scale value; for bus
private car

plane

train

put the scale value; for bus
private car

plane

train

put the scale value; for bus
private car

plane

train

put the scale value; for bus
private car

plane

train

1=<1000; 2= 1000-2000;
3=2000-4000; 4=4000-5000;
5=5000-7000; 6=7000-90003
7=>9000

66

67
68-71

72

73-74

75

76

77-78
78-80

81-82

83-84
85-86
87

88

90-91
92
93
94
95
96
97
98
99

Q 14

Q 15

Q 16

Q 21

Q 22

0
N
u

24
25
26
27
28
29
3O
31
32

(DCHOIDKDCHOKDﬁ)

income

hhld

early
late
one-time

f mode

age
cars
licen.
others
empl.
stud.
others
nat.
res.

197

1-<1000;
332000-4000;
585000-7000;
7->9000

2= 1000-2000;
434000-5000;
6=7000-90007

lsyes; 2=no

coder rank them as the tripmaker,
then write the hypothesized number
respectively, e.g. , tripmaker second
and third preference are plane, and
train respectively, so, in coding
plane8 4 (see field 1-4) will be in
column 68 and train=3 will be in
column 69

1=yes; 2=no

code 1=alone, or the actual number
if they are >1

l=yes; 2=no

l-walk; 2=bus; 3-car: 4- taxi:
Ssdropped off; 6=other

cost of parking
period of parking

time in minutes to reach check-in
counter

code actual min. early

code actual min. late

zero minutes

l=walk3 2=bus: 3=limo; 4=rental car:
Saprivate car; 6=other:
7=someone will pick you up
code #

code # (9=9 or more)
1=yes; 2=no

code #

lsyes: 2=no

lsyes: 2=no

code #

l=Saudi; 2=non Saudi
1=yes: 2=no

198

CODING MANUAL FOR INTERCITY MODE CHOICE MODELS IN SAUDI ARABIA
(for Auto Questionnaire torn)

QUESTION VARIABLE

FIELD NUMBER NAME

INSTRUCTION

 

1-4 none ID

5 Q 1 city

6 Q 2 city
name

7 Q 3 city
name

8 Q 4 trip
purpose

9 Q 5 number
of days

10-11 Q 6 time

12-13 Q 6

coder assigned 4-digit number where
let digit is mode of travel: 1=auto,
2=bus, 3=train, 4=plane
2nd-4th digits: start each sequence
at 001 for mode '

e.g., first auto respondent =1001:
second auto respondent = 1002;...
first plane respondent = 4001;...

coder: write ID number on survey;
upper right-hand corner of first page

code a one-digit number for the name
origin city: coder set 1= Riyadh, 2=
Jeddah, 3=eastern province

code a one-digit number for the
destination city: coder set 1=
Riyadh, 28 Jeddah, 3=eastern province

code a one-digit number for the
residence.city: coder set l= Riyadh,
2= Jeddah, 3=eastern province

1=work/study: 2=personal

bus iness; 3=bus iness , related to
‘w o 1'}: : 4 = A1111n r a ;
5=social/recreational:

6=other: =other.

1=one day; 2=2-7days; 3=more
than 7days

code actual hours

code actual minutes

14-15
16-17

18-19
20-21

22-23
24-25

26

27-29

30-32

33-35

36

37
38
39
4O

41
42
43
44

45
46
47
48

48
50

51
52

53

54

8

10

11

12

13

14

14

cost

comfort

privacy

safety

expenses

income
person

income
hhld

199

code actual # of hours.
code actual # of minutes

time spent at the rest area # of hrs.
time spent at the rest area # of min.

in-vehicle time # of hrs.
in-vehicle time # of min.

l=round-trip: 2=one way

total cost, code to the nearest SR.
oil cost, code to the nearest SR.
other cost, code to the nearest SR.

=yourself: 2=government:
3aCompany; 4=other

put the scale value; for bus
private car

plane

train

put the scale value; for bus
private car

plane

train

put the scale value; for bus
private car

plane

train

put the scale value: for bus
private car

plane

train

1=<1000: 2= 1000-20003
3=2000-4000; 4=4000-50003
5=5000-7000: 6=7000-9000;
=>9000

1=<1000; 2= 1000-20007
3=2000-4000; 4=4000-5000:
5=5000-7000; 6=7000-90003
7=>9000

55
56-59

60

61-62

63

64-65
66
67
68
69
7O
71
72
73

Q

Q

Q 17

000000000 0

15

Q 15

16

18

19
20
21
22
23
24
25
26
27

age
cars
licen.
others
empl.
stud.
others
nat.
res.

200

l=yes; 2=no
coder rank them as the tripmaker,
then write the hypothesized number
respectively,

e.g., tripmaker second. and third
preference are plane, and train
respectively, so, in coding plane=
4 (see field 1-4) will be in column
53 and train=3 will be in column 54

l=yes; 2=no

code l-alone, or the actual number
if they are >1

l=yes: 2=no

code #

code # (9:9 or more)
layes; 2=no

code #

l-yes: 2=no

l-yes: 2=no

code #

l-Saudi: 2=non Saudi
l-yes; 2=no

Appendix D

FORTRAN PROGRAM

201

C*****************************************************************
C*****************************************************************
C*****************************************************************

PROGRAM VALI DATE

************************************************************

TO READ THE FIL MADE FOR B LOGIT AND CALCULATE THE AGGREGATE
PREDICTION FOR EACH MODE IN THE DHAHRAN-RIYADH CORRIDOR
************************************************************
DIMENSION F(30,30,30),S(10,10,10),E(10,10,10)
DIMENSION X(10,10),Z(10),P(10),V(10)
DIMENSION INDEX(10),PRED(10),IND(10),QC(10)
OPEN (1,FILE -'VALD.LOL',STATUS-'OLD')
OPEN (9,FILE -'VAL.DHA')
NDIM-3
NT-3
Explo
RxpNUMEER OP PARAMETERS
NT-NUMBER OF ALTERNATIVE
NN-NUMBER 0F OBSERVATIONS
INITIALIZE F-MATRIX AND z-VECTOR
DO 10 I-1,NT
DO 10 J-1,KR
DO 10 K—1,NT
10 F(I,K,J)-0.0
DO 15 K-1,NT
QC(K)-0.0
IND(K)-O
15 2(R)-O.o
WRITE(9,314)
314 PORMAT<1H1,9X,'ALT.',sx,'ALT.'/8x,'CHOSEN',3x,'PREDICTED',6x,'CHOI
ICE PROBABILITIES 0F ALIERNATIVES')
NN-189
D0 1 Ico-1,NN
C**************************************************
READ (1,30)RNDA,TTHA,TTSA,
*THwA,VHA,TPSA,TTCTA,TRCA,
*QUAL3,QUAL7,
*QUAL11,QUAL15,
*RINCA,RINHHA,RNPA,CPAKA,
*RLICA,AGEA,CARA,STUDA,
*ATA,FREA
3o FORMAT(F2.0,SF5.2,FS.0,F4.0,6F2.0
*,F3.0,2F4.0,F3.0,3F2.0,F5.2)
C*****************************************************************
IF (RNDA .LE. 1.)THEN
DUR-1.
ELSE
DUR-0.0
ENDIF

C)C)C)C)C)C)C)

C)C)C)C)

202

c*mﬂmmmmm*************~k~k**~k*****me:
READ (1,40)TTHB,TTSB,

*THWB,VHB,TFSB,TTCAB,TKCB,

*QUAL1,QUAL5,QUAL9,QUAL13,

*RLATEB,FREB,

*TTHT,TTST, _

*THwT,VHT,TPST,TTCT,TKCT,

*QUAL4,QUAL8,QUAL12,QUAL16,

*RLATET,

*FRET,TTHC,

*THwC,VHC,TTCAC,OIL,

*QUALZ,QUAL6,QUAL10,QUAL14,FREC,IPLA,IBUS,ITRA,ICAR

IF (IPLA .EQ. 1) THEN

LPK-l

IND(1)-IND(1)+1

ENDIP

IF (IBUS .EQ. 1) THEN

IND(2)-IND(2)+1

LPR-z

ENDIF

IP (ICAR .EQ. 1) THEN

IND(3)-IND(3)+1

LPK-3

ENDIP
40 FORMAT(5F5. 2,F 0,F

*SFS. 2 ,/, F5. O,F O,4F2.0,F4.0,

*FS. 2, 3F5. 2, F5. ,F4. O,4F2.0,F5.2,2X,412)
CWWMWWW*******
C CALCULATION OF UTILITY

UTIA~40.34-43.46*VEA-.o32*TTCTA+.39*RINEHA

*+.670*QUAL3+.492*QUAL11+2.1*DUR

CWWWWWWW***WH************
UTIB-5.33-.560*VHB-.032*TTCAB—.7l7*RINHHA

*+.670*QUAL1+.492*QUAL9

C*NWWWWW*W*********************
UTIC--.560*VHC-.032*TTCAC
*+.670*QUAL2+.492*QUAL10
CWWWHW***********************
C WRITE (9,*)VHA,TTCTA,RINHHA,QUAL3,QUALll
PROEApo.o
PROBE-0.0
PROBT-0.0
PROBC-0.0
SUMT-o.o

c CALCULATION OF LOG SUM
ROSA-EXP(UTIA)
ROSB-EXP(UTIB)
ROSC-EXP(UTIC)

C CALCULATION OF PROBABILITIES
SUMT-SUMT+ROSA+ROSE+ROSC

C WRITE (9,*)ICO,ROSA,ROSB,ROSC,SUMT
PROBApROSA/SUMI

F.S 4. O,4F2.0,F4.0,FS.2,
F4
0

203

PROBE-ROSB/SUMI
PROBC-ROSC/SUMT
P(1)-PROBA
P(2)-PROBB
P(3)-PROBC

CWWWWWWW*

PMAXPAMAX1(P(1),P(2),P(3))

CWWWWWW*MW
CWWWWW

C

C

C
313

900

316

315

600

610

615
630

Kx— K
WRITE(9,313)(LL,LL-1,NT)
PORMAT(IEO,27x,IOIa/)
DO 900 IRR~1,NT
INDEX(IRK)-O
IF(P(LPK).EQ.PMAX)QC(LPK)-QC(LPK)+1.
WRITE (9,*)QC(LPR),P(LPR)
DO 316 LL-1,NT
IE(PMAx.EQ.P(LL))IMAxpLL
CONTINUE
WRITE(9,315)ICO,LPK,IMAX,(P(LL),LL~1,NT)
FORMAT(3X,I4,3X,IZ,6X,12,9X,10F8.4)
P(l)-O.
P(2)-o.
P(3)-o.
P(4)-0.
P(5)-o.
P(6)-0.
P(7)-O.
P(8)-0.
P(9)-o.
P(10)-o.o
CONTINUE
OUTPUT OF PREDICTION RATIO
SUM-0.0
DO 600 x_1,NT
PRED(K)-QC(K)/IND(K)
SUMwSUH+QC(K)
TOT-SUM/FLOAT(NN)
WRITE(9,610)TOT
EORMAT(//////,' RATIO OF CHOICES PREDICTED CORRECTLY-',F6.4/)
DO 615 KP1,NT
WRITE(9,630)K,IND(K),QC(K),PRED(K)
PORMAT(/,/,'ALTERNATIVE'.13, ' CHOSEN ',IS, ' TIMES',/,/

OOOOOOOOO

1,'PREDICTED CORRECTLY',F5.0,' TIMES',/,'PREDICTION'RATIOI- ',F6.4)

STOP
END

 

204

C*****************************************************************
C*****************************************************************
C*****************************************************************

PROGRAM VALIDATE

************************************************************

To READ THE FIL MADE FOR B LOGIT AND CALCULATE THE AGGREGATE
PREDICTION FOR EACH MODE IN THE JEDDAE-RIYADM CORRIDOR
************************************************************
DIMENSION F(30,30,30),S(lO,lO,lO),E(10,lO,lO)
DIMENSION X(10,10),2(10),P(10),V(10)
DIMENSION INDEX(10),PRED(10),IND(10),QC(10)
OPEN (1,FILE -'VALJ.LOL',STATUS-'OLD')
OPEN (9,PILE -'VAL.JED')
NDIMpa
NT-3
Explo
KKPNUMBER OF PARAMETERS
NT-NUMEER OF ALTERNATIVE
NN-NUMBER OF OBSERVATIONS
INITIALIZE F-MATRIX AND z-VECTOR
DO 10 I-1,NT
DO 10 J-l,KK
D0 10 K91,NT
10 F(I,K,J)-0.0
Do 15 K91,NT
QC(K)-0.0
IND(K)-O
15 2(x)-o.o
WRITE(9,314)
314 FORMAT<1H1,9X,'ALT.',sx,'ALT.'/8x,'CHOSEN',3x,'PREDICTED',6x,'CHOI
lCE PROBABILITIES OF ALTERNATIVES')
NN-244
DO 1 ICO—1,NN
C**************************************************
READ (1,30)RNDA,TTHA,TTSA,
*THWA,VHA,TESA,TTCTA,TKCA,
*QUAL3,QUAL7,
*QUAL11,QUAL15,
*RINCA,RINHHA,RNPA,CPAKA,
*RLICA,AGEA,CARA,STUDA,
*AIA,FREA
30 FORMAT(F2.0,SFS.2,F5.0,F4.0,6F2.0
*,F3.0,2F4.0,F3.0,3F2.0,F5.2)
C*****************************************************************
IF (RNDA .LE. 1.)THEN
DURpl.
ELSE
DURpo.o

ENDIF
c*****************************************************************

C)C)C)C)C)C)C)

C)C)C)C)

 

205

READ (1,40)TTHB,TTSB,
*THWB,VHB,TFSB,TTCAB,TKCB,
*QUAL1,QUAL5,QUAL9,QUAL13,

*RLATEB,FREB,

*TTHT,TTST,

*THUT,VHT,TFST,TTCT,TKCT,
*QUAL4,QUAL8,QUAL12;QUAL16,

*RLATET,

*FRET,TTHC,

*THWC,VHC,TTCAC,OIL,
*QUALZ,QUAL6,QUAL10,QUAL14,FREC,IPLA,IBUS,ITRA,ICAR

IF (IPLA .EQ. 1) THEN

LPK-l

IND(1)-IND(1)+1

ENDIF

IF (IBUS .EQ. 1) THEN

IND(2)-IND(2)+1

LTK~2

ENDIF

IF (ICAR .EQ. 1) THEN

IND(3)-IND(3)+1

LPK-3

ENDIF

40 FORMAT(5FS.2,F .O,F4.0,4F2.0,F4.0,FS.2,
*SFS.2,/,F5.0,F4.0,4F2.0,F4.0,
*FS.2,3F5.2,FS.O,F4.0,4F2.0,F5.2,2x,412)

CWWWﬁﬁm*ﬂﬂ***********ﬂ*ﬂ******~k*

C CALCULATION OF UTILITY

UTIAp-O.55-2.795*VHA-.OO9*TTCTA+.53*RINHHA
*+.416*QUAL3+.43*QUAL11+3.3*DUR

cummmmwm*m**m**************m******

UTIB-7.69-.426*VHB-.OO9*TTCAB-1.65*RINHHA
*+.416*QUAL1+.43*QUAL9

c***********************************************************************

UTIC--.426*VHC-.OO9*TTCAC
*+.416*QUAL2+.43*QUAL10

c**mmmum*m*mmﬁ****m**ﬁwm********************~k*

C WRITE (9,*)VHA,TTCTA,RINHHA,QUAL3,QUALll

PROBA-0.0

PROBE-0.0

PROBT-0.0

PROBc-0.0

SUMT-0.0

C CALCULATION OF LOG SUM

ROSAFEXP<UTIA)

ROSB-EXP(UTIB)

ROSC-EXP(UTIC)

C CALCULATION OF PROBABILITIES

SUMT-SUMT+ROSA+ROSB+ROSC

C WRITE (9,*)ICO,ROSA,ROSB,ROSC,SUMT

PROBA-ROSA/SUMT

PROBE-ROSB/SUMT

206

PROBC-ROSC/SUMT
P(1)-PROBA
P(2)-PROBB
P(3)-PROEC

C*****************************************************************

PMAX-AMAX1(P(1),P(2),P(3))

C*****************************************************************
C*****************************************************************

C

C

C
313

900

316

315

CH

600

610

615
630

Exp x
WRITE(9,313) (U...LL-1,NT)
PORMAT<1HO,27X,1018/)
DO 900 IRK-1,NT
INDEX(IRK)-0 '
IF(P(LPK).EQ.PMAX)QC(LPK)-QC(LPK)+1.
WRITE (9,*)QC(LPK),P(LPK)
DO 316 LL-1,NT
IF(PMAX.EQ.P(LL))IMAXPLL
CONTINUE
WRITE(9,315)ICO,LPR,IMAx,(P(LL),LL-1,NT)
FORMAT(3X,I4,3X,IZ,6X,IZ,9X,10F8.4)
P(1)-o.
P(2)-0.
P(3)-o.
P(4)-0.
P(5)-o.
P(6)-O.
P(7)-o.
P(8)-O.
P(9)-o.
P(10)-o.o
CONTINUE
OUTPUT 0F PREDICTION RATIO
SUM~0.0
DO 600 xp1,NT
PRED(K)-QC(K)/IND(K)
SUMPSUM+QC(K)
TOT-SUM/FLOAT(NN)
WRITE(9,610)TOT
FORMAT(//////,' RATIO OF CHOICES PREDICTED CORRECTLY-',F6.4/)
Do 615 K91,NT
WRITE(9,63O)K,IND(R),OC(R),PRED(R)
PORMAT(/,/,'ALTERNATIVE'.13, ' CHOSEN ',15, ' TIMES',/,/

CDCDCDCDCDCDCDCDCD

1,'PREDICTED CORRECTLY',F5.0,' TIMES',/,'PREDICTION RATIO - ',F6.4)

STOP
END

 

REFERENCES

 

10.

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Daganzo, C. Multinomial Probit: The Theory and Its Applications to Demand
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McFadden, D. The Measurements of Urban Travel Demand. Journal of
Public Economics, V613, 1974, pp. 303- 328.

McFadden, D. W. T, and K. Train. An Application of Diagnostic Tests for the
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Research Record 637. PP. 39-46. 1977

Kostyniuk, L. P. A Behavioral Coice Model for the Urban Shopping Activity.
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Hensher, D.a., and LwJohnson. Applied Discrete Choice Modelling. Croom
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Hensher, D.a., and PR. Stopher. Behavioral Travel Modelling. Croom Helm,
London. 1979.

Ben-Akiva M. and SR. Lerman. Discrete Choice Analysis. MIT. Cambridge,
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Ben-Akiva, M. E. and Koppelman, F.S. Multidimensional choice models:
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Horowitz, J. Statistical Comparison of Non-Nested Probabilities Discrete
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