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Discrete Choice Method Time Series
Analysis Sumet Ongkittikul (????? ??????????)
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Contents

• Discrete Choice Method
• Section 1 Sat 20 Dec. 03 900 1200
• Section 2 Sun 21 Dec. 03 900 1200
• Case Study Sun 21 Dec. 03 1300 1600
• Time Series Analysis
• Section 1 Sun 28 Dec. 03 900 1200
• Section 2 Sun 28 Dec. 03 1300 1600

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Who am I?

• PhD candidate, Faculty of Social Science,
  Erasmus University Rotterdam,
• and Trainee at TNO Inro, Traffic and Transport
  Department, The Netherlands
• Education
• BEng in Civil Engineering, KMUTT
• MEng in Transportation Engineering, KMUTT
• MA in Transport Economics, ITS, University of
  Leeds
• Fields of interests (Past)
• Input-Output Analysis (Macro Economic Model)
• Freight Transport Flow Models
• Discrete Choice Model (especially in Freight
  Transport)
• Current Interests and Projects
• Relationship between Innovation and Regulatory
  Frameworks in Public Transport PhD Topic
• Future Transport Technologies (around Schipol
  Airport) Study for VW (the Dutch Ministry of
  Transport, Public Works and Water Management)
• Future of Rolling Stock Development Study for
  ProRail (the Dutch Rail Infrastructure Company)

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Discrete Choice Method

• Section 1
• Introduction to Discrete Choice Model
• Logit Model
• Introduction to the Stated Preference Method
• Section 2
• SP Experiments
• The Orthogonal SP Design
• Analysis and Interpretation
• Using the Models Forecasting and Valuing
• Case Study

Discrete Choice Method
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What is a Discrete Variable?

• Discrete Variable
• E.g. Car, People, etc.

• Continuous Variable
• E.g. GDP, Freight Rate, etc.

Introduction to Discrete Choice Model
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What is a Discrete Choice?

• Discrete Choice is more than Discrete Variable
• Discrete Variable
• 1 car lt 2 cars lt 3 cars
• Discrete Choice
• Toyota Honda Nissan
• However, we can adapt like
• Prefer (Toyota) gt Prefer (Honda) gt Prefer (Nissan)

Introduction to Discrete Choice Model
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Underlying Theory

• Discrete Choice Model based on Random Utility
  Theory (RUT) or Random Utility Maximisation (RUM)
• Assume that the decision-maker (DM) prefers an
  alternative that captures by a value, called
  utility, and the DM selects the alternative in
  the choice set with the highest utility

Introduction to Discrete Choice Model
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Utility Theory

• DCM based on the traditional microeconomic theory
  of consumer behaviour
• Rational choice and Preference Theory
• Utility (function) derived from the properties of
  things and the characteristics (Lancaster, 1966,
  1971), which are called Attributes
• Examples of Attributes
• House price, location, size, accessibility,
  etc.
• Restaurant taste, price, quantity, etc.
• Other examples ?,?,?,

Introduction to Discrete Choice Model
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Random Utility Theory

• An individual utility composes of 2 components
  observed and unobserved parts
• A decision maker, labelled n, faces a choice
  among J alternatives.
• Unj Vnj enj
• Unj is an utility of person n that choose J
• Vnj is a known component or deterministic part
• enj is an unknown component (error term)

Introduction to Discrete Choice Model
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Observed and Unobserved Parts

• Observed part
• Choice characteristics (Attributes)
• E.g. price, quality, etc.
• Individual characteristics
• Individual e.g. age, income,
• Organisation e.g. company profile
• Unobserved part
• Unobserved alternative attributes
• Unobserved individual characteristics
• Measurement errors

Introduction to Discrete Choice Model
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What is a Discrete Choice Model?

• Regression Linear Model
• Y a bX
• Y and X are Continuous Variable
• Many examples in previous section

• Discrete Choice Model
• Y a bX
• Y is Discrete Variable (Choices)
• X is Continuous Variable
• (or Discrete in case of dummy variable)
• e.g.
• Y a b(PRICE)
• Y are Pepsi or Coke

Introduction to Discrete Choice Model
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DCM compares to Regression Model

• Regression Model
• Yi ß0 ß1Xiei
• Discrete Choice Model
• Uj ß0 ß1Xj ej ß0 ß1Xj Vj
• Different is the dependent variable (Left hand
  side)
• Yi is continuous
• Ui is discrete

Introduction to Discrete Choice Model
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A Little More Complicated than Regression

• Regression
• Dependent Variable (Left hand side) is
  continuous
• So, there is a value and distribution (mean and
  variance)
• DCM
• Dependent Variable is Choice - Choose or not to
  choose
• Ex. Three Alternative (coding)
• Alt 1 0
• Alt 2 0
• Alt 3 1
• In this case, Alt 3 is chosen

Introduction to Discrete Choice Model
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Probability to Choose A Choice

• Again Ex. Three Alternative
• Alt 1 0
• Alt 2 0
• Alt 3 1
• What can we do is to model as a probability to
  choose a choice.
• For Example, there is 90 probability of a person
  n to choose Alt 3

Introduction to Discrete Choice Model
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DCM as a Probabilistic Function
The alternative with the highest utility is
chosen
Probability of choosing choice i from choice set
Cn
Introduction to Discrete Choice Model
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DCM as a Probabilistic Function

• Discrete Choice Model is a disaggregate model
• Observe individual behaviour (which choice he/she
  chooses)
• So, the model can be interpreted as the
  probability of a n person is likely to choose an
  i alternative
• Further important issue is the model base on the
  different utility between alternatives (Uin gt Ujn)

Introduction to Discrete Choice Model
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General Modelling Assumptions

• From Ben-Akiva and Bierlaire (2000)
• Decision-maker
• defining the decision-making entity and its
  characteristics
• Alternatives
• determining the options available to the
  decision-maker
• Attributes
• measuring the benefits and costs of an
  alternative to the decision-maker
• Decision rule
• describing the process used by the decision-maker
  to choose an alternative.

Introduction to Discrete Choice Model
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History of DCM

• First used in Transport Research
• Model the choice of travelling modes
• Auto
• Bus
• Underground Train
• Attributes are
• Travel time
• Travel cost
• See McFadden (2000) for more detail

Introduction to Discrete Choice Model
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Recommended Reading List

• General Theory of Discrete Choice
• Ben-Akiva Lerman (1985) Discrete choice
  analysis theory and application to travel
  demand
• Ortâuzar Willumsen (19942001) Modelling
  transport
• Others in the list
• SP Design
• Louviere, Swait, Hensher (2000) Stated choice
  methods analysis and application
• Others in the list

Introduction to Discrete Choice Model
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Discrete Choice Models

• There are several DC models are employed
• Logit model
• Multinomial Logit (2 choices or more)
• 2 choices model usually calls Binomial Logit
• Nested Logit (Nested choice structure)
• Probit model
• Other advanced models (e.g. Mixed Logit, GEV)
• The most easiest and widely used is Logit Model
  (covered in this course)

Introduction to Discrete Choice Model
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Logit Model The Definition

• Utility Function
• The Logistic Probability Unit, or the Logit
  model, was first introduced in the context of
  binary choice where the logistic distribution is
  used.
• Logit Model assumes that the error terms (ein) of
  the utility functions are independent and
  identically Gumbel distributed

Logit Model
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Model Specification

• General Specification
• where Vin is a function of zin , sn, and ß
• Jn choice set for person n
• zin attributes of alternative i ? Jn as faced
  by person n
• sn characteristics of person n
• ß parameters

Logit Model
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The Way to Estimate

• This is the most commonly used model
• Coefficients of Vi estimated by maximum
  likelihood
• Cannot regress choices (0-1) because
• Statistical problems

Logit Model
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Scaling Factor

• O is a scaling factor common to all parameter
  estimates
• It allows for the effect of the unobserved
  influences on choice
• As random error increases, then coefficients fall
  and probabilities tend to equal share
• See Wardman (1988)

Logit Model
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Model Estimation

• The estimation provides
• Coefficient estimates (includes scale O)
• t statistics and standard error
• Log-Likelihood measures
• Rho Squared goodness of fit
• Matrix of correlations of estimated coefficients
• (Will talk about this later in the estimation
  topic)

Logit Model
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Example Two Choices

• Commuters choice between Car and Bus for Trip to
  Work
• Vcar ß0Ccar ß1Tcar
• Vbus ß0Cbus ß1Tbus
• Where C is cost and T is time

Logit Model
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Example - Functions
Logit Model
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Numerical Example

• Two modes
• Car and Bus
• Time (T) and Cost (C)
• Vc 3.5 0.25Tc 0.1Cc
• Vb - 0.25Tb 0.1Cb
• Car T 25 C 140
• Bus T 50 C 50

• Vc - 16.75
• Vb - 17.50
• Pc 0.68
• Pb 0.32
• Prob. to choose Car 68
• Prob. to choose Bus 32
• Or Out of 100
• Choose Car 68
• Choose Bus 32

Logit Model
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Properties of Choice Probabilities

• Probabilities range 0 to 1
• E.g. Pc 0.30
• Probabilities sum to one over alternatives
• E.g. in previous example Pc 0.68 and Pb 0.32
• Relation between probabilities and explanatory
  variables is S-shaped
• If we add an alternative, the probability for
  other alternatives drops

Logit Model
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Logit Models in Use

• If the model assumes that the error terms are
  independent and identically Gumbel distributed
  (IID Gumbel) then that model called Logit Model
• General Logit Models are
• Multinomial Logit (MNL)
• 2 choices or more
• If there are 2 choices, also called Binomial
  Logit,
• Nested Logit
• more than 2 choices with hierarchical (nested)
  choices structure
• Other advanced e.g. Random Parameters Logit (not
  covered in this course)

Logit Model
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Some Properties of MNL

• You can see from the function, if bus or car
  attributes change, Prob. Change
• BUT, if there is another bus company enter the
  market
• Vcar ß0Ccar ß1Tcar
• Vblue bus ß0Cblue bus ß1Tblue bus
• Vred bus ß0Cred bus ß1Tred bus
• Assume they have same value
• Before red-bus enter the market
• Pc0.50 Pbus0.50
• If red-bus enter the market
• Pc0.33 Pblue bus0.33 Pred bus0.33
• What Happened??

Logit Model
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IIA Property

• Previous example is a classic Red Bus Blue Bus
  example
• In a mathematical term, the reason behind this
  problem is the IID Gumbel assumption
• The extreme simple covariance matrix, for example
  in the 3 choices Logit model (trinomial)

Logit Model
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When the IIA Problems Occur

• When alternatives are not independent
• Pepsi and Coke Independent
• Pepsi, Coke, and Fanta NOT Independent (or
  correlate)
• Why??
• What can we do?
• When there are taste variations among individuals
  in which case we require random coefficient
  models rather than mean-value models as the MNL

Logit Model
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Nested Logit Model

• To overcome the IIA property, there are several
  models were developed, we will discuss only
  Nested Logit here
• Nested Logit is a PRE-Specified structure of
  alternatives

Logit Model
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Alternative Specific Constant (ASC)

• There may be utility associated with each
  alternative which is constant
• Compare to Regression
• Y a bX a Intercept , b Slope
• In simple way, we can say that ASC is equivalent
  to a (Intercept).
• Adding the same constant to each alternative has
  no effect on choices or probabilities
• Uc k ß0Cc ß1Tc ec
• Ub k ß0Cb ß1Tb eb
• Why??

Logit Model
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ASC

• If n alternatives, n-1 ASCs are required,
  arbitrarily omit a constant for one alternative
• Example for three alternative
• Uc kc ß0Cc ß1Tc ec
• Ub kb ß0Cb ß1Tb eb
• Ur ß0Cr ß1Tr er
• If kc is positive, preference towards alternative
  1, all other things equal

Logit Model
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Properties of ASC

• Set average estimated probabilities equal to the
  actual shares in the sample
• Capture the average impact of omitted variables
• Correct for deviations from logit specification
  (e.g., failures of IIA, not going in to detail
  here).

Logit Model
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Stated Preference Method

• Choice modelling can be based on
• Actual Choices
• Hypothetical Choice
• Stated Preference (SP) experiments offer the
  decision maker hypothetical scenarios and the
  preferences expressed indicate the relative
  importance of the attributes that characterise
  the scenarios

Stated Preference Method
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Stated Choices

• SP based on trade-offs
• For example
• If offered a choice between an option which is 30
  Baht more expensive but 30 minutes quicker than
  another, the preference stated between the two
  options indicate whether the value of time is
  less than or more than 1 Baht per minute

Stated Preference Method
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SP and RP

• SP data the world as it could be
• Stated Preference (SP) data is a choice
  experiment (i.e. data that collected in a
  hypothetical basis)
• RP data the world as it is
• Revealed Preference (RP) data is a behaviour
  observed (i.e. data collected) in an actual
  market

Stated Preference Method
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Variants of SP

• Response indicates only the order of preference
• Choice
• Rating
• Ranking

Stated Preference Method
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Choice

• Respondent expresses a preference amongst two or
  more alternatives
• Typically between 9 and 12 choices offered
• Generally two bus sometimes three options offered
• Generally 4 or 5 attributes

Stated Preference Method
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Rating

• Semantic Scale
• Definitely use Sky Train
• Probably use Sky Train
• Might use either
• Probably use bus
• Definitely use bus
• Responses indicates more than a simple choice bus
  less than strength of preference

Stated Preference Method
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Ranking

• Rank a number of alternatives in order of
  preference
• Typically around 8 alternatives
• Generally 4 or 5 attributes

Stated Preference Method
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Relative Merits of Different Types of SP

• Ranking provides more information
• Ranking is more difficult
• Choice is what we want to forecast
• More reliable responses if real choice context
• Ranking dominated early applications, now choice
  far more common

Stated Preference Method
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Attractions of SP Methods

• Advantages stem primarily from the experiment
  conditions
• Reduce correlation problems
• Sufficient variation in data
• Better trade-off between variables
• Analyse new alternatives
• More data per person
• Can omit variables not interested in
• Create market where none exist

Stated Preference Method
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Check List for this Section

• What is a Discrete Choice Model?
• What are important components of DCM?
• What is Logit Model?
• How does this model working?
• What is IIA problem?
• What is the different between RP and SP?

Discrete Choice Method