# Methodological Approach

Methodological Approach Following recent advances in the travel demand and traffic forecasting field, development of a model for mode/destination choice necessitates the use of some consistent theory of travelers’ decision-making processes. Of the decision- making theories available, one that is based on the microeconomic concept of utility maximization has enjoyed widespread acceptance in mode/destination choice modeling. The basic assumption is that a traveler will select the combination of mode and destination that provides the most utility. The problem then becomes one of developing an expression for the utility provided by various mode and destination alternatives. Because it is unlikely that individual travelers’ utility functions can ever be specified with certainty, the unspecifiable portion is assumed to be random. To illustrate this approach, consider a utility function of the following form:

im mk imk im k

V b z ε= + (8.4)

where

Vim = total utility (specifiable and unspecifiable) provided by mode/destination alternative m to a traveler i,

bmk = coefficient estimated from traveler survey data for mode/destination alternative m corresponding to mode/destination or traveler characteristic k,

zimk = traveler or mode/destination characteristic k (income, travel time of mode, commercial floor space at destination, etc.) for mode/destination alternative m for traveler i, and

εim = unspecifiable portion of the utility of mode/destination alternative m for traveler i, which will be assumed to be random.

For notational convenience, define the specifiable nonrandom portion of utility Vim as

im mk imk k

U b z= (8.5)

With these definitions of utility, the probability that a traveler will choose some alternative, say m, is equal to the probability that the given alternative’s utility is greater than the utility of all other possible alternatives. The probabilistic component arises from the fact that the unspecifiable portion of the utility expression is not known and is assumed to be a random variable. The basic probability statement is

[ ]ε ε= + > +probim im im is isP U U for all s m≠ (8.6)

where

Pim = probability that traveler i will select alternative m,

prob[⋅] = notation for probability,

s = notation for available alternatives, and other terms are as defined previously.

With this basic probability and utility expression and an assumed random

distribution of the unspecifiable components of utility (εim), a probabilistic choice model can be derived and the coefficients in the utility function can be estimated with data collected from traveler surveys, along the same lines as for the coefficients in the trip generation models. A popular approach to deriving such a probabilistic choice model is to assume that the random, unspecifiable component of utility is generalized extreme value distributed. With this assumption, a rather lengthy and involved derivation gives rise to the logit model formulation

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