Trip Generation with Count Data Models

Trip Generation with Count Data Models Although linear regression has been a popular method for estimating trip generation models, there is a problem in that the estimated linear regression models can produce fractions of trips for a given time period. As an example with one working member would produce 1.398 peak-hour social/recreational trips during the major holiday. Because fractions of trips are

not realistic, a modeling approach that gives the probability of making a nonnegative-integer number of trips (0, 1, 2, 3, . . .) may be more appropriate. One such model is the Poisson regression, which can be formulated for trip generation (for a given trip type) as

( ) !

i iT i

i ie P T

Tλ λ−= (8.2)

where

Ti = number of vehicle-based trips of a given type (shopping or social/recreational) made in some specified time period by household i,

P(Ti) = probability of household i making exactly Ti trips (where Ti is a nonnegative integer),

e = base of the natural logarithm (e = 2.718), and

λi = Poisson parameter for household i, which is equal to household i’s expected number of vehicle-based trips in some specified time period, E [Ti].

Poisson regressions are estimated by specifying the Poisson parameter λi (the expected number of trips of a specific type made by household i over some time period). The most common relationship between explanatory variables (variables that determine the Poisson parameter) and the Poisson parameter is the log-linear relationship

i i eλ = Z (8.3)

where

B = vector of estimable coefficients,

Zi = vector of household characteristics determining trip generation, and

other terms are as defined previously.

Note that the Poisson parameter λi (the expected number of trips of a specific type made by household i over some time period) is a real number (with fractions of trips) but gives the probability of making a specified nonnegative-integer number of trips (Ti).