Estimation of Singly-Constrained Nested Spatial Interaction Models

In singly-constrained entropy models, the observed response of the system represents trade-offs between macrospatial accessibility measures from zones to facilities and more microspatial and other intrinsic attributes of attractiveness within the facilities themselves. In this paper, a two-stage nested recursive estimation procedure which separates these effects is introduced. For origin-constrained models, the first stage involves determination of conditional probabilities of zone of origin given destination, which best explain the origin-specific and spatial-interaction constraints. In the second stage, destination probabilities are estimated using Kullback's method, such as to satisfy the intrinsic destination-specific quality constraints, to minimize the divergence from residual destination-probabilities representing the quantity or choice-statistical component of attractiveness and to maintain the value of the Legendre transform of the conditional entropy evaluated from the first stage. Functional forms of the quantity component are related to the nature of the choice process, and their indices determined to minimize the Kullback information gain between the model destination-probabilities and observed destination-probabilities.