interveningOpportunities: Intervening opportunities

In SEEG-Oxford/movement: Modelling and Analysing Human Movement Data

Intervening opportunities

Description

The intervening-opportunities model (IO) assumes that the number of persons going a given distance is directly proportional to the number of opportunities at that distance and inversely proportional to the number of intervening opportunities (Stouffer 1940):

T_{ij} = \frac{N_j}{d_{ij} + N_i}

Where N_i is the population in location i, and (d_{ij} + N_j) is the population in all locations between ij. From there we apply a stochastic approach to derive a probability that a trip will terminate in location i is equal to the probability that i contains an acceptable destination and that the acceptable destination is closer to the origin i has not been found. Following Simini et al. 2012 the connectivity between i and j becomes:

T_{ij} = e^{ -\lambda (s_{ij} + N_i)^{\alpha}} - e^{ -\lambda (s_{ij} + N_i + N_j)^{\alpha}}

Where e^(-\lambda) is the probability that a single opportunity is not sufficiently attractive as destination, and \lambda and \alpha are fitting parameters.

Usage

interveningOpportunities(theta = 0.001, L = 1e-05)

Arguments

theta	Model parameter with default value and the limits theta = [0, Inf].
L	Model parameter with default value and the limits L = [0, Inf].

Value

A flux model object with the intervening opportunities flux function and a set of starting parameters.

Note

Limits 0 and Inf will be changed internally to the numerically safe approximations 0 -> sqrt(.Machine$double.eps) and Inf -> sqrt(.Machine$double.xmax), respectively.

References

Simini, F., Gonzalez, M. C., Maritan, A. & Barabasi (2012), A.-L. A universal model for mobility and migration patterns. Nature, 484, 96-100. Stouffer S. A. (1940). Intervening opportunities: a theory relating mobility and distance. Am. Sociol. Rev. 5, 845-867.

See Also

movement, originalRadiation, radiationWithSelection, uniformSelection, gravity, gravityWithDistance

SEEG-Oxford/movement documentation built on April 17, 2023, 4:17 p.m.