gravity: Gravity model

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

Gravity model

Description

The gravity law assumes that the number of people moving between locations is proportional to some power of the origin and destination population, and decays by distance between them following:

T_{ij} = \frac{m_i^\alpha \times n_j^\beta }{f(r_{ij})}

where, m_i represents the population at origin, n_j the population at the destination and r_{ij} the distance between them. \alpha and \beta are tuning parameters fitted to each subpopulation size, and f(r_{ij}) is a distance-dependent functional form.

Usage

gravity(theta = 0.01, alpha = 0.06, beta = 0.03, gamma = 0.01)

Arguments

theta	Model parameter with default value and the limits theta = [0, Inf].
alpha	Model parameter with default value and the limits alpha = [-Inf, Inf].
beta	Model parameter with default value and the limits alpha = [-Inf, Inf].
gamma	Model parameter with default value and the limits gamma = [-Inf, Inf].

Value

A flux model object with the gravity 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

Zipf, G.K. (1946). The P1 P2 / D hypothesis: on the intercity movement of persons. Am. Sociol. Rev., 11, 677-686. Balcan, D., Colizza, V., Gonc, B. & Hu, H. (2009). Multiscale mobility networks and the spatial. Proc. Natl. Acad. Sci. U. S. A., 106, 21484-9.

See Also

movement, originalRadiation, radiationWithSelection, uniformSelection, interveningOpportunities, gravityWithDistance

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