sim.gravity.duration: Simulate connectivity values using gravity model with trip...

In gilesjohnr/hmob: Tools for analyzing human mobility data

Description

This function simulates a connectivity matrix supplied model parameters in a gravitym odel formula that incorporates trip duration by using a conditional dispersal kernel (f(d_ij | λ_ij)) in the denominator. The gravity model still uses a Gamma distribution as the dispersal kernel, but this is scaled by the probability Pr(λ_ij | d_ij) according to Bayes theorem. If a vector of shape (s) and rate (r) parameters is supplied, the function will simulate route specific dispersal kernels based on the origin location (i). A null model (where all model parameters = 1) can be simulated by supplying only population sizes (N) and pairwise distances (D).

θ * ( N_i^ω_1 N_j^ω_2 / f(d_ij | λ_ij) )

Usage

sim.gravity.duration(
  N,
  D,
  theta = 1,
  omega.1 = 1,
  omega.2 = 1,
  gamma = 1,
  lambda,
  alpha = 1,
  counts = FALSE
)

Arguments

N	vector of population sizes
D	matrix of distances among all ij pairs
theta	scalar giving the proportionality constant of gravity formula (default = 1)
omega.1	scalar giving exponential scaling of origin population size (default = 1)
omega.2	scalar giving exponential scaling of destination population size (default = 1)
gamma	scalar giving the dispersal kernel paramater (default = 1)
lambda	matrix of trip duration decay parameters for each ij route
alpha	model fitting parameter for the ECDF of lambda (default = 1)
counts	logical indicating whether or not to return a count variable by scaling the connectivity matrix by origin population size (N_i) (default = FALSE)

Value

a matrix with values between 0 and 1 (if counts = FALSE) or positive integers (if counts = TRUE)

Author(s)

John Giles

See Also

Other simulation: calc.hpd(), calc.prop.inf(), calc.prop.remain(), calc.timing.magnitude(), calc.wait.time(), decay.func(), get.age.beta(), get.beta.params(), sim.TSIR.full(), sim.TSIR(), sim.combine.dual(), sim.combine(), sim.gravity(), sim.lambda(), sim.pi(), sim.rho(), sim.tau()

Other gravity: fit.gravity(), fit.prob.travel(), sim.gravity()

gilesjohnr/hmob documentation built on Aug. 8, 2020, 1:26 a.m.