TDLM (version 1.0.0)

gof: Compute goodness-of-fit measures between observed and simulated OD matrices

Description

This function returns a data.frame where each row provides one or several goodness-of-fit measures between a simulated and an observed Origin-Destination matrix.

Usage

gof(
  sim,
  obs,
  measures = "all",
  distance = NULL,
  bin_size = 2,
  use_proba = FALSE,
  check_names = FALSE
)

Value

A data.frame providing one or several goodness-of-fit measure(s) between simulated OD(s) and an observed OD. Each row corresponds to a matrix sorted according to the list (or list of list) elements (names are used if provided).

Arguments

sim

an object of class TDLM (output of run_law_model(), run_law() or run_model()). A matrix or a list of matrices can also be used (see Note).

obs

a squared matrix representing the observed mobility flows.

measures

a vector of string(s) indicating which goodness-of-fit measure(s) to chose (see Details). If "all" is specified, then all measures will be calculated.

distance

a squared matrix representing the distance between locations. Only necessary for the distance-based measures.

bin_size

a numeric value indicating the size of bin used to discretize the distance distribution to compute CPC_d (2 "km" by default).

use_proba

a boolean indicating if the proba matrix should be used instead of the simulated OD matrix to compute the measure(s). Only valid for the output from run_law_model() with argument write_proba = TRUE (see Note).

check_names

a boolean indicating if the ID location are used as matrix rownames and colnames and if they should be checked (see Note).

Author

Maxime Lenormand ()

Details

With nn the number of locations, T_ijT_ij the observed flow between location ii and location jj (argument obs), T_ijT_ij a simulated flow between location ii and location jj (a matrix from argument sim), N=_i,j=1^n T_ijN=_i,j=1^n T_ij the sum of observed flows and N=_i,j=1^n T_ijT=_i,j=1^n T_ij the sum of simulated flows.

Several goodness-of-fit measures have been considered measures = c("CPC", "NRMSE", "KL", "CPL", "CPC_d", "KS"). The Common Part of Commuters Gargiulo2012,Lenormand2012,Lenormand2016TDLM,

CPC(T,T) = 2_i,j=1^n min(T_ij,T_ij)N + N CPC(T,T) = 2_i,j=1^n min(T_ij,T_ij)N + N

the Normalized Root Mean Square Error (NRMSE),

NRMSE(T,T) = _i,j=1^n (T_ij-T_ij)^2N NRMSE(T,T) = _i,j=1^n (T_ij-T_ij)^2N

the Kullback–Leibler divergence Kullback1951TDLM,

KL(T,T) = _i,j=1^n T_ijN(T_ijNNT_ij) KL(T,T) = _i,j=1^n T_ijN(T_ijNNT_ij)

the Common Part of Links (CPL) Lenormand2016TDLM,

CPL(T,T) = 2_i,j=1^n 1_T_ij>0 1_T_ij>0_i,j=1^n 1_T_ij>0 + _i,j=1^n 1_T_ij>0 CPL(T,T) = 2_i,j=1^n 1_T_ij>0 1_T_ij>0_i,j=1^n 1_T_ij>0 + _i,j=1^n 1_T_ij>0

the Common Part of Commuters based on the disance Lenormand2016TDLM, noted CPC_d. Let us consider N_kN_k (and N_kN_k) the sum of observed (and simulated) flows at a distance comprised in the bin [bin_size*k-bin_size, bin_size*k[.

CPC_d(T,T) = 2_k=1^ min(N_k,N_k)N+N CPC_d(T,T) = 2_k=1^ min(N_k,N_k)N+N

and the Kolmogorv-Smirnov statistic and p-value Massey1951TDLM , noted KS. It is based on the observed and simulated flow distance distribution and computed with the ks_test function from the Ecume package.

References

Lenormand2016TDLM

Gargiulo2012TDLM

Lenormand2012TDLM

Kullback1951TDLM

Massey1951TDLM

See Also

run_law_model() run_law() run_model() run_law_model() check_format_names()

Examples

data(mass)
data(distance)
data(od)

mi <- as.numeric(mass[, 1])
mj <- mi
Oi <- as.numeric(mass[, 2])
Dj <- as.numeric(mass[, 3])

res <- run_law_model(
  law = "GravExp", mass_origin = mi, mass_destination = mj,
  distance = distance, opportunity = NULL, param = 0.01,
  model = "DCM", nb_trips = NULL, out_trips = Oi, in_trips = Dj,
  average = FALSE, nbrep = 1, maxiter = 50, mindiff = 0.01,
  write_proba = FALSE,
  check_names = FALSE
)

gof(
  sim = res, obs = od, measures = "CPC", distance = NULL, bin_size = 2,
  use_proba = FALSE,
  check_names = FALSE
)