TDLM (version 1.1.1)

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 (OD) 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 measures between simulated OD(s) and an observed OD. Each row corresponds to a matrix sorted according to the list (or list of lists) 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 square matrix representing the observed mobility flows.

measures

A character vector or a single character string indicating which goodness-of-fit measure(s) to compute (see Details). Available options are "CPC", "NRMSE", "KL", "CPL", "CPC_d" and "KS". If "all" is specified, all measures will be calculated.

distance

A square matrix representing the distances between locations. This is only necessary for distance-based measures.

bin_size

A numeric value indicating the size of bins used to discretize the distance distribution when computing CPC_d (default is 2 kilometers).

use_proba

A boolean indicating whether the proba matrix should be used instead of the simulated OD matrix to compute the measure(s). This is only valid for output from run_law_model() with the argument write_proba = TRUE (see Note).

check_names

A boolean indicating whether the location IDs used as matrix rownames and colnames should be checked for consistency (see Note).

Author

Maxime Lenormand ()

Details

Several goodness-of-fit measures are considered, such as the Common Part of Commuters (CPC), the Common Part of Links (CPL), and the Common Part of Commuters based on the distance (CPC_d), as described in Lenormand et al. (2016). It also includes classical metrics such as the Normalized Root Mean Square Error (NRMSE), the Kullback–Leibler divergence (KL), and the Kolmogorov-Smirnov statistic and p-value (KS). These measures are based on the observed and simulated flow distance distributions and are computed using the ks_test function from the Ecume package.

References

Lenormand M, Bassolas A, Ramasco JJ (2016) Systematic comparison of trip distribution laws and models. Journal of Transport Geography 51, 158-169.

See Also

For more details illustrated with a practical example, see the vignette: https://epivec.github.io/TDLM/articles/TDLM.html#goodness-of-fit-measures.

Associated functions: run_law(), run_model(), run_law_model().

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)