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Estimate mobility flows based on different trip distribution laws

Source: R/run_law.R
run_law.Rd

This function estimates mobility flows using different distribution laws and models. As described in Lenormand et al. (2016), the function uses a two-step approach to generate mobility flows by separating the trip distribution law (gravity or intervening opportunities) from the modeling approach used to generate the flows based on this law. This function only uses the first step to generate a probability distribution based on the different laws.

Usage

run_law(
  law = "Unif",
  mass_origin,
  mass_destination = mass_origin,
  distance = NULL,
  opportunity = NULL,
  param = NULL,
  check_names = FALSE
)

Arguments

law

A character indicating which law to use (see Details).

mass_origin

A numeric vector representing the mass at the origin (i.e. demand).

mass_destination

A numeric vector representing the mass at the destination (i.e. attractiveness).

distance

A squared matrix representing the distance between locations (see Details).

opportunity

A squared matrix representing the number of opportunities between locations (see Details). Can be easily computed with extract_opportunities().

param

A numeric vector or a single numeric value used to adjust the importance of distance or opportunity associated with the chosen law. Not necessary for the original radiation law or the uniform law (see Details).

check_names

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

Value

An object of class TDLM. An object of class TDLM. A list of list of matrice containing for each parameter value the matrix of probabilities (called proba). If length(param) = 1 or law = "Rad" or law = "Unif" only a list of matrices will be returned.

Details

We compute the matrix proba estimating the probability to observe a trip from one location to another. This probability is based on the demand (argument mass_origin) and the attractiveness (argument mass_destination). Note that the population is typically used as a surrogate for both quantities (this is why mass_destination = mass_origin by default). It also depends on the distance between locations (argument distance) OR the number of opportunities between locations (argument opportunity) depending on the chosen law. Both the effect of the distance and the number of opportunities can be adjusted with a parameter (argument param) except for the original radiation law and the uniform law.

In this package we consider eight probabilistic laws described in details in Lenormand et al. (2016). Four gravity laws (Barthelemy, 2011), three intervening opportunity laws (Schneider, 1959; Simini et al., 2012; Yang et al., 2014) and a uniform law.

  1. Gravity law with an exponential distance decay function (law = "GravExp"). The arguments mass_origin, mass_destination (optional), distance and param will be used.

  2. Normalized gravity law with an exponential distance decay function (law = "NGravExp"). The arguments mass_origin, mass_destination (optional), distance and param will be used.

  3. Gravity law with a power distance decay function (law = "GravPow"). The arguments mass_origin, mass_destination (optional), distance and param will be used.

  4. Normalized gravity law with a power distance decay function (law = "NGravPow"). The arguments mass_origin, mass_destination (optional), distance and param will be used.

  5. Schneider's intervening opportunities law (law = "Schneider"). The arguments mass_origin, mass_destination (optional), opportunity and param will be used.

  6. Radiation law (law = "Rad"). The arguments mass_origin, mass_destination (optional) and opportunity will be used.

  7. Extended radiation law (law = "RadExt"). The arguments mass_origin, mass_destination (optional), opportunity and param will be used.

  8. Uniform law (law = "Unif"). The argument mass_origin will be used to extract the number of locations.

Note

All inputs should be based on the same number of locations, sorted in the same order. It is recommended to use the location ID as matrix rownames and matrix colnames and to set check_names = TRUE to verify that everything is consistent before running this function (check_names = FALSE by default). Note that the function check_format_names() can be used to validate all inputs before running the main package's functions.

References

Barthelemy M (2011). Spatial Networks. Physics Reports 499, 1-101.

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

Schneider M (1959) Gravity models and trip distribution theory. Papers of the regional science association 5, 51-58.

Simini F, González MC, Maritan A & Barabási A (2012) A universal model for mobility and migration patterns. Nature 484, 96-100.

Yang Y, Herrera C, Eagle N & González MC (2014) Limits of Predictability in Commuting Flows in the Absence of Data for Calibration. Scientific Reports 4, 5662.

See also

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

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

Author

Maxime Lenormand (maxime.lenormand@inrae.fr)

Examples

data(mass)
data(distance)

mi <- as.numeric(mass[, 1])
mj <- mi

res <- run_law(
  law = "GravExp", mass_origin = mi, mass_destination = mj,
  distance = distance, opportunity = NULL, param = 0.01,
  check_names = FALSE
)

# print(res)