Type:	Package
Title:	Mobility Network Analysis
Version:	1.1.0
Date:	2024-09-12
Description:	Implements the method to analyse weighted mobility networks or distribution networks as outlined in: Block, P., Stadtfeld, C., & Robins, G. (2022) <doi:10.1016/j.socnet.2021.08.003>. The purpose of the model is to analyse the structure of mobility, incorporating exogenous predictors pertaining to individuals and locations known from classical mobility analyses, as well as modelling emergent mobility patterns akin to structural patterns known from the statistical analysis of social networks.
Depends:	R (≥ 4.2)
License:	GPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
Imports:	snowfall (≥ 1.84-6.2), methods
RoxygenNote:	7.3.2
Suggests:	knitr, rmarkdown
NeedsCompilation:	no
Packaged:	2024-09-12 12:04:04 UTC; per
Author:	Per Block [cre, aut, cph], Christoph Stadtfeld [aut], Nico Keiser [aut], Marion Hoffman [aut]
Maintainer:	Per Block <block@soziologie.uzh.ch>
Repository:	CRAN
Date/Publication:	2024-09-12 17:00:02 UTC

MoNAn: Mobility Network Analysis

Description

Implements the method to analyse weighted mobility networks or distribution networks as outlined in: Block, P., Stadtfeld, C., & Robins, G. (2022) doi:10.1016/j.socnet.2021.08.003. The purpose of the model is to analyse the structure of mobility, incorporating exogenous predictors pertaining to individuals and locations known from classical mobility analyses, as well as modelling emergent mobility patterns akin to structural patterns known from the statistical analysis of social networks.

Author(s)

Maintainer: Per Block block@soziologie.uzh.ch (ORCID) [copyright holder]

Authors:

• Christoph Stadtfeld (ORCID)

• Nico Keiser (ORCID)

• Marion Hoffman (ORCID)

addEffect

Description

A function to add addtional effects to a moman effects object

Usage

addEffect(effectsObject, effectName, ...)

Arguments

Value

An object of type effectsList.monan

Examples

# Create effects object and add effects
myE1 <- createEffects(myState)
myE1 <- addEffect(myE1, loops)
myE1 <- addEffect(myE1, reciprocity_basic)
myE1 <- addEffect(myE1, effectName = same_covariate, attribute.index = "region")

# Or simpler
myE1 <- createEffects(myState) |>
  addEffect(loops) |>
  addEffect(reciprocity_basic) |>
  addEffect(same_covariate, attribute.index = "region")

alter_covariate

Description

Are locations higher on some attribute v more popular targets of mobility? E.g., do workers have a tendency to move to larger organisations?

Usage

alter_covariate(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  loop.contribution = TRUE,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

associativity_all_AC_covar_bin

Description

Do individuals with the same attribute tend to use the same paths and individuals with different attributes to move to different places? This statistic gives a positive contribution to all cliques of individuals with the same (binary) covariate who use the same path. It's a geometrically-weighted statistic, so the more cliques we add, the less they matter.

Usage

associativity_all_AC_covar_bin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

associativity_one_AC_covar_bin

Description

Do individuals with the same attribute tend to use the same paths and individuals with different attributes to move to different places? This statistic gives a positive contribution to all cliques of individuals with the value 1 of a binary covariate who use the same path. It's a geometrically-weighted statistic, so the more cliques we add, the less they matter.

Usage

associativity_one_AC_covar_bin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

autoCorrelationTest

Description

The autoCorrelationTest indicates the degree to which the values of the dependent variable of consecutive draws from the chain in phase 3 are correlated. Here lower values are better. Values above 0.5 are very problematic and indicate that a higher thinning is needed.

Usage

autoCorrelationTest(ans)

Arguments

Value

A number indicating the auto-correlation.

Examples

# regression diagnostics
autoCorrelationTest(myResDN)

avoiding_dissimilar_covar_bin

Description

Do individuals with different attributes to move to different places? This statistic gives a negative contribution to pairs of dissimilar individuals following the same path.

Usage

avoiding_dissimilar_covar_bin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

avoiding_dissimilar_covar_cont

Description

Do individuals with different attributes tend to move to different places? This statistic gives a contribution to all pairs of individuals who use the same path that is weighted by the absolute difference between their continuous attribute.

Usage

avoiding_dissimilar_covar_cont(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_AC

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin? The functional form of this statistic assumes that there are decreasing additional returns to more others on the same mobility path. For example, the probability to choose a mobility path that already contains 20 other individuals is hardly different from a path with 25 other individuals; however, there is a substantial difference in the comparison of paths with 2 or 7 other individuals.

Usage

concentration_AC(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_AC_dyad_covar

Description

Are bandwagon effects (concentration) particularly prevalent between locations that share characteristics as encoded in a binary dyadic covariate? E.g., do workers follow the moves of other workers mainly in case they go to organisations in the same region?

Usage

concentration_AC_dyad_covar(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_AC_resource_covar_bin

Description

Is there a bandwaggon effect in mobility, akin to the concentration_AC effect, but where people of group 1 only consider others of group 1 in their decision to move?

Usage

concentration_AC_resource_covar_bin(
  dep.var = 1,
  state,
  resource.attribute.index,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_GW

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin? The functional form of this statistic assumes that there are decreasing additional returns to more others on the same mobility path. For example, the probability to choose a mobility path that already contains 20 other individuals is hardly different from a path with 25 other individuals; however, there is a substantial difference in the comparison of paths with 2 or 7 other individuals.

Usage

concentration_GW(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_GW_dyad_covar

Description

Are bandwagon effects (concentration) particularly prevalent between locations that share characteristics as encoded in a binary dyadic covariate? E.g., do workers follow the moves of other workers mainly in case they go to organisations in the same region?

Usage

concentration_GW_dyad_covar(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_GW_resource_covar_bin

Description

Is there a bandwaggon effect in mobility, akin to the concentration_GW effect, but where people of group 1 only consider others of group 1 in their decision to move?

Usage

concentration_GW_resource_covar_bin(
  dep.var = 1,
  state,
  resource.attribute.index,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_basic

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin?

Usage

concentration_basic(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_basic_cube

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin?

Usage

concentration_basic_cube(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_basic_squared

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin?

Usage

concentration_basic_squared(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_norm

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin?

Usage

concentration_norm(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_norm_squared

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin?

Usage

concentration_norm_squared(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_prop

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin? The functional form of this statistic assumes that individuals consider the proportions of individuals (coming from the same origin) going to a certain destination, instead of the total number.

Usage

concentration_prop(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_prop_orig_cov

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin? The functional form of this statistic assumes that individuals consider the proportions of individuals (coming from the same origin) going to a certain destination, instead of the total number. This is weighted by an attribute of the origin, to model differences in concentration by origin characteristic.

Usage

concentration_prop_orig_cov(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

concentration_rankGW

Description

Is there a bandwagon effect in mobility, i.e. do mobile individuals move to locations that are the destination of many others from their origin? The functional form of this statistic assumes that there are increasing returns to choosing more populated paths but the return of using a path only depends on the ranking of this path in terms of number of people using it among all paths (and not the actual numbers of people on this path).

Usage

concentration_rankGW(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  lambda = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

createAlgorithm

Description

Specifies the algorithm used in the estimation based on characteristics of the state and the effects.

Usage

createAlgorithm(
  state,
  effects,
  multinomialProposal = FALSE,
  burnInN1 = NULL,
  thinningN1 = NULL,
  iterationsN1 = NULL,
  gainN1 = 0.1,
  burnInN2 = NULL,
  thinningN2 = NULL,
  initialIterationsN2 = 50,
  nsubN2 = 4,
  initGain = 0.6,
  burnInN3 = NULL,
  thinningN3 = NULL,
  iterationsN3 = 500,
  allowLoops = NULL
)

monanAlgorithmCreate(
  state,
  effects,
  multinomialProposal = FALSE,
  burnInN1 = NULL,
  thinningN1 = NULL,
  iterationsN1 = NULL,
  gainN1 = 0.1,
  burnInN2 = NULL,
  thinningN2 = NULL,
  initialIterationsN2 = 50,
  nsubN2 = 4,
  initGain = 0.6,
  burnInN3 = NULL,
  thinningN3 = NULL,
  iterationsN3 = 500,
  allowLoops = NULL
)

Arguments

Value

An object of class "algorithm.monan".

See Also

createProcessState(), createEffectsObject(), estimateMobilityNetwork()

Examples

# define algorithm based on state and effects characteristics
myAlg <- createAlgorithm(myState, myEffects, multinomialProposal = FALSE)

createEdgelist

Description

Creates an edgelist object, which is the standard format of the outcome to be modelled by MoNAn.

Usage

createEdgelist(el, nodeSet = NULL, nodes = NULL, edges = NULL)

monanDependent(el, nodeSet = NULL, nodes = NULL, edges = NULL)

Arguments

Value

An object of class "edgelist.monan".

See Also

createProcessState()

Examples

# create an object of class edgelist.monan
transfers <- createEdgelist(mobilityEdgelist, c("organisations", "organisations", "people"))

createEffects

Description

Generates an empty effects object to which new effects can be added consecutively

Usage

createEffects(state)

Arguments

Value

An empty effects object of class effectsList.monan

Examples

#' myE1 <- createEffects(myState)

createEffectsObject

Description

Specifies the model with endogenous and exogenous predictors. The predictors in the model are called “effects”.

Usage

createEffectsObject(effectInit, checkProcessState = NULL)

Arguments

Value

An object of class "effectsList.monan".

Examples

# create an effects object
myEffects <- createEffectsObject(
  list(
    list("loops"),
    list("reciprocity_min"),
    list("dyadic_covariate", attribute.index = "sameRegion"),
    list("alter_covariate", attribute.index = "size"),
    list("resource_covar_to_node_covar",
      attribute.index = "region",
      resource.attribute.index = "sex"
    ),
    list("loops_resource_covar", resource.attribute.index = "sex")
  )
)

createNetwork

Description

Defines a network between locations, generally to be used as a predictor in the model. NOTE: The outcome variable of the model is not defined as a network, but as an edgelist!

Usage

createNetwork(
  m,
  isSymmetric = FALSE,
  isBipartite = FALSE,
  nodeSet = NULL,
  nodes = NULL
)

dyadicCovar(
  m,
  isSymmetric = FALSE,
  isBipartite = FALSE,
  nodeSet = NULL,
  nodes = NULL
)

Arguments

Value

An object of class "network.monan".

See Also

createProcessState(), createEdgelist()

Examples

# create an object of class network.monan
sameRegion <- outer(orgRegion, orgRegion, "==") * 1
sameRegion <- createNetwork(sameRegion, nodeSet = c("organisations", "organisations"))

createNodeSet

Description

Determines and names the nodesets of individuals and locations that make up the mobility network.

Usage

createNodeSet(x = NULL, isPresent = NULL, considerWhenSampling = NULL)

monanEdges(x = NULL, isPresent = NULL, considerWhenSampling = NULL)

monanNodes(x = NULL, isPresent = NULL, considerWhenSampling = NULL)

Arguments

Value

An object of class "nodeSet.monan".

See Also

createProcessState()

Examples

# create an object of class nodeSet.monan
people <- createNodeSet(1:nrow(mobilityEdgelist))
organisations <- createNodeSet(length(orgRegion))

createNodeVariable

Description

Assigns a covariate to one nodeset, i.e., an exogenous characteristic of mobile individuals/resources or locations.

Usage

createNodeVariable(
  values,
  range = NULL,
  nodeSet = NULL,
  nodes = NULL,
  edges = NULL,
  addSame = NULL,
  addSim = NULL
)

monadicCovar(
  values,
  range = NULL,
  nodeSet = NULL,
  nodes = NULL,
  edges = NULL,
  addSame = NULL,
  addSim = NULL
)

Arguments

Value

An object of class "nodeVar.monan".

See Also

createProcessState()

Examples

# create an object of class nodeVar.monan
region <- createNodeVariable(orgRegion, nodeSet = "organisations")
size <- createNodeVariable(orgSize, nodeSet = "organisations", addSim = TRUE)
sex <- createNodeVariable(indSex, nodeSet = "people")

createProcessState

Description

Creates the "Process state", i.e., a MoNAn object that stores all information about the data that will be used in the estimation. This includes the outcome variable (edgelist), the nodesets, and all covariates.

Usage

createProcessState(elements, dependentVariable)

Arguments

Value

An object of class "processState.monan".

See Also

createEdgelist(), createNodeSet(), createNodeVariable(), createNetwork()

Examples

# Create a process state out of the mobility data objects:
# create objects (which are later combined to the process state)
transfers <- createEdgelist(mobilityEdgelist,
  nodeSet = c("organisations", "organisations", "people")
)
people <- createNodeSet(1:nrow(mobilityEdgelist))
organisations <- createNodeSet(1:length(orgRegion))
sameRegion <- outer(orgRegion, orgRegion, "==") * 1
sameRegion <- createNetwork(sameRegion,
  nodeSet = c("organisations", "organisations")
)
region <- createNodeVariable(orgRegion, nodeSet = "organisations")
size <- createNodeVariable(orgSize, nodeSet = "organisations", addSim = TRUE)
sex <- createNodeVariable(indSex, nodeSet = "people")

# combine created objects to the process state
myState <- createProcessState(list(
    transfers = transfers,
    people = people,
    organisations = organisations,
    sameRegion = sameRegion,
    region = region,
    size = size,
    sex = sex),
  dependentVariable = "transfers")

createWeightedCache

Description

Since MoNAn version 1.0.0, this function no longer exists.

Usage

createWeightedCache(processState, resourceCovariates = NULL)

Arguments

Value

Outdated.

crowding_out_prop_covar_bin

Description

Is the tendency to stay in vs. move out of a location of individuals of type non-w dependent on the proportion of individuals of type w moving into the location? This is especially geared towards modelling how some locations become more or less attractive dependent on the change in composition for particular groups. This models segregation dynamics.

Usage

crowding_out_prop_covar_bin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

dyadic_covariate

Description

Is mobility between locations predicted by the dyadic covariate u? E.g., is mobility likely between organisations that are in the same region? Note that in many cases dyadic covariates can convey the same information as the ‘same covariate’ or the ‘covariate similarity’ effects.

Usage

dyadic_covariate(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

dyadic_covariate_resource_attribute

Description

Is mobility between locations predicted by the dyadic covariate u weighted by the individual covariate w? E.g., is mobility of women more likely between organisations that are in the same region? Note that this effect can be used to also model the interaction between the ‘same covariate’/‘covariate similarity’ effect and individual attributes, since sameness and similarity between locations can be translated into dyadic covariates.

Usage

dyadic_covariate_resource_attribute(
  dep.var = 1,
  attribute.index,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

estimateMobilityNetwork

Description

The core function of the package in which the model for the analysis of mobility tables is estimated.

Usage

estimateMobilityNetwork(
  state,
  effects,
  algorithm,
  initialParameters = NULL,
  prevAns = NULL,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE,
  returnDeps = FALSE,
  fish = FALSE,
  saveAlg = TRUE,
  cache = NULL
)

estimateDistributionNetwork(
  state,
  effects,
  algorithm,
  initialParameters = NULL,
  prevAns = NULL,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE,
  returnDeps = FALSE,
  fish = FALSE,
  saveAlg = TRUE,
  cache = NULL
)

monan07(
  state,
  effects,
  algorithm,
  initialParameters = NULL,
  prevAns = NULL,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE,
  returnDeps = FALSE,
  fish = FALSE,
  saveAlg = TRUE,
  cache = NULL
)

monanEstimate(
  state,
  effects,
  algorithm,
  initialParameters = NULL,
  prevAns = NULL,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE,
  returnDeps = FALSE,
  fish = FALSE,
  saveAlg = TRUE,
  cache = NULL
)

## S3 method for class 'result.monan'
print(x, covMat = FALSE, ...)

Arguments

Value

The function estimateMobilityNetwork returns an object of class "result.monan" that contains the estimates, standard errors, and convergence statistics. Furthermore, the covariance matrix used to calculate the standard errors is included, which also shows collinearity between effects. In case returnDeps = TRUE, the simulations of Phase 3 are included, too.

The function print.result.monan prints the results from a monan estimation with three columns indicating the estimate, the standard error, and the convergence statistic.

See Also

createProcessState(), createEffectsObject(), createAlgorithm()

Examples

# estimate mobility network model

myAlg_short <- createAlgorithm(myState, myEffects, multinomialProposal = FALSE,
                               nsubN2 = 1, iterationsN3 = 100)

myResDN <- estimateMobilityNetwork(myState, myEffects, myAlg_short,
                                   initialParameters = NULL,
                                   # in case a pseudo-likelihood estimation was run, replace with
                                   # initialParameters = initEst,
                                   parallel = TRUE, cpus = 4,
                                   verbose = TRUE,
                                   returnDeps = TRUE,
                                   fish = FALSE
)

# check convergence
max(abs(myResDN$convergenceStatistics))

# view results
myResDN

myResDN

extractTraces

Description

This function shows the values of simulated statistics in Phase 3 for subsequent draws from the chain. Ideally, the plots show points randomly scattered around the red line, which indicates the statistics in the data.

Usage

extractTraces(ans, effects)

## S3 method for class 'traces.monan'
plot(x, ...)

Arguments

Value

The function extractTraces returns a list that includes (1) the observed statistics for all effects, (2) the distribution of statistics for all simulations and (3) effect names. It is recommended to use the plotting function to inspect the traces.

The function plot.traces.monan shows a scatter plot of the statistics of simulated networks from phase three of the esimtation.

See Also

createEffectsObject()

Examples

# regression diagnostics
traces <- extractTraces(myResDN, myEffects)


plot(traces)

getIndegree

Description

Calculates the weighted indegree distribution of all locations in the network. The weighted indegree is simply the column sum of the mobility table.

Usage

getIndegree(cache, dep.var, lvls, ...)

Arguments

Value

The degree distribution of simulated networks.

See Also

gofMobilityNetwork()

getMultinomialStatistics

Description

One updating step in simulating the mobility network model can be expressed as a multinomial logit model. Extracting the statistics for such a model allows a straight-forward estimation of a multinomial logit model to get initial estimates for the full mobility model, which increases the chances of model convergence in the first run of the estimation considerably.

Usage

getMultinomialStatistics(state, effects, cache = NULL)

Arguments

Value

A data frame with N * M rows (N = mobile individuals, M = number of locations) that specifies for each observation the statistics associated with moving to this location.

See Also

createProcessState(), createEffectsObject()

Examples

myStatisticsFrame <- getMultinomialStatistics(myState, myEffects)

getTieWeights

Description

Extracts the distribution of tie weights in the mobility network.

Usage

getTieWeights(cache, dep.var, lvls, ...)

Arguments

Value

The tie weight distribution of simulated networks.

See Also

gofMobilityNetwork()

gofMobilityNetwork

Description

Akin to ERGMs, goodness of fit testing is available to see whether auxiliary statistics are well captured by the model. The logic behind gof testing for network models is outlined in Hunter et al. (2008) and Lospinoso and Snijders (2019).

Usage

gofMobilityNetwork(ans, gofFunction, lvls = NULL, simulations = NULL)

gofDistributionNetwork(ans, gofFunction, lvls = NULL, simulations = NULL)

monanGOF(ans, gofFunction, lvls = NULL, simulations = NULL)

## S3 method for class 'gof.stats.monan'
plot(x, lvls, ...)

Arguments

Value

The function gofMobilityNetwork returns a list containing (1) the observed values of the auxiliary statistics and (2) a list of the simulated values of the auxiliary statistics.

The function plot.gof.stats.monan returns violin plots of the gof tests with observed values superimposed in red.

References

Hunter, D. R., Goodreau, S. M., & Handcock, M. S. (2008). Goodness of fit of social network models. Journal of the american statistical association, 103(481), 248-258.

Lospinoso, J., & Snijders, T. A. (2019). Goodness of fit for stochastic actor-oriented models. Methodological Innovations, 12(3).

See Also

getIndegree(), getTieWeights()

Examples

# goodness of fit
myGofIndegree <- gofMobilityNetwork(ans = myResDN, 
                                    gofFunction = getIndegree, 
                                    lvls = 1:100)

myGofTieWeight <- gofMobilityNetwork(ans = myResDN, 
                                     gofFunction = getTieWeights, 
                                     lvls = 1:30)


plot(myGofIndegree,  lvls = 20:70)
plot(myGofTieWeight, lvls = 1:15)

in_ties_loops

Description

Are individuals that are in locations with a large inflow more likely to stay in their current location?

Usage

in_ties_loops(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

in_weights_AC

Description

Is there a preferential attachment in the mobility network, i.e., do individuals move particularly to popular destinations? The geometrically weighted version avoids degeneracy.

Usage

in_weights_AC(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

in_weights_GW

Description

Is there a preferential attachment in the mobility network, i.e., do individuals move particularly to popular destinations? The geometrically weighted version avoids degeneracy.

Usage

in_weights_GW(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

in_weights_exponent

Description

Is there a preferential attachment in the mobility network, i.e., do individuals move particularly to popular destinations?

Usage

in_weights_exponent(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  exponent = 0.5
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

joining_similar_avoiding_dissimilar_covar_bin

Description

Do individuals with the same attribute tend to use the same paths and individuals with different attributes to move to different places? This statistic gives a positive contribution to all pairs of individuals with the same (binary) covariate who use the same path and a negative one to pairs of dissimilar individuals following the same path.

Usage

joining_similar_avoiding_dissimilar_covar_bin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

joining_similar_avoiding_dissimilar_covar_cont

Description

Do individuals with the same attribute tend to use the same paths and individuals with different attributes to move to different places? This statistic gives a contribution to all pairs of individuals who use the same path that is weighted by the similarity between their continuous attribute. This similarity weight is measured as the range of the attribute, minus twice the absolute difference between their covariates, normalized by the range (the weight of a pair is equal to 1 if both individuals have the same attribute, and -1 if the absolute difference between their attributes is equal to the range).

Usage

joining_similar_avoiding_dissimilar_covar_cont(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops

Description

Do individuals stay in their location of origin, compared to going to a different location?

Usage

loops(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_AC

Description

Do individuals stay in their current location, in case many other from their current location also stay? This effect tests whether the ‘benefit’ of staying in the origin location depends on the number of others also staying. Note that this effect should be modelled alongside the loops effect.

Usage

loops_AC(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_GW

Description

Do individuals stay in their current location, in case many other from their current location also stay? This effect tests whether the ‘benefit’ of staying in the origin location depends on the number of others also staying. Note that this effect should be modelled alongside the loops effect.

Usage

loops_GW(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_additional_origin

Description

This effect models loops for cases in which individuals have more than one origin. The additional origin not specified in the mobility data is included as a resource.attribute.index. The question modeled is: Do individuals stay in the additional location of origin, compared to going to a different location?

Usage

loops_additional_origin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_node_covar

Description

Are locations with specific attributes ‘stickier’ than others, i.e., do individuals have a higher propensity to stay in some locations? E.g., are individuals working in organisations in one region less likely to change their employer?

Usage

loops_node_covar(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_resource_covar

Description

Are individuals with certain characteristics more likely to remain in their current location? For example, are men more likely to remain in their current organisation, while women are more likely to move employer?

Usage

loops_resource_covar(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_resource_covar_node_covar

Description

This is an interaction of the previous two effects: Do individuals with certain characteristics have a tendency to stay in locations of certain types? Note that this effect should be included alongside the main effects of ‘loops by individual covariate’ and ‘loops by location covariate’.

Usage

loops_resource_covar_node_covar(
  dep.var = 1,
  resource.attribute.index,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

loops_x_loops_additional_origin

Description

This effect is specified for cases in which individuals have more than one origin. The additional origin not specified in the mobility data is included as a resource.attribute.index. The question modeled is: Do individuals stay in the additional location of origin if this is additionally their origin as specified in the mobility data, compared to going to a different location?

Usage

loops_x_loops_additional_origin(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

Example Data for the MoNAn Package

Description

These are example data for the MoNAn package and can be used to estimate a mobility network. The raw example data is synthetic (i.e., made up). This fictitious example contains 17 organisations representing a labour market that are located in two regions (north and south). 742 workers are employed in these organisations at two time-points. Some are mobile while others work in the same organisation at both time-points. The following objects are provided for this purpose:

mobilityEdgelist

The data frame indicates the origin at time 1 (first column) and the destination at time 2 (second column) for each of the 742 individuals between the 17 organisations. Note that some workers stay in their organisation, i.e. their origin equals their destination.

orgRegion

Categorical characteristic describing whether the organisation is located on the northern (1) or southern (0) region.

orgSize

Continuous measure representing the size of each organisation based on assets and revenue.

indSex

Individual-level characteristics representing sex.

Format

mobilityEdgelist A data frame with 742 rows and 2 columns.

orgRegion An object with 17 values.

orgSize An object with 17 values.

indSex An object with 742 values.

monanDataCreate

Description

A function to create a moman process state, i.e., a MoNAn object that stores all information about the data that will be used in the estimation. This includes the outcome variable (edgelist), the nodesets, and all covariates.

Usage

monanDataCreate(...)

Arguments

Value

An object of class "processState.monan".

Examples

#' # create objects (which are later combined to the process state)
transfers <- createEdgelist(mobilityEdgelist,
  nodeSet = c("organisations", "organisations", "people")
)
people <- createNodeSet(1:nrow(mobilityEdgelist))
organisations <- createNodeSet(1:length(orgRegion))
sameRegion <- outer(orgRegion, orgRegion, "==") * 1
sameRegion <- createNetwork(sameRegion,
  nodeSet = c("organisations", "organisations")
)
region <- createNodeVariable(orgRegion, nodeSet = "organisations")
size <- createNodeVariable(orgSize, nodeSet = "organisations", addSim = TRUE)
sex <- createNodeVariable(indSex, nodeSet = "people")

monanDataCreate(transfers, people, organisations, 
                sameRegion, region, size, sex)

Exemplary Outcome Objects for the MoNAn Package

Description

These are exemplary outcome objects for the MoNAn package and can be used in order not to run all precedent functions and thus save time. The following products are provided:

Format

myState An object of class "processState.monan" created by the function createProcessState().

myEffects An object of class "effectsList.monan" created by the function createEffectsObject() or createEffects().

myAlg An object of class "algorithm.monan" created by the function createAlgorithm().

myResDN An object of class "result.monan" created by the function estimateMobilityNetwork().

mySimDN An object of class "sims.monan" created by the function simulateMobilityNetworks().

present_relations

Description

Do individuals move along many or few paths out of their origin? This models whether individuals have a tendency against being the only one moving to a particular destination from their origin.

Usage

present_relations(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

print.effectsList.monan

Description

print.effectsList.monan

Usage

## S3 method for class 'effectsList.monan'
print(x, ...)

Arguments

Value

The function print.effectsList.monan gives an overview of the specified effects.

Examples

myEffects

print.processState.monan

Description

print.processState.monan

Usage

## S3 method for class 'processState.monan'
print(x, ...)

Arguments

Value

The function print.processState.monan gives an overview of the information included in the state object.

Examples

myState

reciprocity_AC

Description

Do individuals move to destinations that send many individuals to ego’s origin? The number of incoming individuals has decreasing returns, that is, every additionally incoming individual influences ego’s choice less.

Usage

reciprocity_AC(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_AC_dyad_covar

Description

Is reciprocity in mobility particularly prevalent between locations weighted by a dyadic covariate? E.g., do workers move to organisations similar in some way to ego’s origin?

Usage

reciprocity_AC_dyad_covar(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_AC_dyad_covar_bin

Description

Is reciprocity in mobility particularly prevalent between locations that share characteristics as encoded in a binary dyadic covariate? E.g., do workers move to organisations in the same region that send more workers to ego’s origin?

Usage

reciprocity_AC_dyad_covar_bin(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_GW

Description

Do individuals move to destinations that send many individuals to ego’s origin? The number of incoming individuals has decreasing returns, that is, every additionally incoming individual influences ego’s choice less.

Usage

reciprocity_GW(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_GW_dyad_covar

Description

Is reciprocity in mobility particularly prevalent between locations weighted by a dyadic covariate? E.g., do workers move to organisations similar in some way to ego’s origin?

Usage

reciprocity_GW_dyad_covar(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_GW_dyad_covar_bin

Description

Is reciprocity in mobility particularly prevalent between locations that share characteristics as encoded in a binary dyadic covariate? E.g., do workers move to organisations in the same region that send more workers to ego’s origin?

Usage

reciprocity_GW_dyad_covar_bin(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 2
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_basic

Description

Do individuals move to destinations dependent on the number of individuals that move to ego’s origin from that destination?

Usage

reciprocity_basic(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_min

Description

Do individuals move to destinations that send more individuals to ego’s origin? This version of the effect is the minimum of the moves in either direction, thereby guarding against degeneracy and guaranteeing sample size consistency. It counts the ‘raw’ number of reciprocated transitions in the mobility network.

Usage

reciprocity_min(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_min_dyad_covar

Description

Do individuals move to destinations that send more individuals to ego’s origin? This is weighted by a dydic covariate. This version of the effect is the minimum of the moves in either direction, thereby guarding against degeneracy and guaranteeing sample size consistency. It counts the ‘raw’ number of reciprocated transitions in the mobility network.

Usage

reciprocity_min_dyad_covar(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

reciprocity_min_resource_covar

Description

Do people reciprocate moves to other locations specifically if they and others have a higher value on some covariate? For example, do women move to organisations that send women to their origin organisation?

Usage

reciprocity_min_resource_covar(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

resource_covar_to_node_covar

Description

Do individuals with some individual attribute w tend to move to locations with some location characteristic v? E.g., do women move to larger organisations than men?

Usage

resource_covar_to_node_covar(
  dep.var = 1,
  resource.attribute.index,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  loop.contribution = FALSE,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

same_covariate

Description

Is mobility more likely between locations that are identical on some attribute v? E.g., is mobility more likely between organisations that are located in the same region?

Usage

same_covariate(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

scoreTest

Description

Based on an estimated model, a score-type test is available that shows whether statistics representing non-included effects are well represented. If this is not the case, it is likely that including them will result in significant estimates.

Usage

scoreTest(ans, effects)

## S3 method for class 'scoretest.monan'
print(x, ...)

Arguments

Value

The function scoreTest returns basic values to calculate parametric and non-parametric p-values for each tested effect.

The function print.scoretest.monan shows parametric and non-parametric p-values for each tested effect.

See Also

createEffectsObject()

Examples

# test whether other effects should be included
myEffects2 <- createEffects(myState) |>
  addEffect(transitivity_min)

test_ME.2 <- scoreTest(myResDN, myEffects2)


test_ME.2

sim_covariate

Description

Is mobility more likely between locations that are similar on some attribute v? E.g., is mobility more likely between organisations that have a similar size?

Usage

sim_covariate(
  dep.var = 1,
  attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

simulateMobilityNetworks

Description

Simulates mobility networks for given data, effects, and parameters. This function is mainly interesting to explore the behavior of the model or to do counter-factual simulations.

Usage

simulateMobilityNetworks(
  state,
  effects,
  parameters,
  allowLoops,
  burnin,
  thinning,
  nSimulations,
  cache = NULL
)

simulateDistributionNetworks(
  state,
  effects,
  parameters,
  allowLoops,
  burnin,
  thinning,
  nSimulations,
  cache = NULL
)

monanSimulate(
  state,
  effects,
  parameters,
  allowLoops,
  burnin,
  thinning,
  nSimulations,
  cache = NULL
)

Arguments

Value

An object of class "sims.monan" with nSimulations entries, where each entry contains a further list with the state and the cache of the current simulation stored.

Examples

# simulate a mobility network
# note that thinning and burn-in values are for this example only
# in real cases, choose values aprrox. times 10
mySimDN <- simulateMobilityNetworks(
  myState,
  myEffects,
  parameters = c(2, 1, 1.5, 0.1, -1, -0.5),
  allowLoops = TRUE,
  burnin = 450,
  thinning = 150,
  nSimulations = 10
)

mySimDN[[1]]

staying_by_prop_bin_inflow

Description

Is the tendency to stay in vs. move out of a location dependent on the proportion of individuals of type w that enter the location? This is especially geared towards modelling how some locations become more or less attractive dependent on the change in composition.

Usage

staying_by_prop_bin_inflow(
  dep.var = 1,
  resource.attribute.index,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

target_change_match

Description

Function to test effects

Usage

target_change_match(edge, j_new, effectName, ...)

Arguments

Details

Tests for specific resources and new proposed destination whether the change statistic and the difference between two target statistics before and after change match

Value

a vector containing (the change stat),(the target stat before change) (the target stat after change),(whether this matches exactly), (whether it matches rounded)

test_effect Test for each person in the example data and one randomly selected alternative destination whether change and target statistics match.

Description

test_effect

Test for each person in the example data and one randomly selected alternative destination whether change and target statistics match.

Usage

test_effect(effectName, ...)

Arguments

Value

A data frame containing for each person in the example data: Origin; Destination; Suggested destination; Change statistic; Target before change; Target after change; Whether this is an exact match; Whether this is a match rounded to 8 digits. In case the last column contains values that are not all "1", the tested function does not work properly.

Examples

test_loop <- test_effect("loops")

transitivity_AC

Description

Is mobility clustered in groups? This is represented by the count of transitive triads among three nodes, where the number of two-paths is geometrically weighted down to avoid degeneracy.

Usage

transitivity_AC(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 1.1
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

transitivity_GW

Description

Is mobility clustered in groups? This is represented by the count of transitive triads among three nodes, where the number of two-paths is geometrically weighted down to avoid degeneracy.

Usage

transitivity_GW(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE,
  alpha = 1.1
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

transitivity_basic

Description

Is mobility clustered in groups? This is represented by the count of transitive triads among three nodes. This effect is prone to degeneracy.

Usage

transitivity_basic(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

transitivity_min

Description

Is mobility clustered in groups? This is represented by the minimum of reciprocated mobility being present among three nodes. Using the minimum ensures that the effect is not degenerate and it is sample size consistent.

Usage

transitivity_min(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

transitivity_netflow

Description

Do individuals move in one direction in locally ordered triads? E.g., is there a local hierarchy that individuals follow when moving between locations? The effect is sample size consistent.

Usage

transitivity_netflow(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

triad120C

Description

Models the prevalence of the 120C triad

Usage

triad120C(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

triad120D

Description

Models the prevalence of the 120D triad

Usage

triad120D(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.

triad120U

Description

Models the prevalence of the 120U triad

Usage

triad120U(
  dep.var = 1,
  state,
  cache,
  i,
  j,
  edge,
  update,
  getTargetContribution = FALSE
)

Arguments

Value

Returns the change statistic or target statistic of the effect for internal use by the estimation algorithm.