estimate {goldfish}

Estimate a model

Description

Estimates parameters for a dynamic network model via maximum likelihood implementing the iterative Newton-Raphson procedure as describe in Stadtfeld and Block (2017).

Usage

estimate(
  x,
  model = c("DyNAM", "REM", "DyNAMi"),
  subModel = c("choice", "rate", "choice_coordination"),
  estimationInit = NULL,
  preprocessingInit = NULL,
  preprocessingOnly = FALSE,
  envir = new.env(),
  progress = getOption("progress"),
  verbose = getOption("verbose")
)

Arguments

x

a formula that defines at the left-hand side the dependent network (see defineDependentEvents()) and at the right-hand side the effects and the variables for which the effects are expected to occur (see vignette("goldfishEffects")).

model

a character string defining the model type. Current options include "DyNAM", "DyNAMi" or "REM"

DyNAM

Dynamic Network Actor Models (Stadtfeld, Hollway and Block, 2017 and Stadtfeld and Block, 2017)

DyNAMi

Dynamic Network Actor Models for interactions (Hoffman et al., 2020)

REM

Relational Event Model (Butts, 2008)

subModel

a character string defining the submodel type. Current options include "choice", "rate" or "choice_coordination"

choice

a multinomial receiver choice model model = "DyNAM" (Stadtfeld and Block, 2017), or the general Relational event model model = "REM" (Butts, 2008). A multinomial group choice model model = "DyNAMi" (Hoffman et al., 2020)

choice_coordination

a multinomial-multinomial model for coordination ties model = "DyNAM" (Stadtfeld, Hollway and Block, 2017)

rate

A individual activity rates model model = "DyNAM" (Stadtfeld and Block, 2017). Two rate models, one for individuals joining groups and one for individuals leaving groups, jointly estimated model = "DyNAMi"(Hoffman et al., 2020)

estimationInit

a list containing lower level technical parameters for estimation. It may contain:

initialParameters

a numeric vector. It includes initial parameters of the estimation. Default is set to NULL.

fixedParameters

a numeric vector. It specifies which component of the coefficient parameters (intercept included) is fixed and the value it takes during estimation, e.g., if the vector is c(2, NA) then the first component of the parameter is fixed to 2 during the estimation process. Default is set to NULL, i.e. all parameters are estimated. Note that it must be consistent with initialParameters.

maxIterations

maximum number of iterations of the Gauss/Fisher scoring method for the estimation. Default is set to 20.

maxScoreStopCriterion

maximum absolute score criteria for successful convergence. Default value is 0.001

initialDamping

a numeric vector used to declare the initial damping factor for each parameter. It controls the size of the update step during the iterative estimation process. The default is set to 30 when the formula has windowed effects or 10 in another case, see vignette("goldfishEffects").

dampingIncreaseFactor

a numeric value. It controls the factor that increases the damping of the parameters when improvements in the estimation are found.

dampingDecreaseFactor

a numeric value. Controls the factor that decreases the damping of the parameters when no improvements in the estimation are found.

returnIntervalLogL

a logical value. Whether to keep the log-likelihood of each event from the final iteration of the Gauss/Fisher estimation method.

engine

a string indicating the estimation engine to be used. Current options include "default", "default_c", and "gather_compute". The default value is "default", it is an estimation routine implemented in pure R code. "default_c" uses a C implementation of the "default" routine. "gather_compute" uses a C implementation with a different data structure that reduces the time but it can increase the memory usage.

startTime

a numerical value or a date-time character with the same time-zone formatting as the times in event that indicates the starting time to be considered during estimation. Note: it is only use during preprocessing

endTime

a numerical value or a date-time character with the same time-zone formatting as the times in event that indicates the end time to be considered during estimation. Note: it is only use during preprocessing

opportunitiesList

a list containing for each dependent event the list of available nodes for the choice model, this list should be the same length as the dependent events list (ONLY for choice models).

preprocessingInit

a preprocessed.goldfish object computed for the current formula, allows skipping the preprocessing step.

preprocessingOnly

logical indicating whether only preprocessed statistics should be returned rather than a result.goldfish object with the estimated coefficients.

envir

an environment where formula objects and their linked objects are available.

progress

logical indicating whether should print a minimal output to the console of the progress of the preprocessing and estimation processes.

verbose

logical indicating whether should print very detailed intermediate results of the iterative Newton-Raphson procedure; slows down the routine significantly.

Details

Missing data is imputed during the preprocessing stage. For network data missing values are replaced by a zero value, it means that is assuming a not tie/event explicitly. For attributes missing values are replaced by the mean value, if missing values are presented during events updates they are replace by the mean of the attribute in that moment of time.

Value

returns an object of class() "result.goldfish" when preprocessingOnly = FALSE or a preprocessed statistics object of class "preprocessed.goldfish" when preprocessingOnly = TRUE.

An object of class "result.goldfish" is a list including:

parameters

a numeric vector with the coefficients estimates.

standardErrors

a numeric vector with the standard errors of the coefficients estimates.

logLikelihood

the log-likelihood of the estimated model

finalScore

a vector with the final score reach by the parameters during estimation.

finalInformationMatrix

a matrix with the final values of the negative Fisher information matrix. The inverse of this matrix gives the variance-covariance matrix for the parameters estimates.

convergence

a list with two elements. The first element (isConverged) is a logical value that indicates the convergence of the model. The second element (maxAbsScore) reports the final maximum absolute score in the final iteration.

nIterations

an integer with the total number of iterations performed during the estimation process.

nEvents

an integer reporting the number of events considered in the model.

names

a matrix with a description of the effects used for model fitting. It includes the name of the object used to calculate the effects and additional parameter description.

formula

a formula with the information of the model fitted.

model

a character value of the model type.

subModel

a character value of the subModel type.

rightCensored

a logical value indicating if the estimation process considered right-censored events. Only it is considered for DyNAM-rate (model = "DyNAM" and subModel = "rate") or REM (model = "REM") models, and when the model includes the intercept.

DyNAM

The actor-oriented models that the goldfish package implements have been called Dynamic Network Actor Models (DyNAMs). The model is a two-step process. In the first step, the waiting time until an actor i initiates the next relational event is modeled (model = "DyNAM" and subModel = "rate") by an exponential distribution depending on the actor activity rate. In the second step, the conditional probability of i choosing j as the event receiver is modeled (model = "DyNAM" and subModel = "choice") by a multinomial probability distribution with a linear predictor. These two-steps are assumed to be conditionally independent given the process state (Stadtfeld, 2012), due to this assumption is possible to estimate these components by different calls of the estimate function.

Waiting times

When DyNAM-rate (model = "DyNAM" and subModel = "rate") model is used to estimate the first step component of the process, or the REM model = "REM" model is used. It is important to add a time intercept to model the waiting times between events, in this way the algorithm considers the right-censored intervals in the estimation process.

In the case that the intercept is not included in the formula. The model reflects the likelihood of an event being the next in the sequence. This specification is useful for scenarios where the researcher doesn't have access to the exact interevent times. For this ordinal case the likelihood of an event is merely a multinomial probability (Butts, 2008).

References

Butts C. (2008). A Relational Event Framework for Social Action. Sociological Methodology 38 (1). doi:10.1111/j.1467-9531.2008.00203.x

Hoffman, M., Block P., Elmer T., and Stadtfeld C. (2020). A model for the dynamics of face-to-face interactions in social groups. Network Science, 8(S1), S4-S25. doi:10.1017/nws.2020.3

Stadtfeld, C. (2012). Events in Social Networks: A Stochastic Actor-oriented Framework for Dynamic Event Processes in Social Networks. KIT Scientific Publishing. doi:10.5445/KSP/1000025407

Stadtfeld, C., and Block, P. (2017). Interactions, Actors, and Time: Dynamic Network Actor Models for Relational Events. Sociological Science 4 (1), 318-52. doi:10.15195/v4.a14

Stadtfeld, C., Hollway, J., and Block, P. (2017). Dynamic Network Actor Models: Investigating Coordination Ties Through Time. Sociological Methodology 47 (1). doi:10.1177/0081175017709295

See Also

defineDependentEvents(), defineGlobalAttribute(), defineNetwork(), defineNodes(), linkEvents()

Examples

# A multinomial receiver choice model
data("Social_Evolution")
callNetwork <- defineNetwork(nodes = actors, directed = TRUE)
callNetwork <- linkEvents(
  x = callNetwork, changeEvent = calls,
  nodes = actors
)
callsDependent <- defineDependentEvents(
  events = calls, nodes = actors,
  defaultNetwork = callNetwork
)



mod01 <- estimate(callsDependent ~ inertia + recip + trans,
  model = "DyNAM", subModel = "choice",
  estimationInit = list(engine = "default_c")
)
summary(mod01)

# A individual activity rates model
mod02 <- estimate(callsDependent ~ 1 + nodeTrans + indeg + outdeg,
  model = "DyNAM", subModel = "rate",
  estimationInit = list(engine = "default_c")
)
summary(mod02)


# A multinomial-multinomial choice model for coordination ties
data("Fisheries_Treaties_6070")
states <- defineNodes(states)
states <- linkEvents(states, sovchanges, attribute = "present")
states <- linkEvents(states, regchanges, attribute = "regime")
states <- linkEvents(states, gdpchanges, attribute = "gdp")

bilatnet <- defineNetwork(bilatnet, nodes = states, directed = FALSE)
bilatnet <- linkEvents(bilatnet, bilatchanges, nodes = states)

contignet <- defineNetwork(contignet, nodes = states, directed = FALSE)
contignet <- linkEvents(contignet, contigchanges, nodes = states)

createBilat <- defineDependentEvents(
  events = bilatchanges[bilatchanges$increment == 1, ],
  nodes = states, defaultNetwork = bilatnet
)

partnerModel <- estimate(
  createBilat ~
    inertia(bilatnet) +
    indeg(bilatnet, ignoreRep = TRUE) +
    trans(bilatnet, ignoreRep = TRUE) +
    tie(contignet) +
    alter(states$regime) +
    diff(states$regime) +
    alter(states$gdp) +
    diff(states$gdp),
  model = "DyNAM", subModel = "choice_coordination",
  estimationInit = list(initialDamping = 40, maxIterations = 30)
)
summary(partnerModel)