parallel_gergm: A Function to estimate a number of GERGMs in parallel, each...

Description Usage Arguments Value Examples

View source: R/parallel_gergm.R

Description

Allows the user to run multiple specifications at once in parallel. All variables (excluding formula_list, observed_network_list, covariate_data_list, network_data_list, cores and generate_plots) be be either specified as a single value or as a vector of values equal to the length of formula_list, if the user wishes to use different values for each specification.

Usage

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parallel_gergm(formula_list, observed_network_list,
  covariate_data_list = NULL, network_data_list = NULL, cores = 1,
  normalization_type = c("log", "division"), network_is_directed = TRUE,
  use_MPLE_only = FALSE, transformation_type = c("Cauchy", "LogCauchy",
  "Gaussian", "LogNormal"), estimation_method = c("Gibbs", "Metropolis"),
  maximum_number_of_lambda_updates = 10,
  maximum_number_of_theta_updates = 10,
  number_of_networks_to_simulate = 500, thin = 1, proposal_variance = 0.1,
  downweight_statistics_together = TRUE, MCMC_burnin = 100, seed = 123,
  convergence_tolerance = 0.01, MPLE_gain_factor = 0,
  acceptable_fit_p_value_threshold = 0.05, force_x_theta_updates = 1,
  force_x_lambda_updates = 1, output_directory = NULL, output_name = NULL,
  generate_plots = TRUE, verbose = TRUE,
  hyperparameter_optimization = FALSE, stop_for_degeneracy = FALSE,
  target_accept_rate = 0.25, theta_grid_optimization_list = NULL,
  beta_correlation_model = FALSE, weighted_MPLE = FALSE,
  fine_grained_pv_optimization = FALSE, parallel = FALSE,
  parallel_statistic_calculation = FALSE, cores_per_model = 1,
  use_stochastic_MH = FALSE, stochastic_MH_proportion = 0.25, ...)

Arguments

formula_list

A list of formula objects that specifies the relationship between statistics and the observed network for each gergm. See the gergm() documentation for more details.

observed_network_list

A list of observed networks (as numeric matrices to be used with each specification).

covariate_data_list

An optional list of covariate data frames (may include NULL entries if no covariates are needed in some specifications)

network_data_list

An optional list of of lists of network covariates to be included in each specification (one list per specification – may also be left NULL for some specifications). The list object corresponding to each specification must have entries for network covariates named as they appear in the corresponding equation. For example if the user specified a 'netcov(distance)' term, the corresponding list object for that specification would need a $distance entry containing the corresponding matrix object.

cores

The number of cores to be used for parallelization.

normalization_type

If only a raw_network is provided the function will automatically check to determine if all edges fall in the [0,1] interval. If edges are determined to fall outside of this interval, then a trasformation onto the interval may be specified. If "division" is selected, then the data will have a value added to them such that the minimum value is at least zero (if necessary) and then all edge values will be divided by the maximum to ensure that the maximum value is in [0,1]. If "log" is selected, then the data will have a value added to them such that the minimum value is at least zero (if necessary), then 1 will be added to all edge values before they are logged and then divided by the largest value, again ensuring that the resulting network is on [0,1]. Defaults to "log" and need not be set to NULL if providing covariates as it will be ignored.

network_is_directed

Logical specifying whether or not the observed network is directed. Default is TRUE.

use_MPLE_only

Logical specifying whether or not only the maximum pseudo likelihood estimates should be obtained. In this case, no simulations will be performed. Default is FALSE.

transformation_type

Specifies how covariates are transformed onto the raw network. When working with heavy tailed data that are not strictly positive, select "Cauchy" to transform the data using a Cauchy distribution. If data are strictly positive and heavy tailed (such as financial data) it is suggested the user select "LogCauchy" to perform a Log-Cauchy transformation of the data. For a tranformation of the data using a Gaussian distribution, select "Gaussian" and for strictly positive raw networks, select "LogNormal". The Default value is "Cauchy".

estimation_method

Simulation method for MCMC estimation. Default is "Gibbs" which will generally be faster with well behaved networks but will not allow for exponential down weighting.

maximum_number_of_lambda_updates

Maximum number of iterations of outer MCMC loop which alternately estimates transform parameters and ERGM parameters. In the case that data_transformation = NULL, this argument is ignored. Default is 10.

maximum_number_of_theta_updates

Maximum number of iterations within the MCMC inner loop which estimates the ERGM parameters. Default is 100.

number_of_networks_to_simulate

Number of simulations generated for estimation via MCMC. Default is 500.

thin

The proportion of samples that are kept from each simulation. For example, thin = 1/200 will keep every 200th network in the overall simulated sample. Default is 1.

proposal_variance

The variance specified for the Metropolis Hastings simulation method. This parameter is inversely proportional to the average acceptance rate of the M-H sampler and should be adjusted so that the average acceptance rate is approximately 0.25. Default is 0.1.

downweight_statistics_together

Logical specifying whether or not the weights should be applied inside or outside the sum. Default is TRUE and user should not select FALSE under normal circumstances.

MCMC_burnin

Number of samples from the MCMC simulation procedure that will be discarded before drawing the samples used for estimation. Default is 100.

seed

Seed used for reproducibility. Default is 123.

convergence_tolerance

Threshold designated for stopping criterion. If the difference of parameter estimates from one iteration to the next all have a p -value (under a paired t-test) greater than this value, the parameter estimates are declared to have converged. Default is 0.01.

MPLE_gain_factor

Multiplicative constant between 0 and 1 that controls how far away the initial theta estimates will be from the standard MPLEs via a one step Fisher update. In the case of strongly dependent data, it is suggested to use a value of 0.10. Default is 0.

acceptable_fit_p_value_threshold

A p-value threshold for how closely statistics of observed network conform to statistics of networks simulated from GERGM parameterized by converged final parameter estimates. Default value is 0.05.

force_x_theta_updates

Defaults to 1 where theta estimation is not allowed to converge until thetas have updated for x iterations . Useful when model is not degenerate but simulated statistics do not match observed network well when algorithm stops after first y updates.

force_x_lambda_updates

Defaults to 1 where lambda estimation is not allowed to converge until lambdas have updated for x iterations . Useful when model is not degenerate but simulated statistics do not match observed network well when algorithm stops after first y updates.

output_directory

The directory where you would like output generated by the GERGM estimation procedure to be saved (if output_name is specified). This includes, GOF, trace, and parameter estimate plots, as well as a summary of the estimation procedure and an .Rdata file containing the GERGM object returned by this function. May be left as NULL if the user would prefer all plots be printed to the graphics device.

output_name

The common name stem you would like to assign to all objects output by the gergm function. Default value of NULL will not save any output directly to .pdf files, it will be printed to the console instead. Must be a character string or NULL. For example, if "Test" is supplied as the output_name, then 4 files will be output: "Test_GOF.pdf", "Test_Parameter_Estim ates.pdf", "Test_GERGM_Object.Rdata", "Test_Estimation_Log.txt", and "Test_Trace_Plot.pdf". Must be the same length as the number of specifications or specification_i will be automatically used to distinguish between specifications.

generate_plots

Defaults to TRUE, if FALSE, then no diagnostic or parameter plots are generated.

verbose

Defaults to TRUE (providing lots of output while model is running). Can be set to FALSE if the user wishes to see less output.

hyperparameter_optimization

Logical indicating whether automatic hyperparameter optimization should be used. Defaults to FALSE. If TRUE, then the algorithm will automatically seek to find an optimal burnin and number of networks to simulate, and if using Metropolis Hasings, will attempt to select a proposal variance that leads to a acceptance rate within +-0.05 of target_accept_rate. Furthermore, if degeneracy is detected, the algorithm will attempt to adress the issue automatically. WARNING: This feature is experimental, and may greatly increase runtime. Please monitor console output!

stop_for_degeneracy

When TRUE, automatically stops estimation when degeneracy is detected, even when hyperparameter_optimization is set to TRUE. Defaults to FALSE. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

target_accept_rate

The target Metropolis Hastings acceptance rate. Defaults to 0.25

theta_grid_optimization_list

Defaults to NULL. This highly experimental feature may allow the user to address model degeneracy arising from a suboptimal theta initialization. It performs a grid search around the theta values calculated via MPLE to select a potentially improved initialization. The runtime complexity of this feature grows exponentially in the size of the grid and number of parameters – use with great care. This feature may only be used if hyperparameter_optimization = TRUE, and if a list object of the following form is provided: list(grid_steps = 2, step_size = 0.5, cores = 2, iteration_fraction = 0.5). grid_steps indicates the number of steps out the grid search will perform, step_size indicates the fraction of the MPLE theta estimate that each grid search step will change by, cores indicates the number of cores to be used for parallel optimization, and iteration_fraction indicates the fraction of the number of MCMC iterations that will be used for each grid point (should be set less than 1 to speed up optimization). In general grid_steps should be smaller the more structural parameters the user wishes to specify. For example, with 5 structural parameters (mutual, ttriads, etc.), grid_steps = 3 will result in a (2*3+1)^5 = 16807 parameter grid search. Again this feature is highly experimental and should only be used as a last resort (after playing with exponential down weighting and the MPLE_gain_factor). SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

beta_correlation_model

Defaults to FALSE. If TRUE, then the beta correlation model is estimated. A correlation network must be provided, but all covariates and undirected statistics may be supplied as normal. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

weighted_MPLE

Defaults to FALSE. Should be used whenever the user is specifying statistics with alpha down weighting. Tends to provide better initialization when downweight_statistics_together = FALSE. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

fine_grained_pv_optimization

Logical indicating whether fine grained proposal variance optimization should be used. This will often slow down proposal variance optimization, but may provide better results. Highly recommended if running a correlation model. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

parallel

Logical indicating whether the weighted MPLE objective and any other operations that can be easily parallelized should be calculated in parallel. Defaults to FALSE. If TRUE, a significant speedup in computation may be possible. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

parallel_statistic_calculation

Logical indicating whether network statistics should be calculated in parallel. This will tend to be slower for networks with les than ~30 nodes but may provide a substantial speedup for larger networks. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

cores_per_model

Numeric value defaulting to 1. Can be set to any number up to the number of threads/cores available on your machine. Will be used to speed up computations if parallel = TRUE. Note that this will be the number of croes requested by EACH model, so plan accordingly! SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

use_stochastic_MH

A logical indicating whether a stochastic approximation to the h statistics should be used under Metropolis Hastings in-between thinned samples. This may dramatically speed up estimation. Defualts to FALSE. HIGHLY EXPERIMENTAL! SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

stochastic_MH_proportion

Percentage of dyads/triads to use for approximation, defaults to 0.25. SPECIFY SINGLE VALUE, MUST BE CONSTANT ACROSS SPECIFICATIONS.

...

Optional arguments, currently unsupported.

Value

A list of gergm objects for each model specified.

Examples

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## Not run: 
set.seed(12345)
net <- matrix(runif(100,0,1),10,10)
colnames(net) <- rownames(net) <- letters[1:10]
node_level_covariates <- data.frame(Age = c(25,30,34,27,36,39,27,28,35,40),
                           Height = c(70,70,67,58,65,67,64,74,76,80),
                           Type = c("A","B","B","A","A","A","B","B","C","C"))
rownames(node_level_covariates) <- letters[1:10]
network_covariate <- net + matrix(rnorm(100,0,.5),10,10)

network_data_list <- list(network_covariate = network_covariate)

formula <- net ~ edges + sender("Age") +
  netcov("network_covariate") + nodematch("Type",base = "A")
formula2 <- net ~ edges +
  netcov("network_covariate") + nodemix("Type",base = "A")

form_list <- list(f1 = formula,
                  f2 = formula2)

testl <- parallel_gergm(formula_list = form_list,
                        observed_network_list = net,
                        covariate_data_list = node_level_covariates,
                        network_data_list = network_data_list,
                        cores = 2,
                        number_of_networks_to_simulate = 10000,
                        thin = 1/100,
                        proposal_variance = 0.1,
                        MCMC_burnin = 5000)

## End(Not run)

matthewjdenny/GERGM documentation built on May 15, 2018, 4:22 p.m.