An R package to estimate Generalized Exponential Random Graph Models
PLEASE REPORT ANY BUGS OR ERRORS TO mdenny@psu.edu.
[08/06/16] A major update to all aspects of the package has been pushed to the public GERGM repo and will shortly be up on CRAN. Here are some highlights:
gergm() function send you updates about estimation to a designated slack channel. This is as close to having the package text message users as we could get. Useful for keeping up to date on long running models.An R package which implements the Generalized Exponential Random Graph Model (GERGM) with an extension to estimation via Metropolis Hastings. The relevant papers detailing the model can be found at the links below:
See the Requirements for using C++ code with R section in the following tutorial: Using C++ and R code Together with Rcpp. You will likely need to install either Xcode or Rtools depending on whether you are using a Mac or Windows machine before you can use the package.
The easiest way to do this is to install the package from CRAN via the standard install.packages command:
install.packages("GERGM")This will take care of some weird compilation issues that can arise, and is the best option for most people. If you want the most current development version of the package (available here), you will need to start by making sure you have Hadley Wickham's devtools package installed.
install.packages("devtools")Now we can install from Github using the following line:
devtools::install_github("matthewjdenny/GERGM")I have had success installing this way on most major operating systems with R 3.2.0+ installed, but if you do not have the latest version of R installed, or run into some install errors (please email if you do), it should work as long as you install the dependencies first with the following block of code:
install.packages( pkgs = c("BH","RcppArmadillo","ggplot2","methods",
"stringr","igraph", "plyr", "parallel", "coda", "vegan", "scales",
"RcppParallel","slackr"), dependencies = TRUE) Once the GERGM package is installed, you may access its functionality as you would any other package by calling:
library(GERGM)If all went well, check out the ?GERGM help file to see a full working example with info on how the data should look.
To use this package, first load in the network you wish to use as a (square) matrix, following the example provided below. You may then use the gergm() function to estimate a model using any combination of the following statistics: out2stars(alpha = 1), in2stars(alpha = 1), ctriads(alpha = 1), mutual(alpha = 1), ttriads(alpha = 1), absdiff(covariate = "MyCov"), sender(covariate = "MyCov"), reciever(covariate = "MyCov"), nodematch(covariate), nodemix(covariate, base = "MyBase"), netcov(network), and edges(alpha = 1, method = c("regression","endogenous")). Note that the edges term must be specified if the user wishes to include an intercept (strongly recommended). The user may select the "regression" method (default) to include an intercept in the lambda transformation of the network, or "endogenous" to include the intercept as in a traditional ERGM model. To use exponential down-weighting for any of the network level terms, simply specify a value for alpha less than 1. The (alpha = 1) term may be omitted from the structural terms if no exponential down-weighting is required. In this case, the terms may be provided as: out2stars, in2stars, ctriads, mutual, ttriads, edges.
If the network is undirected the user may only specify the following terms: twostars(alpha = 1), ttriads(alpha = 1), absdiff(covariate = "MyCov"), sender(covariate = "MyCov"), nodematch(covariate), nodemix(covariate, base = "MyBase"), netcov(network), and edges(alpha = 1, method = c("regression","endogenous")). The gergm() function will provide all of the estimation and diagnostic functionality and the parameters of this function can be queried by typing ?gergm into the R console. You may also generate diagnostic plots using a GERGM Object returned by the gergm() function by using any of the following functions: Estimate_Plot(), GOF(), Trace_Plot(). The user may also investigate the sensitivity of parameter estimates using the hysteresis() function. This function simulates large numbers of networks at parameter values around the estimated parameter values an plots the mean network density at each of these values to examine whether the model becomes degenerate due to small deviations in the parameter estimates. See the following reference for details:
The user may also predict edge values (one at a time, conditioning on the rest of the edge values, and estimated parameters), using the conditional_edge_prediction() and conditional_edge_prediction_plot() functions.
Here are two simple working examples using the gergm() function:
library(GERGM)
########################### 1. No Covariates #############################
# Preparing an unbounded network without covariates for gergm estimation #
set.seed(12345)
net <- matrix(rnorm(100,0,20),10,10)
colnames(net) <- rownames(net) <- letters[1:10]
formula <- net ~ edges(method = "endogenous") + mutual + ttriads
test <- gergm(formula,
normalization_type = "division",
network_is_directed = TRUE,
number_of_networks_to_simulate = 40000,
thin = 1/10,
proposal_variance = 0.2,
MCMC_burnin = 10000,
seed = 456,
convergence_tolerance = 0.01,
force_x_theta_update = 4)
########################### 2. Covariates #############################
# Preparing an unbounded network with covariates for gergm estimation #
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)
formula <- net ~ edges(method = "regression") + mutual + ttriads + sender("Age") +
netcov("network_covariate") + nodemix("Type",base = "A")
test <- gergm(formula,
covariate_data = node_level_covariates,
number_of_networks_to_simulate = 100000,
thin = 1/10,
proposal_variance = 0.2,
MCMC_burnin = 50000,
seed = 456,
convergence_tolerance = 0.01,
force_x_theta_update = 2)
# Generate Estimate Plot
Estimate_Plot(test)
# Generate GOF Plot
GOF(test)
# Generate Trace Plot
Trace_Plot(test)
# Generate Hysteresis plots for all structural parameter estimates
hysteresis_results <- hysteresis(test,
networks_to_simulate = 1000,
burnin = 500,
range = 2,
steps = 20,
simulation_method = "Metropolis",
proposal_variance = 0.2)
Following on from the example above, we can also predict individual edge values, conditioning on the rest of the observed edges and estimated parameters. These predictions can then be plotted as a grid of box plots for each individual edge, as in the following example code:
test2 <- conditional_edge_prediction(
GERGM_Object = test,
number_of_networks_to_simulate = 1000,
thin = 1,
proposal_variance = 0.5,
MCMC_burnin = 1000,
seed = 123)
# set working directory where we want to save the file. Only outputs a PDF
# because plotting is too slow in the graphics device.
setwd("~/Desktop")
conditional_edge_prediction_plot(edge_prediction_results = test2,
filename = "test.pdf",
plot_size = 20,
node_name_cex = 6)
# make a scatter plot of predicted vs observed edge values
conditional_edge_prediction_correlation_plot(edge_prediction_results = test2)
# set x and y limits manually
conditional_edge_prediction_correlation_plot(edge_prediction_results = test2,
xlim = c(-10,10),
ylim = c(-10,10))There is also now functionality to run multiple gergm() model specifications in parallel using the parallel_gergm() function. This can come in very handy if the user wishes to specify the same model but for a large number of networks, or multiple models for the same network. Another useful (experimental) feature that can now be turned out is hyperparameter_optimization = TRUE, which will seek to automatically optimize the number of networks simulated during MCMC, the burnin, the Metropolis Hastings proposal variance and will seek to address any issues with model degeneracy that arise during estimation by reducing exponential weights if using Metropolis Hastings. This feature is generally meant to make it easier and less time intensive to find a model that fits the data well.
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 +netcov("network_covariate") + nodematch("Type",base = "A")
formula2 <- net ~ edges + sender("Age") +
netcov("network_covariate") + nodemix("Type",base = "A")
form_list <- list(f1 = formula,
f2 = formula2)
testp <- 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 = 1/10,
proposal_variance = 0.1,
MCMC_burnin = 5000)Finally, if you specified an output_directory and output_name, you will want to check the output_directory which will contain a number of .pdf's which can aide in assessing model fit and in determining the statistical significance of theta parameter estimates.
If output_name is specified in the gergm() function, then five files will be automatically generated and saved to the output_directory. The example file names provided below are for output_name = "Test":
gergm() functionafter estimation.gergm() function.The GERGM package incorporates a number of advanced features that are designed to aid in model fitting and evaluation, and expand the applicability of the model to a wider range of networks and network statistics.
gergm() optional argumentsconvergence_tolerance parameter ( which defaults to 0.5). However, if the user suspects that the theta parameter estimates have not actually converged, despite the t-test p-values, then they can for the model to perform a certain number of theta updates. This is a particularly useful feature in helping to determine whether a specification suffers from likelihood degeneracy. The user can set the number of theta updates to be higher than the convergence_tolerance parameter threshold would suggest, and see if theta parameter estimates diverge. If they do not, this is some indication that the estimation procedure is stable. However, in general, it is advisable to leave this parameter set to its default value of 1.force_x_theta_updates parameter, but is primarily useful for improving model fit. It may be the case that the model detects convergence, but due to slight changes in the lambda parameters at their last update, model fit may be impacted. Setting a higer value for this parameter can force the model to really "settle down" before completing estimation. In general, it is advisable to leave this parameter set to its default value of 1.target_accept_rate. This adaptive metropolis step is done before the main estimation step, so it will not interfere with the usability of the MH samples we gather. The second function of this option is to attempt to automatically deal with likelihood degeneracy through the use of exponential down-weights (when using Metropolis-Hastings for estimation). If the estimation procedure detects problems with estimation (theta estimates zooming off to positive or negative infinity), the alpha weights for each of the endogenous statistics will be set to 90 percent of its current value. Decreasing these weights has been found to make it computationally easier to fit a model, however, the user is strongly encouraged to set alpha weights themselves or use the theta_grid_optimization_list option to improve initialization.theta_grid_optimization_list -- 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:
theta_grid_optimization_list = list(
grid_steps = 2,
step_size = 0.5,
cores = 2,
iteration_fraction = 0.5). alpha weights on any endogenous statistics that are less than 1. It will tend to slow down MPLE, but is optimized for parallelization, so it can take advantage of the parallel option.cores parameter. Since the operations governed by this parameter are easy to parallelize, it is possible to realize a significant speedup in their calculation, particularly when using weighted MPLE for large networks.parallel = TRUE and/or parallel_statistic_calculation = TRUE, this is the number of cores that will be allocated for parallelization. Don't set this to a number greater than the number of threads your computer can support.slackr_integration_list -- An optional list object that contains information necessary to provide updates about model fitting progress to a Slack channel (https://slack.com/) of your choosing. This can be useful if models take a long time to run, and you wish to receive updates on their progress (or if they become degenerate). Before you can get this option to work, you will need to turn on "web hook integration" for your slack channel. If you go to the Chanel Settings -> Add an app or integration pane and search for "web hook integration", you should be able to turn this option on. From there you will get an incoming webhook url that you will need to copy and save for use with the gergm() function. It is also probably advisable to create a separate channel for updates, as these may end up swamping #general. Once you have a channel and incoming webhook url, you will need to enter your information as a list argument in the gergm(). The list object must be of the following form:
slackr_integration_list = list(
model_name = "descriptive model name",
channel = "#yourchannelname",
incoming_webhook_url = "https://hooks.slack.com/services/XX/YY/ZZ")Note that the model_name is a way to distinguish multiple models that can simultaneously post information to the same slack channel if you so desire, because model_name will appear as the name of the poster on the slack channel. If all goes well, and the computer you are running the GERGM estimation on has internet access, your slack channel will receive updates when you start estimation, after each lambda/theta parameter update, if the model becomes degenerate, and when it completes running. This feature is still in development.
So far, this package has been tested successfully on OSX, CentOS 7, Ubuntu and Windows 7. Please email me at mdenny@psu.edu if you have success on another OS or run into any problems.