mmsbm: Dynamic mixed-membership stochastic blockmodel with...
In NetMix: Dynamic Mixed-Membership Network Regression Model

mmsbm

R Documentation

Dynamic mixed-membership stochastic blockmodel with covariates

Description

The function estimates a dynamic mixed-membership stochastic blockmodel that incorporates covariates.

Usage

mmsbm(
  formula.dyad,
  formula.monad = ~1,
  senderID,
  receiverID,
  nodeID = NULL,
  timeID = NULL,
  data.dyad,
  data.monad = NULL,
  n.blocks,
  n.hmmstates = 1,
  directed = TRUE,
  mmsbm.control = list()
)

Arguments

`formula.dyad`	A `formula` object. The variable in `data.dyad` that contains binary edges should be used as a LHS, and any dyadic predictors can be included on the RHS (when no dyadic covariates are available, use `y ~ 1`). Same syntax as a `glm` formula.
`formula.monad`	An optional `formula` object. LHS is ignored. RHS contains names of nodal atrributes found in `data.monad`.
`senderID`	Character string. Quoted name of the variable in `data.dyad` identifying the sender node. For undirected networks, the variable simply contains name of first node in dyad. Cannot contain special charecter "'@'".
`receiverID`	Character string. Quoted name of the variable in `data.dyad` identifying the receiver node. For undirected networks, the variable simply contains name of second node in dyad. Cannot contain special charecter "'@'".
`nodeID`	Character string. Quoted name of the variable in `data.monad` identifying a node in either `data.dyad[,senderID]` or `data.dyad[,senderID]`. If not `NULL`, every node `data.dyad[,senderID]` or `data.dyad[,senderID]` must be present in `data.monad[,nodeID]`. Cannot contain special charecter "'@'".
`timeID`	Character string. Quoted name of the variable in both `data.dyad` and `data.monad` indicating the time in which network (and correspding nodal atrributes) were observed. The variable itself must be composed of integers. Cannot contain special charecter "'@'".
`data.dyad`	Data frame. Sociomatrix in “long” (i.e. dyadic) format. Must contain at least three variables: the sender identifier (or identifier of the first node in an undirected networks dyad), the receiver identifier (or identifier of the second node in an undirected network dyad), and the value of the edge between them. Currently, only edges between zero and one (inclusive) are supported.
`data.monad`	Data frame. Nodal atributes. Must contain a node identifier matching the names of nodes used in the `data.dyad` data frame.
`n.blocks`	Integer value. How many latent groups should be used to estimate the model?
`n.hmmstates`	Integer value. How many hidden Markov state should be used in the HMM? Defaults to 1 (i.e. no HMM).
`directed`	Boolean. Is the network directed? Defaults to `TRUE`.
`mmsbm.control`	A named list of optional algorithm control parameters. seed Integer. Seed the RNG. By default, a random seed is generated and returned for reproducibility purposes. nstart Integer. Number of random initialization trials. Defaults to 5. spectral Boolean. Type of initialization algorithm for mixed-membership vectors in static case. If `TRUE` (default), use spectral clustering with degree correction; otherwise, use kmeans algorithm. init_gibbs Boolean. Should a collapsed Gibbs sampler of non-regression mmsbm be used to initialize mixed-membership vectors, instead of a spectral or simple kmeans initialization? Setting to `TRUE` will result in slower initialization and faster model estimation. When `TRUE`, results are typically very sensitive to choice of alpha (see below). alpha Numeric positive value. Concentration parameter for collapsed Gibbs sampler to find initial mixed-membership values when `init_gibbs=TRUE`. Defaults to 1.0. missing Means of handling missing data. One of "indicator method" (default) or "listwise deletion". svi Boolean; should stochastic variational inference be used? Defaults to `TRUE`. vi_iter Number of maximum iterations in stochastic variational updates. Defaults to 5e2. batch_size When `svi=TRUE`, proportion of nodes sampled in each local. Defaults to 0.05 when `svi=TRUE`, and to 1.0 otherwise. forget_rate When `svi=TRUE`, value between (0.5,1], controlling speed of decay of weight of prior parameter values in global steps. Defaults to 0.75 when `svi=TRUE`, and to 0.0 otherwise. delay When `svi=TRUE`, non-negative value controlling weight of past iterations in global steps. Defaults to 1.0 when `svi=TRUE`, and ignored otherwise. opt_iter Number of maximum iterations of BFGS in global step. Defaults to 10e3. hessian Boolean indicating whether the Hessian matrix of regression coefficients should e returned. Defaults to `TRUE`. assortative Boolean indicating whether blockmodel should be assortative (i.e. stronger connections within groups) or disassortative (i.e. stronger connections between groups). Defaults to `TRUE`. mu_block Numeric vector with two elements: prior mean of blockmodel's main diagonal elements, and and prior mean of blockmodel's offdiagonal elements. Defaults to `c(5.0, -5.0)` if `assortative=TRUE` (default) and to `c(-5.0, 5.0)` otherwise. var_block Numeric vector with two positive elements: prior variance of blockmodel's main diagonal elements, and and prior variance of blockmodel's offdiagonal elements. Defaults to `c(5.0, 5.0)`. mu_beta Either single numeric value, in which case the same prior mean is applied to all monadic coefficients, or an array that is `npredictors` by `n.blocks` by `n.hmmstates`, where `npredictors` is the number of monadic predictors for which a prior mean is being set (prior means need not be set for all) predictors). The rows in the array should be named to identify which variables a prior mean is being set for. Defaults to a common prior mean of 0.0 for all monadic coefficients. var_beta See `mu_beta`. Defaults to a single common prior variance of 5.0 for all (standardized) monadic coefficients. mu_gamma Either a single numeric value, in which case the same prior mean is applied to all dyadic coefficients, or a named vector of numeric values (with names corresponding to the name of the variable for which a prior mean is being set). Defaults to a common prior mean of 0.0 for all dyadic coefficients. var_gamma See `mu_gamma`. Defaults to a single common prior variance of 5.0 for all (standardized) dyadic coefficients. eta Numeric positive value. Concentration hyper-parameter for HMM. Defaults to 1.0. se_sim Number of samples from variational posterior of latent variables on which approximation to variance-covariance matrices are based. Defaults to 10. dyad_vcov_samp Maximum number of dyads to sample in computation of variance-covariance of dyadic and blockmodel parameters, when compared to ten percent of the observed dyads. Defaults to 1000. fixed_mm Optional character vector, with `"nodeID@timeID"` as elements, indicating which mixed-membership vectors should remain constant at their initial values throughout estimation. When only one year is observed, elements should be `"nodeID@1"`. Typically used with `mm_init_t`. mm_init_t Matrix, `n.blocks` by nodes across years. Optional initial values for mixed-membership vectors. Although initial values need not be provided for all nodes, column names must have a `nodeID@timeID` format to avoid ambiguity. When only one year is observed, names should be `"nodeID@1"`. kappa_init_t Matrix, `n.hmmstates` by number of years. Optional initial values for variational parameters for state probabilities. Columns must be named according to unique year values. b_init_t Matrix, `n.blocks` by `n.blocks`. Optional initial values for blockmodel. beta_init Array, `predictors` by `n.blocks` by `n.hmmstates`. Optional initial values for monadic coefficients. If gamma_init Vector. Optional initial values for dyadic coefficients. permute Boolean. Should all permutations be tested to realign initial block models in dynamic case? If `FALSE`, realignment is done via faster graph matching algorithm, but may not be exact. Defaults to `TRUE`. conv_tol Numeric value. Absolute tolerance for VI convergence. Defaults to 1e-3. verbose Boolean. Should extra information be printed as model iterates? Defaults to FALSE.

Value

Object of class mmsbm. List with named components:

MixedMembership: Matrix of variational posterior of mean of mixed-membership vectors. nodes by n.blocks.
BlockModel: n.blocks by n.blocks matrix of estimated tie log-odds between members of corresponding latent groups. The blockmodel.
vcov_blockmodel: If hessian=TRUE, variance-covariance matrix of parameters in blockmodel, ordered in column-major order.
MonadCoef: Array of estimated coefficient values for monadic covariates. Has n.blocks columns, and n.hmmstates slices.
vcov_monad: If hessian=TRUE, variance-covariance matrix of monadic coefficients.
DyadCoef: Vector estimated coefficient values for dyadic covariates.
vcov_dyad: If hessian=TRUE, variance-covariance matrix of dyadic coefficients.
TransitionKernel: Matrix of estimated HMM transition probabilities.
Kappa: Matrix of marginal probabilities of being in an HMM state at any given point in time. n.hmmstates by years (or whatever time interval networks are observed at).
LowerBound: Final LB value
lb: Vector of all LB across iterations, useful to check early convergence issues.
niter: Final number of VI iterations.
converged: Convergence indicator; zero indicates failure to converge.
NodeIndex: Order in which nodes are stored in all return objects.
monadic.data, dyadic.data: Model frames used during estimation (stripped of attributes).
forms: Values of selected formal arguments used by other methods.
seed: The value of RNG seed used during estimation.
call: Original (unevaluated) function call.

Author(s)

Santiago Olivella (olivella@unc.edu), Adeline Lo (aylo@wisc.edu), Tyler Pratt (tyler.pratt@yale.edu), Kosuke Imai (imai@harvard.edu)

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
## Setting to `hessian=TRUE` increases computation time
## but is needed if standard errors are to be computed. 
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

NetMix documentation built on Nov. 16, 2022, 5:15 p.m.