lsjm: Latent Space Joint Model

In lvm4net: Latent Variable Models for Networks

Description

Function to joint modelling of multiple network views using the Latent Space Jont Model (LSJM) Gollini and Murphy (2016). The LSJM merges the information given by the multiple network views by assuming that the probability of a node being connected with other nodes in each view is explained by a unique latent variable.

Usage

lsjm(Y, D, sigma = 1, xi = rep(0, length(Y)), psi2 = rep(2,
  length(Y)), Niter = 500, tol = 0.1^2, preit = 20,
  randomZ = FALSE)

Arguments

Y	list containing a (N x N) binary adjacency matrix for each network view.
D	integer dimension of the latent space
sigma	(D x D) variance/covariance matrix of the prior distribution for the latent positions. Default sigma = 1
xi	vector of means of the prior distributions of α. Default xi = 0
psi2	vector of variances of the prior distributions of α. Default psi2 = 2
Niter	maximum number of iterations. Default Niter = 500
tol	desired tolerance. Default tol = 0.1^2
preit	Preliminary number of iterations default preit = 20
randomZ	logical; If randomZ = TRUE random initialization for the latent positions is used. If randomZ = FALSE and D = 2 or 3 the latent positions are initialized using the Fruchterman-Reingold method and multidimensional scaling is used for D = 1 or D > 3. Default randomZ = FALSE

Value

List containing:

• EZ (N x D) matrix containing the posterior means of the latent positions

• VZ (D x D) matrix containing the posterior variance of the latent positions

• lsmEZ list contatining a (N x D) matrix for each network view containing the posterior means of the latent positions under each model in the latent space.

• lsmVZ list contatining a (D x D) matrix for each network view containing the posterior variance of the latent positions under each model in the latent space.

• xiT vector of means of the posterior distributions of α

• psi2T vector of variances of the posterior distributions of α

• Ell expected log-likelihood

References

Gollini, I., and Murphy, T. B. (2016), 'Joint Modelling of Multiple Network Views', Journal of Computational and Graphical Statistics, 25(1), 246-265 http://arxiv.org/abs/1301.3759.

Examples

## Simulate Undirected Network
  N <- 20
  Ndata <- 2
   Y <- list()
   Y[[1]] <- network(N, directed = FALSE)[,]
   ### create a new view that is similar to the original
   
  for(nd in 2:Ndata){
    Y[[nd]] <- Y[[nd - 1]] - sample(c(-1, 0, 1), N * N, replace = TRUE, 
   prob = c(.05, .85, .1))
    Y[[nd]] <- 1 * (Y[[nd]]  > 0 )
  diag(Y[[nd]]) <- 0
   }

par(mfrow = c(1, 2))
z <- plotY(Y[[1]], verbose = TRUE, main = 'Network 1')
plotY(Y[[2]], EZ = z, main = 'Network 2')
par(mfrow = c(1, 1))

modLSJM <- lsjm(Y, D = 2) 
plot(modLSJM, Y, drawCB = TRUE)
plot(modLSJM, Y, drawCB = TRUE, plotZtilde = TRUE)

Example output

Loading required package: MASS
Loading required package: ergm
Loading required package: network
network: Classes for Relational Data
Version 1.14-377 created on 2019-03-04.
copyright (c) 2005, Carter T. Butts, University of California-Irvine
                    Mark S. Handcock, University of California -- Los Angeles
                    David R. Hunter, Penn State University
                    Martina Morris, University of Washington
                    Skye Bender-deMoll, University of Washington
 For citation information, type citation("network").
 Type help("network-package") to get started.


ergm: version 3.9.4, created on 2018-08-15
Copyright (c) 2018, Mark S. Handcock, University of California -- Los Angeles
                    David R. Hunter, Penn State University
                    Carter T. Butts, University of California -- Irvine
                    Steven M. Goodreau, University of Washington
                    Pavel N. Krivitsky, University of Wollongong
                    Martina Morris, University of Washington
                    with contributions from
                    Li Wang
                    Kirk Li, University of Washington
                    Skye Bender-deMoll, University of Washington
Based on "statnet" project software (statnet.org).
For license and citation information see statnet.org/attribution
or type citation("ergm").

NOTE: Versions before 3.6.1 had a bug in the implementation of the bd()
constriant which distorted the sampled distribution somewhat. In
addition, Sampson's Monks datasets had mislabeled vertices. See the
NEWS and the documentation for more details.

Loading required package: ellipse

Attaching package: 'ellipse'

The following object is masked from 'package:graphics':

    pairs

lvm4net documentation built on June 13, 2019, 5:03 p.m.