lsm: Latent Space Model

In lvm4net: Latent Variable Models for Networks

Description

Latent space models (LSM) are a well known family of latent variable models for network data introduced by Hoff et al. (2002) under the basic assumption that each node has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater the probability of them being connected. Unfortunately, the posterior distribution of the LSM cannot be computed analytically. For this reason we propose a variational inferential approach which proves to be less computationally intensive than the MCMC procedure proposed in Hoff et al. (2002) (implemented in the latentnet package) and can therefore easily handle large networks. Salter-Townshend and Murphy (2013) applied variational methods to fit the LSM with the Euclidean distance in the VBLPCM package. In this package, a distance model with squared Euclidean distance is used. We follow the notation of Gollini and Murphy (2016).

Usage

lsm(Y, D, sigma = 1, xi = 0, psi2 = 2, Niter = 100, Miniter = 10,
  tol = 0.1^2, randomZ = FALSE, nstart = 1)

Arguments

Y	(N x N) binary adjacency matrix
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	mean of the prior distribution of α. Default xi = 0
psi2	variance of the prior distribution of α. Default psi2 = 2
Niter	maximum number of iterations. Default Niter = 100
Miniter	minimum number of iterations. Default Miniter = 10
tol	desired tolerance. Default tol = 0.1^2
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
nstart	number of starts

Value

List containing:

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

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

• xiT mean of the posterior distribution of α

• psi2T variance of the posterior distribution 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.

Hoff, P., Raftery, A., and Handcock, M. (2002), "Latent Space Approaches to Social Network Analysis", Journal of the American Statistical Association, 97, 1090–1098.

See Also

plot.lsm

Examples

### Simulate Undirected Network
N <- 20
Y <- network(N, directed = FALSE)[,]

modLSM <- lsm(Y, D = 2) 
plot(modLSM, Y)

Example output

Loading required package: MASS
Loading required package: ergm
Loading required package: network
network: Classes for Relational Data
Version 1.13.0.1 created on 2015-08-31.
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.