lta: Latent Trait Analysis

In lvm4net: Latent Variable Models for Networks

Description

Latent trait analysis (LTA) can be used to model the dependence in the receiver nodes by using a continuous D-dimensional latent variable. The function lta makes use of a variational inferential approach. For more details see Gollini, I. (in press) and Gollini, I., and Murphy, T. B. (2014).

Usage

lta(X, D, nstarts = 3, tol = 0.1^2, maxiter = 250, pdGH = 21)

Arguments

X	(N x M) binary incidence matrix
D	dimension of the continuous latent variable
nstarts	number of starts. Default nstarts = 3
tol	desired tolerance for convergence. Default tol = 0.1^2
maxiter	maximum number of iterations. Default maxiter = 500
pdGH	number of quadrature points for the Gauss-Hermite quadrature. Default pdGH = 21

Value

List containing the following information for each model fitted:

• b intercepts for the logistic response function

• w slopes for the logistic response function

• mu (N x D) matrix containing posterior means for the latent variable

• C list of N (D x D) matrices containing posterior variances for the latent variable

• LL log likelihood

• BIC Bayesian Information Criterion (BIC) (Schwarz (1978))

If multiple models are fitted the output contains also a table to compare the BIC for all models fitted.

References

Gollini, I. (in press) 'A mixture model approach for clustering bipartite networks', Challenges in Social Network Research Volume in the Lecture Notes in Social Networks (LNSN - Series of Springer). Preprint: https://arxiv.org/abs/1905.02659.

Gollini, I., and Murphy, T. B. (2014), 'Mixture of Latent Trait Analyzers for Model-Based Clustering of Categorical Data', Statistics and Computing, 24(4), 569-588 http://arxiv.org/abs/1301.2167.

See Also

mlta

Examples

### Simulate Bipartite Network
set.seed(1)
X <- matrix(rbinom(4 * 12, size = 1, prob = 0.4), nrow = 12, ncol = 4)

resLTA <- lta(X, D = 1:2) 

Example output

Loading required package: MASS
Loading required package: ergm
Loading required package: network
network: Classes for Relational Data
Version 1.16.1 created on 2020-10-06.
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 3.11.0, created on 2020-10-14
Copyright (c) 2020, 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, UNSW Sydney
                    Martina Morris, University of Washington
                    with contributions from
                    Li Wang
                    Kirk Li, University of Washington
                    Skye Bender-deMoll, University of Washington
                    Chad Klumb
                    Michał Bojanowski, Kozminski University
                    Ben Bolker
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()
constraint which distorted the sampled distribution somewhat. In
addition, Sampson's Monks datasets had mislabeled vertices. See the
NEWS and the documentation for more details.

NOTE: Some common term arguments pertaining to vertex attribute and
level selection have changed in 3.10.0. See terms help for more
details. Use ‘options(ergm.term=list(version="3.9.4"))’ to use old
behavior.

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