lvm4net (version 0.3)

lca: Latent Class Analysis

Description

Latent class analysis (LCA) can be used to find groups in the sender nodes (with the condition of independence within the groups). For more details see Gollini, I. (in press) and Gollini, I., and Murphy, T. B. (2014).

Usage

lca(X, G, nstarts = 3, tol = 0.1^2, maxiter = 250)

Arguments

X

(N x M) binary incidence matrix

G

number of groups

nstarts

integer number of different starts for the EM algorithm. Default nstarts = 3.

tol

desired tolerance for convergence. Default tol = 0.1^2

maxiter

maximum number of iterations. Default maxiter = 500

Value

List containing the following information for each model fitted:

• p (G x M) matrix containing the conditional probability of observing a link to sender nodes if the receiver nodes are from group g.

• eta \(\eta_g\) is the mixing proportion for the group \(g (g = 1,..., G)\), that corresponds to the prior probability that a randomly chosen sender node is in the g-th group.

• z (N x G) matrix containing posterior probability for each sender node to belong to each group

• 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

# NOT RUN {
### Simulate Bipartite Network
set.seed(1)
X <- matrix(rbinom(4 * 12, size = 1, prob = 0.4), nrow = 12, ncol = 4)

resLCA <- lca(X, G = 2:3)
# }