Latent Trait Analysis

Source: R/lta.R

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).

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)