`lvm4net`

: Latent Variable Models for Networks `lvm4net`

provides a range of tools for latent variable models for network data. Most of the models are implemented using a fast variational inference approach.

**Latent space models for one-mode binary networks**: the function `lsm`

implements the latent space model (LSM) introduced by Hoff et al. (2002) using a variational inference and squared Euclidian distance; the function `lsjm`

implements latent space joint model (LSJM) for multiplex networks introduced by Gollini and Murphy (2016). These models assume that each node of a network has a latent position in a latent space: the closer two nodes are in the latent space, the more likely they are connected.

**Latent variable models for binary bipartite networks**: the function `lca`

implements the latent class analysis (LCA) to find groups in the sender nodes (with the condition of independence within the groups); the function `lta`

implements the latent trait analysis (LTA) to model the dependence in the receiver nodes by using a continuous latent variable; the function `mlta`

implements the mixture of latent trait analyzers (MLTA) introduced by Gollini and Murphy (2014) and Gollini (in press) to identify groups assuming the existence of a latent trait describing the dependence structure between receiver nodes within groups of sender nodes and therefore capturing the heterogeneity of sender nodes’ behaviour within groups. `lta`

and `mlta`

use variational inference.

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: arXiv: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, arXiv:1301.2167.Gollini, I., and Murphy, T. B. (2016), “Joint Modelling of Multiple Network Views”,

*Journal of Computational and Graphical Statistics*, arXiv: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.