knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )

```
library(MLVSBM)
```

The package deals with multilevel network defined as the junction of two interaction network (adjacency matrices) linked by an affiliation relationship (affiliation matrix).

First, we're going to simulate a multilevel network with 100 individuals and 3 clusters of individuals for the lower level and 50 organizations and 3 clusters for the upper level. The inter-organizational level will have an assortative structure and will be undirected, the inter-individual's one a core-periphery structure and will be directed. Affiliation matrix will be generated by a power law and the dependency between the latent blocks of the two levels will be strong.

set.seed(123) my_mlvsbm <- MLVSBM::mlvsbm_simulate_network( n = list(I = 60, O = 40), # Number of nodes for the lower level and the upper level Q = list(I = 3, O = 3), # Number of blocks for the lower level and the upper level pi = c(.5, .3, .2), # Block proportion for the upper level, must sum to one gamma = matrix(c(.8, .1, .1, # Block proportion for the lower level, .1, .8, .1, .1, .1, .8), # each column must sum to one nrow = 3, ncol = 3, byrow = TRUE), alpha = list(I = matrix(c(.1, .1, .3, .1, .2, .5, .1, .5, .5), nrow = 3, ncol = 3, byrow = TRUE), # Connection matrix O = matrix(c(.5, .1, .1, .1, .5, .1, .1, .1, .5), nrow = 3, ncol = 3, byrow = TRUE)),# between blocks directed = list(I = TRUE, O = FALSE), # Are the upper and lower level directed or not ? affiliation = "preferential", # How the affiliation matrix is generated no_empty_org = FALSE) # May the affiliation matrix have column suming to 0

The network is stocked in an `R6`

object of type `MLVSBM`

.

Now, we are going to create a multilevel network object from 2 existing adjacency matrix and an affiliation matrix :

lower_level <- my_mlvsbm$adjacency_matrix$I # matrix of size nI x nI upper_level <- my_mlvsbm$adjacency_matrix$O # matrix of size nO x nO affiliation <- my_mlvsbm$affiliation_matrix # matrix of size nI x nO my_mlvsbm2 <- MLVSBM::mlvsbm_create_network(X = list(I = lower_level, O = upper_level), A = affiliation)

We can now infer the parameters, blocks and edge probabilities of our network by
using the `mlvlsbm_estimate_network()`

function on an `MLVSBM`

object. It will return the
best model for this network as another R6 object of type `FitMLVSBM`

.

fit <- MLVSBM::mlvsbm_estimate_network(my_mlvsbm, nb_cores = 1L)

Generic functions are provided to print, plot, extract the model parameters and predict the existence of a dyad for the fitted network.

print(fit) plot(fit, type = "matrix") coef(fit) pred <- predict(fit)

Output of the algorithm are stocked in the `MLVSBM`

and `FitMLVSBM`

objects.
The `MLVSBM`

object stocks information of the observed or simulated network and a
list of all the fitted SBM and MLVSBM models.

my_mlvsbm$ICL # A data frame of the inferred models my_fit <- my_mlvsbm$fittedmodels[[which.max(my_mlvsbm$ICL$ICL)]] # The fitted model with index the highest ICL my_mlvsbm$ICL_sbm # The ICL of the SBM my_sbm_lower <- my_mlvsbm$fittedmodels_sbm$lower[[3]] # A fitted SBM for the lower level with 3 blocks my_sbm_upper <- my_mlvsbm$fittedmodels_sbm$upper[[2]] # A fitted SBM for the upper level with 2 blocks

You can also get the parameters and the clustering of the fitted model from the
`FitMLVSBM`

object as follows:

fit$parameters # The connectivity and membership parameters of the model fit$Z # The block membership of each nodes fit$vbound # A vector of the varational bound of the VEM algorithm tau <- fit$membership # The variational parameters of the model pred <- fit$X_hat # The links predictions for each level

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