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This vignette illustrates the use of the
estimateMultiplexSBM
function and the methods accompanying
the R6 classes multiplexSBMfit
on the war
data
set.
The packages required for the analysis are sbm plus some others for data manipulation and representation:
The war
data set comes in the sbm
package:
This data set contains a list of two networks
(belligerent
and alliance
) where the nodes are
countries; an edge in the network belligerent
means that
the two countries have been at war at least once between years 1816 to
2007; an edge in network alliance
means that the two
countries have had a formal alliance between years 1816 and 2012. The
network belligerent
have less nodes since countries which
have not been at war at all are not considered.
These two networks were extracted from https://correlatesofwar.org/ (see Sarkees and Wayman (2010) for war data, and Gibler (2008) for formal alliance). Version 4.0 was used for war data and version 4.1 for formal alliance.
Since they don’t have the same size, we choose to only consider nodes (countries) which were at war with at least one other country. This corresponds to the first 83 nodes in the Alliance network.
A <- as.matrix(get.adjacency(war$alliance))
#> This graph was created by an old(er) igraph version.
#> Call upgrade_graph() on it to use with the current igraph version
#> For now we convert it on the fly...
A <- A[1:83, 1:83]
B <- as.matrix(get.adjacency(war$belligerent))
#> This graph was created by an old(er) igraph version.
#> Call upgrade_graph() on it to use with the current igraph version
#> For now we convert it on the fly...
We can start with a plot of this multiplex network:
netA <- defineSBM(A, model = "bernoulli", dimLabels = "country")
netB <- defineSBM(B, model = "bernoulli", dimLabels = "country")
plotMyMultiplexMatrix(list(netA, netB))
We run the estimation of this multiplex model. By setting
dependent=FALSE
, we declare that we consider the two layers
to be independent conditionally on the latent block variables.
MultiplexFitIndep <- estimateMultiplexSBM(list(netA, netB), dependent = FALSE,
estimOptions = list(verbosity = 0))
We can retrieve the clustering
clust_country_indep <- MultiplexFitIndep$memberships[[1]]
sort(clust_country_indep)
#> United States of America Canada
#> 1 1
#> Belize El Salvador
#> 2 2
#> Colombia Ecuador
#> 2 2
#> Bolivia Uruguay
#> 2 2
#> Bahamas Cuba
#> 3 3
#> Haiti Dominican Republic
#> 3 3
#> Jamaica Trinidad and Tobago
#> 3 3
#> Barbados Dominica
#> 3 3
#> Grenada St. Lucia
#> 3 3
#> St. Vincent and the Grenadines Antigua & Barbuda
#> 3 3
#> St. Kitts and Nevis Mexico
#> 3 3
#> Guatemala Honduras
#> 3 3
#> Nicaragua Costa Rica
#> 3 3
#> Panama Venezuela
#> 3 3
#> Guyana Suriname
#> 3 3
#> Peru Brazil
#> 3 3
#> Paraguay Chile
#> 3 3
#> Argentina United Kingdom
#> 3 4
#> Netherlands Belgium
#> 4 4
#> Luxembourg France
#> 4 4
#> Spain Portugal
#> 4 4
#> Germany German Federal Republic
#> 4 4
#> Poland Hungary
#> 4 4
#> Czech Republic Italy
#> 4 4
#> Greece Norway
#> 4 4
#> Denmark Iceland
#> 4 4
#> Bavaria German Democratic Republic
#> 5 5
#> Baden Wuerttemburg
#> 5 5
#> Austria-Hungary Austria
#> 5 5
#> Czechoslovakia Slovakia
#> 5 5
#> Malta Albania
#> 5 5
#> Croatia Yugoslavia
#> 5 5
#> Bosnia and Herzegovina Cyprus
#> 5 5
#> Bulgaria Moldova
#> 5 5
#> Romania Russia
#> 5 5
#> Estonia Latvia
#> 5 5
#> Lithuania Ukraine
#> 5 5
#> Belarus Armenia
#> 5 5
#> Georgia Azerbaijan
#> 5 5
#> Finland Sweden
#> 5 5
#> Cape Verde Sao Tome and Principe
#> 5 5
#> Guinea-Bissau
#> 5
And we can plot the reorganized adjacency matrices or the corresponding expectations:
Now we assume that the two layers are dependent conditionally to the
latent block variables. We then set dependent = TRUE
MultiplexFitdep <- estimateMultiplexSBM(list(netA, netB), dependent = TRUE,
estimOptions = list(verbosity = 0))
We can retrieve the clustering and compare it to the one obtained in the independent case.
clust_country_dep <- MultiplexFitdep$memberships[[1]]
sort(clust_country_indep)
#> United States of America Canada
#> 1 1
#> Belize El Salvador
#> 2 2
#> Colombia Ecuador
#> 2 2
#> Bolivia Uruguay
#> 2 2
#> Bahamas Cuba
#> 3 3
#> Haiti Dominican Republic
#> 3 3
#> Jamaica Trinidad and Tobago
#> 3 3
#> Barbados Dominica
#> 3 3
#> Grenada St. Lucia
#> 3 3
#> St. Vincent and the Grenadines Antigua & Barbuda
#> 3 3
#> St. Kitts and Nevis Mexico
#> 3 3
#> Guatemala Honduras
#> 3 3
#> Nicaragua Costa Rica
#> 3 3
#> Panama Venezuela
#> 3 3
#> Guyana Suriname
#> 3 3
#> Peru Brazil
#> 3 3
#> Paraguay Chile
#> 3 3
#> Argentina United Kingdom
#> 3 4
#> Netherlands Belgium
#> 4 4
#> Luxembourg France
#> 4 4
#> Spain Portugal
#> 4 4
#> Germany German Federal Republic
#> 4 4
#> Poland Hungary
#> 4 4
#> Czech Republic Italy
#> 4 4
#> Greece Norway
#> 4 4
#> Denmark Iceland
#> 4 4
#> Bavaria German Democratic Republic
#> 5 5
#> Baden Wuerttemburg
#> 5 5
#> Austria-Hungary Austria
#> 5 5
#> Czechoslovakia Slovakia
#> 5 5
#> Malta Albania
#> 5 5
#> Croatia Yugoslavia
#> 5 5
#> Bosnia and Herzegovina Cyprus
#> 5 5
#> Bulgaria Moldova
#> 5 5
#> Romania Russia
#> 5 5
#> Estonia Latvia
#> 5 5
#> Lithuania Ukraine
#> 5 5
#> Belarus Armenia
#> 5 5
#> Georgia Azerbaijan
#> 5 5
#> Finland Sweden
#> 5 5
#> Cape Verde Sao Tome and Principe
#> 5 5
#> Guinea-Bissau
#> 5
aricode::ARI(clust_country_indep, clust_country_dep)
#> [1] 0.8886699
On top of the clustering comparison, we can compare the ICL criterion to see which of the dependent or independent models is a best fit:
We can do the same plots for the reorganized matrices and the corresponding expectations. Note that the expectations correspond to the marginal expectation of each layer and it may be relevant to have a look at the conditional expectations.
plot(MultiplexFitdep, type = "expected")
#> Warning in self$predict(): provided expectations are the marginal expectations
#> in the dependent case
For instance, we may want to compare the marginal distribution for two countries in their given blocks to have being at war while they are allied at some point (before or after):
p11 <- MultiplexFitdep$connectParam$prob11
p01 <- MultiplexFitdep$connectParam$prob01
p10 <- MultiplexFitdep$connectParam$prob10
# conditional probabilities of being at war while having been or will
# be allied
round(p11/(p11 + p10), 2)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.09 0.10 0.03 0.43
#> [2,] 0.10 0.11 0.09 0.14
#> [3,] 0.03 0.09 0.05 0.03
#> [4,] 0.43 0.14 0.03 0.01
# marginal probabilities of being at war
round(p11 + p01, 2)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.07 0.04 0.03 0.14
#> [2,] 0.04 0.10 0.04 0.13
#> [3,] 0.03 0.04 0.05 0.03
#> [4,] 0.14 0.13 0.03 0.02
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.