Stochastic Block Model Prior class

An S4 class to represent a Stochastic Block Model. Such model can be used to cluster graph vertex, and model a square adjacency matrix \(X\) with the following generative model : $$ \pi \sim Dirichlet(\alpha)$$ $$ Z_i \sim \mathcal{M}(1,\pi)$$ $$ \theta_{kl} \sim Beta(a_0,b_0)$$ $$ X_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{B}(\theta_{kl})$$ These classes mainly store the prior parameters value \(\alpha,a_0,b_0\) of this generative model. The Sbm-class must be used when fitting a simple Sbm whereas the SbmPrior-class must be used when fitting a CombinedModels-class.

SbmPrior(a0 = 1, b0 = 1, type = "guess")

Sbm(alpha = 1, a0 = 1, b0 = 1, type = "guess")

Arguments

a0

Beta prior parameter over links (default to 1)

b0

Beta prior parameter over no-links (default to 1)

type

define the type of networks (either "directed", "undirected" or "guess", default to "guess"), for undirected graphs the adjacency matrix is supposed to be symmetric.

alpha

Dirichlet prior parameter over the cluster proportions (default to 1)

Value

a SbmPrior-class object a Sbm-class object

References

Nowicki, Krzysztof and Tom A B Snijders (2001). “Estimation and prediction for stochastic block structures”. In:Journal of the American statistical association 96.455, pp. 1077–1087

See also

greed

SbmFit-class,SbmPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, greed()

Examples

Sbm()
#> An object of class "Sbm"
#> Slot "alpha":
#> [1] 1
#> 
#> Slot "a0":
#> [1] 1
#> 
#> Slot "b0":
#> [1] 1
#> 
#> Slot "type":
#> [1] "guess"
#> 
SbmPrior()
#> An object of class "SbmPrior"
#> Slot "a0":
#> [1] 1
#> 
#> Slot "b0":
#> [1] 1
#> 
#> Slot "type":
#> [1] "guess"
#> 
SbmPrior(type = "undirected")
#> An object of class "SbmPrior"
#> Slot "a0":
#> [1] 1
#> 
#> Slot "b0":
#> [1] 1
#> 
#> Slot "type":
#> [1] "undirected"
#> 
Sbm()
#> An object of class "Sbm"
#> Slot "alpha":
#> [1] 1
#> 
#> Slot "a0":
#> [1] 1
#> 
#> Slot "b0":
#> [1] 1
#> 
#> Slot "type":
#> [1] "guess"
#> 
Sbm(type = "undirected")
#> An object of class "Sbm"
#> Slot "alpha":
#> [1] 1
#> 
#> Slot "a0":
#> [1] 1
#> 
#> Slot "b0":
#> [1] 1
#> 
#> Slot "type":
#> [1] "undirected"
#>