randnet (version 0.7)

LRBIC: selecting number of communities by asymptotic likelihood ratio

Description

selecting number of communities by asymptotic likelihood ratio based the methdo of Wang and Bickel 2015

Usage

LRBIC(A, Kmax, lambda = NULL, model = "both")

Value

a list of

SBM.K

estimated number of communities under SBM

DCSBM.K

estimated number of communities under DCSBM

SBM.BIC

the BIC values for the K sequence under SBM

DCSBM.BIC

the BIC values for the K sequence under DCSBM

Arguments

A

adjacency matrix

Kmax

the largest possible number of communities to check

lambda

a tuning parameter. By default, will use the number recommended in the paper.

model

selecting K under which model. If set to be "SBM", the calculation will be done under SBM. If set to be "DCSBM", the calculation will be done under DCSBM. The default value is "both" so will give two selections under SBM and DCSBM respectively.

Author

Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li

Details

Note that the method cannot distinguish SBM and DCSBM, though different calculation is done under the two models. So it is not valid to compare across models. The theoretical analysis of the method is done under maximum likelhood and variational EM. But as suggested in the paper, we use spectral clustering for community detection before fitting maximum likelhood.

References

Wang, Y. R. & Bickel, P. J. Likelihood-based model selection for stochastic block models The Annals of Statistics, Institute of Mathematical Statistics, 2017, 45, 500-528

See Also

BHMC.estimate, ECV.block, NCV.select

Examples

dt <- BlockModel.Gen(30,300,K=3,beta=0.2,rho=0.9,simple=FALSE,power=TRUE)


A <- dt$A


### test LRBIC

lrbic <- LRBIC(A,6,model="both")

lrbic$SBM.K

lrbic$DCSBM.K