multiviewtest (version 2.0.1)

test_indep_com: Pseudo pseudolikelihood ratio test for dependent communities

Description

Implements the pseudo pseudolikelihood ratio test described in Section 3 of Gao et. al. (2019) "Testing for Association in Multi-View Network Data" for testing for dependence between communities in two network data views. Fits stochastic block models in each view.

Usage

test_indep_com(
  X,
  K1 = NULL,
  K2 = NULL,
  nperm = 200,
  step = 0.001,
  maxiter = 1000,
  parallel = FALSE
)

Arguments

X

Multi-view data with two views; a list of two n x n adjacency matrices.

K1

An optional argument containing the number of communities in View 1. If left out, then the number of communities is chosen with the method of Le and Levina (2015).

K2

An optional argument containing the number of communities in View 2. If left out, then the number of communities is chosen with the method of Le and Levina (2015).

nperm

An integer specifying the number of permutations to use for the permutation procedure. The default number is 200.

step

A numeric value containing the fixed step size to be used in the optimization algorithm for estimating Pi. The default step size is 0.001.

maxiter

A numeric value containing the maximum number of iterations to run in the optimization algorithm. The default maximum is 1000.

parallel

An optional argument; if true, do parallel computing using the doParallel package

Value

A list containing the following output components:

K1

The number of communities in view 1

K2

The number of communities in view 2

Pi.est

The estimated Pi matrix

P2LRstat

The pseudo likelihood ratio test statistic

pval

The p-value

modelfit1

The parameter estimates and community assignment estimates from View 1.

modelfit2

The parameter estimates and community assignment estimates from View 2.

References

Amini, A. A., Chen, A., Bickel, P. J., & Levina, E. (2013). Pseudo-likelihood methods for community detection in large sparse networks. The Annals of Statistics, 41(4), 2097-2122.

Gao, L.L., Witten, D., Bien, J. Testing for Association in Multi-View Network Data, preprint.

Le, C. M., & Levina, E. (2015). Estimating the number of communities in networks by spectral methods. arXiv preprint arXiv:1507.00827.

Examples

# NOT RUN {
set.seed(1)
n <- 50
Pi <- diag(c(0.5, 0.5))
theta1 <- rbind(c(0.5, 0.1), c(0.1, 0.5))
theta2 <- cbind(c(0.1, 0.5), c(0.5, 0.1))

# 50 draws from a multi-view SBM with perfectly dependent communities
dat <- mv_sbm_gen(n, Pi, theta1, theta2)

# Test H0: communities are independent
# Data was generated under the alternative hypothesis 
results <- test_indep_com(dat$data, nperm=25)
results$pval

# }