NetworkChange: Changepoint analysis of a degree-corrected multilinear tensor model

Description

NetworkChange implements Bayesian multiple changepoint models to network time series data using a degree-corrected multilinear tensor decomposition method

Usage

NetworkChange(
  Y,
  R = 2,
  m = 1,
  initial.s = NULL,
  mcmc = 100,
  burnin = 100,
  verbose = 0,
  thin = 1,
  reduce.mcmc = NULL,
  degree.normal = "eigen",
  UL.Normal = "Orthonormal",
  DIC = FALSE,
  Waic = FALSE,
  marginal = FALSE,
  plotUU = FALSE,
  plotZ = FALSE,
  constant = FALSE,
  b0 = 0,
  B0 = 1,
  c0 = NULL,
  d0 = NULL,
  u0 = NULL,
  u1 = NULL,
  v0 = NULL,
  v1 = NULL,
  a = NULL,
  b = NULL
)

Arguments

Reponse tensor

Dimension of latent space. The default is 2.

Number of change point. If m = 0 is specified, the result should be the same as NetworkStatic.

initial.s

The starting value of latent state vector. The default is sampling from equal probabilities for all states.

mcmc

The number of MCMC iterations after burnin.

burnin

The number of burn-in iterations for the sampler.

verbose

A switch which determines whether or not the progress of the sampler is printed to the screen. If verbose is greater than 0 the iteration number, the \(\beta\) vector, and the error variance are printed to the screen every verboseth iteration.

thin

The thinning interval used in the simulation. The number of MCMC iterations must be divisible by this value.

reduce.mcmc

The number of reduced MCMC iterations for marginal likelihood computations. If reduce.mcmc = NULL, mcmc/thin is used.

degree.normal

A null model for degree correction. Users can choose "NULL", "eigen" or "Lsym." "NULL" is no degree correction. "eigen" is a principal eigen-matrix consisting of the first eigenvalue and the corresponding eigenvector. " Lsym" is a modularity matrix. Default is "eigen."

UL.Normal

Transformation of sampled U. Users can choose "NULL", "Normal" or "Orthonormal." "NULL" is no normalization. "Normal" is the standard normalization. "Orthonormal" is the Gram-Schmidt orthgonalization. Default is "NULL."

DIC

If DIC = TRUE, the deviation information criterion is computed.

Waic

If Waic = TRUE, the Watanabe information criterion is computed.

marginal

If marginal = TRUE, the log marignal likelihood is computed using the method of Chib (1995).

plotUU

If plotUU = TRUE and verbose > 0, then the plot of the latent space will be printed to the screen at every verboseth iteration. The default is plotUU = FALSE.

plotZ

If plotZ = TRUE and verbose > 0, then the plot of the degree-corrected input matrix will be printed to the screen with the sampled mean values at every verboseth iteration. The default is plotUU = FALSE.

constant

If constant = TRUE, constant parameter is sampled and saved in the output as attribute bmat. Default is constant = FALSE.

The prior mean of \(\beta\). This must be a scalar. The default value is 0.

The prior variance of \(\beta\). This must be a scalar. The default value is 1.

= 0.1

\(u_0/2\) is the shape parameter for the inverse Gamma prior on variance parameters for U. The default is 10.

\(u_1/2\) is the scale parameter for the inverse Gamma prior on variance parameters for U. The default is 1.

\(v_0/2\) is the shape parameter for the inverse Gamma prior on variance parameters for V. The default is 10.

\(v_1/2\) is the scale parameter for the inverse Gamma prior on variance parameters for V. The default is the time length of Y.

\(a\) is the shape1 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states.

\(b\) is the shape2 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states.

Value

An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package. The object contains an attribute Waic.out that contains results of WAIC and the log-marginal likelihood of the model (logmarglike). The object also contains an attribute prob.state storage matrix that contains the probability of \(state_i\) for each period

References

Jong Hee Park and Yunkyun Sohn. 2020. "Detecting Structural Change in Longitudinal Network Data." Bayesian Analysis. Vol.15, No.1, pp.133-157.

Peter D. Hoff 2011. "Hierarchical Multilinear Models for Multiway Data." Computational Statistics \& Data Analysis. 55: 530-543.

Siddhartha Chib. 1998. "Estimation and comparison of multiple change-point models." Journal of Econometrics. 86: 221-241.

Examples

Run this code

# NOT RUN {
   
# }
# NOT RUN {
   set.seed(1973)
   \## Generate an array (30 by 30 by 40) with block transitions
   from 2 blocks to 3 blocks
   Y <- MakeBlockNetworkChange(n=10, T=40, type ="split")
   G <- 100 ## Small mcmc scans to save time

   \## Fit multiple models for break number detection using Bayesian model comparison
   out0 <- NetworkStatic(Y, R=2, mcmc=G, burnin=G, verbose=G, Waic=TRUE)
   out1 <- NetworkChange(Y, R=2, m=1, mcmc=G, burnin=G, verbose=G, Waic=TRUE)
   out2 <- NetworkChange(Y, R=2, m=2, mcmc=G, burnin=G, verbose=G, Waic=TRUE)
   out3 <- NetworkChange(Y, R=2, m=3, mcmc=G, burnin=G, verbose=G, Waic=TRUE)
   outlist <- list(out0, out1, out2, out3)

   \## The most probable model given break number 0 to 3 and data is out1 according to WAIC 
   WaicCompare(outlist)

   plotU(out1)
 
   plotV(out1)
   
# }