MCMCbinaryChange {MCMCpack}

Markov Chain Monte Carlo for a Binary Multiple Changepoint Model

Description

This function generates a sample from the posterior distribution of a binary model with multiple changepoints. The function uses the Markov chain Monte Carlo method of Chib (1998). The user supplies data and priors, and a sample from the posterior distribution is returned as an mcmc object, which can be subsequently analyzed with functions provided in the coda package.

Usage

MCMCbinaryChange(
  data,
  m = 1,
  c0 = 1,
  d0 = 1,
  a = NULL,
  b = NULL,
  burnin = 10000,
  mcmc = 10000,
  thin = 1,
  verbose = 0,
  seed = NA,
  phi.start = NA,
  P.start = NA,
  marginal.likelihood = c("none", "Chib95"),
  ...
)

Arguments

data

The data.

m

The number of changepoints.

c0

c_0 is the shape1 parameter for Beta prior on \phi (the mean).

d0

d_0 is the shape2 parameter for Beta prior on \phi (the mean).

a

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

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.

burnin

The number of burn-in iterations for the sampler.

mcmc

The number of MCMC iterations after burn-in.

thin

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

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 and the posterior density samples are printed to the screen every verboseth iteration.

seed

The seed for the random number generator. If NA, current R system seed is used.

phi.start

The starting values for the mean. The default value of NA will use draws from the Uniform distribution.

P.start

The starting values for the transition matrix. A user should provide a square matrix with dimension equal to the number of states. By default, draws from the Beta(0.9, 0.1) are used to construct a proper transition matrix for each raw except the last raw.

marginal.likelihood

How should the marginal likelihood be calculated? Options are: none in which case the marginal likelihood will not be calculated, and Chib95 in which case the method of Chib (1995) is used.

...

further arguments to be passed

Details

MCMCbinaryChange simulates from the posterior distribution of a binary model with multiple changepoints.

The model takes the following form:

Y_t \sim \mathcal{B}ernoulli(\phi_i),\;\; i = 1, \ldots, k

Where k is the number of states.

We assume Beta priors for \phi_{i} and for transition probabilities:

\phi_i \sim \mathcal{B}eta(c_0, d_0)

And:

p_{mm} \sim \mathcal{B}eta{a}{b},\;\; m = 1, \ldots, k

Where M is 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 prob.state storage matrix that contains the probability of state_i for each period, and the log-marginal likelihood of the model (logmarglike).

References

Jong Hee Park. 2011. “Changepoint Analysis of Binary and Ordinal Probit Models: An Application to Bank Rate Policy Under the Interwar Gold Standard." Political Analysis. 19: 188-204. <doi:10.1093/pan/mpr007>

Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park. 2011. “MCMCpack: Markov Chain Monte Carlo in R.”, Journal of Statistical Software. 42(9): 1-21. doi:10.18637/jss.v042.i09.

Siddhartha Chib. 1995. “Marginal Likelihood from the Gibbs Output.” Journal of the American Statistical Association. 90: 1313-1321. <doi: 10.1080/01621459.1995.10476635>

See Also

MCMCpoissonChange,plotState, plotChangepoint

Examples

    ## Not run: 
    set.seed(19173)
    true.phi<- c(0.5, 0.8, 0.4)

    ## two breaks at c(80, 180)
    y1 <- rbinom(80, 1,  true.phi[1])
    y2 <- rbinom(100, 1, true.phi[2])
    y3 <- rbinom(120, 1, true.phi[3])
    y  <- as.ts(c(y1, y2, y3))

    model0 <- MCMCbinaryChange(y, m=0, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model1 <- MCMCbinaryChange(y, m=1, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model2 <- MCMCbinaryChange(y, m=2, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model3 <- MCMCbinaryChange(y, m=3, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model4 <- MCMCbinaryChange(y, m=4, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model5 <- MCMCbinaryChange(y, m=5, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")

    print(BayesFactor(model0, model1, model2, model3, model4, model5))

    ## plot two plots in one screen
    par(mfrow=c(attr(model2, "m") + 1, 1), mai=c(0.4, 0.6, 0.3, 0.05))
    plotState(model2, legend.control = c(1, 0.6))
    plotChangepoint(model2, verbose = TRUE, ylab="Density", start=1, overlay=TRUE)

    
## End(Not run)