MCMCpack: MCMCbinaryChange – R documentation

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MCMCbinaryChange

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 φ (the mean).
`d0`	d_0 is the shape2 parameter for Beta prior on φ (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 `verbose`th 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(φ_i),\;\; i = 1, …, k

Where k is the number of states.

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

φ_i \sim \mathcal{B}eta(c_0, d_0)

And:

p_{mm} \sim \mathcal{B}eta{a}{b},\;\; m = 1, …, 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. https://www.jstatsoft.org/v42/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>

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)

MCMCpack

Markov Chain Monte Carlo (MCMC) Package

v1.5-0

GPL-3

Authors

Andrew D. Martin [aut], Kevin M. Quinn [aut], Jong Hee Park [aut,cre], Ghislain Vieilledent [ctb], Michael Malecki[ctb], Matthew Blackwell [ctb], Keith Poole [ctb], Craig Reed [ctb], Ben Goodrich [ctb], Ross Ihaka [cph], The R Development Core Team [cph], The R Foundation [cph], Pierre L'Ecuyer [cph], Makoto Matsumoto [cph], Takuji Nishimura [cph]

Initial release

2021-01-19