MCMCprobitChange | R Documentation |
This function generates a sample from the posterior distribution of a linear Gaussian 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.
MCMCprobitChange(
formula,
data = parent.frame(),
m = 1,
burnin = 10000,
mcmc = 10000,
thin = 1,
verbose = 0,
seed = NA,
beta.start = NA,
P.start = NA,
b0 = NULL,
B0 = NULL,
a = NULL,
b = NULL,
marginal.likelihood = c("none", "Chib95"),
...
)
formula |
Model formula. |
data |
Data frame. |
m |
The number of changepoints. |
burnin |
The number of burn-in iterations for the sampler. |
mcmc |
The number of MCMC iterations after burnin. |
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 |
seed |
The seed for the random number generator. If NA, the Mersenne
Twister generator is used with default seed 12345; if an integer is passed
it is used to seed the Mersenne twister. The user can also pass a list of
length two to use the L'Ecuyer random number generator, which is suitable
for parallel computation. The first element of the list is the L'Ecuyer
seed, which is a vector of length six or NA (if NA a default seed of
|
beta.start |
The starting values for the |
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 |
b0 |
The prior mean of |
B0 |
The prior precision of |
a |
|
b |
|
marginal.likelihood |
How should the marginal likelihood be calculated?
Options are: |
... |
further arguments to be passed |
MCMCprobitChange
simulates from the posterior distribution of a
probit regression model with multiple parameter breaks. The simulation is
based on Chib (1998) and Park (2011).
The model takes the following form:
\Pr(y_t = 1) = \Phi(x_i'\beta_m) \;\; m = 1, \ldots, M
Where M
is the number of states, and \beta_m
is a parameter when a state is m
at t
.
We assume Gaussian distribution for prior of \beta
:
\beta_m \sim \mathcal{N}(b_0,B_0^{-1}),\;\; m = 1, \ldots, M
And:
p_{mm} \sim \mathcal{B}eta(a, b),\;\; m = 1, \ldots, M
Where M
is the number of states.
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, the log-likelihood of
the model (loglike
), and the log-marginal likelihood of the model
(logmarglike
).
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v042.i09")}.
Siddhartha Chib. 1998. “Estimation and comparison of multiple change-point models.” Journal of Econometrics. 86: 221-241.
Albert, J. H. and S. Chib. 1993. “Bayesian Analysis of Binary and Polychotomous Response Data.” J. Amer. Statist. Assoc. 88, 669-679
plotState
, plotChangepoint
## Not run:
set.seed(1973)
x1 <- rnorm(300, 0, 1)
true.beta <- c(-.5, .2, 1)
true.alpha <- c(.1, -1., .2)
X <- cbind(1, x1)
## set two true breaks at 100 and 200
true.phi1 <- pnorm(true.alpha[1] + x1[1:100]*true.beta[1])
true.phi2 <- pnorm(true.alpha[2] + x1[101:200]*true.beta[2])
true.phi3 <- pnorm(true.alpha[3] + x1[201:300]*true.beta[3])
## generate y
y1 <- rbinom(100, 1, true.phi1)
y2 <- rbinom(100, 1, true.phi2)
y3 <- rbinom(100, 1, true.phi3)
Y <- as.ts(c(y1, y2, y3))
## fit multiple models with a varying number of breaks
out0 <- MCMCprobitChange(formula=Y~X-1, data=parent.frame(), m=0,
mcmc=1000, burnin=1000, thin=1, verbose=1000,
b0 = 0, B0 = 0.1, a = 1, b = 1, marginal.likelihood = c("Chib95"))
out1 <- MCMCprobitChange(formula=Y~X-1, data=parent.frame(), m=1,
mcmc=1000, burnin=1000, thin=1, verbose=1000,
b0 = 0, B0 = 0.1, a = 1, b = 1, marginal.likelihood = c("Chib95"))
out2 <- MCMCprobitChange(formula=Y~X-1, data=parent.frame(), m=2,
mcmc=1000, burnin=1000, thin=1, verbose=1000,
b0 = 0, B0 = 0.1, a = 1, b = 1, marginal.likelihood = c("Chib95"))
out3 <- MCMCprobitChange(formula=Y~X-1, data=parent.frame(), m=3,
mcmc=1000, burnin=1000, thin=1, verbose=1000,
b0 = 0, B0 = 0.1, a = 1, b = 1, marginal.likelihood = c("Chib95"))
## find the most reasonable one
BayesFactor(out0, out1, out2, out3)
## draw plots using the "right" model
plotState(out2)
plotChangepoint(out2)
## End(Not run)
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