MCMCoprobitChange  R Documentation 
This function generates a sample from the posterior distribution of an ordered probit regression model with multiple parameter breaks. 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.
MCMCoprobitChange(
formula,
data = parent.frame(),
m = 1,
burnin = 1000,
mcmc = 1000,
thin = 1,
tune = NA,
verbose = 0,
seed = NA,
beta.start = NA,
gamma.start = NA,
P.start = NA,
b0 = NULL,
B0 = NULL,
a = NULL,
b = NULL,
marginal.likelihood = c("none", "Chib95"),
gamma.fixed = 0,
...
)
formula 
Model formula. 
data 
Data frame. 
m 
The number of changepoints. 
burnin 
The number of burnin 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. 
tune 
The tuning parameter for the MetropolisHastings step. Default of NA corresponds to a choice of 0.05 divided by the number of categories in the response variable. 
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 
gamma.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: 
gamma.fixed 
1 if users want to constrain 
... 
further arguments to be passed 
MCMCoprobitChange
simulates from the posterior distribution of an
ordinal probit regression model with multiple parameter breaks. The
simulation of latent states is based on the linear approximation method
discussed in Park (2011).
The model takes the following form:
\Pr(y_t = 1) = \Phi(\gamma_{c, m}  x_i'\beta_m)  \Phi(\gamma_{c1, m}  x_i'\beta_m)\;\; m = 1, \ldots, M
Where M
is the number of states, and \gamma_{c, m}
and
\beta_m
are paramters 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.
Note that when the fitted changepoint model has very few observations in any of states, the marginal likelihood outcome can be “nan," which indicates that too many breaks are assumed given the model and data.
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 loglikelihood of
the model (loglike
), and the logmarginal 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: 188204. <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): 121. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v042.i09")}.
Siddhartha Chib. 1998. “Estimation and comparison of multiple changepoint models.” Journal of Econometrics. 86: 221241.
plotState
, plotChangepoint
set.seed(1909)
N < 200
x1 < rnorm(N, 1, .5);
## set a true break at 100
z1 < 1 + x1[1:100] + rnorm(100);
z2 < 1 0.2*x1[101:200] + rnorm(100);
z < c(z1, z2);
y < z
## generate y
y[z < 1] < 1;
y[z >= 1 & z < 2] < 2;
y[z >= 2] < 3;
## inputs
formula < y ~ x1
## fit multiple models with a varying number of breaks
out1 < MCMCoprobitChange(formula, m=1,
mcmc=100, burnin=100, thin=1, tune=c(.5, .5), verbose=100,
b0=0, B0=0.1, marginal.likelihood = "Chib95")
out2 < MCMCoprobitChange(formula, m=2,
mcmc=100, burnin=100, thin=1, tune=c(.5, .5, .5), verbose=100,
b0=0, B0=0.1, marginal.likelihood = "Chib95")
## Do model comparison
## NOTE: the chain should be run longer than this example!
BayesFactor(out1, out2)
## draw plots using the "right" model
plotState(out1)
plotChangepoint(out1)
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