MCMCnegbinChange  R Documentation 
This function generates a sample from the posterior distribution of a Negative Binomial regression model with multiple changepoints. For the changepoints, the sampler 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.
MCMCnegbinChange(
formula,
data = parent.frame(),
m = 1,
fixed.m = TRUE,
b0 = 0,
B0 = 1,
a = NULL,
b = NULL,
e = 2,
f = 2,
g = 10,
burnin = 1000,
mcmc = 1000,
thin = 1,
verbose = 0,
seed = NA,
beta.start = NA,
P.start = NA,
rho.start = NA,
rho.step,
nu.start = NA,
marginal.likelihood = c("none", "Chib95"),
...
)
formula 
Model formula. 
data 
Data frame. 
m 
The number of changepoints. 
fixed.m 
A logical indicator for whether or not the number of
changepoints in the sampler should be exactly equal to 
b0 
The prior mean of 
B0 
The prior precision of 
a 

b 

e 
The hyperprior for the distribution 
f 
The hyperprior for the distribution 
g 
The hyperprior for the distribution 
burnin 
The number of burnin iterations for the sampler. 
mcmc 
The number of Metropolis iterations for the sampler. 
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 value 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 
rho.start 
The starting value for the 
rho.step 
Tuning parameter for the slice sampling approach to
sampling 
nu.start 
The starting values for the random effect,

marginal.likelihood 
How should the marginal likelihood be calculated?
Options are: 
... 
further arguments to be passed. 
MCMCnegbinChange
simulates from the posterior distribution of a
Negative Binomial regression model with multiple changepoints using the methods of
Chib (1998) and FruehwirthSchnatter et al (2009). The details of the
model are discussed in Blackwell (2017).
The model takes the following form:
y_t \sim \mathcal{P}oisson(\nu_t\mu_t)
\mu_t = x_t ' \beta_m,\;\; m = 1, \ldots, M
\nu_t \sim \mathcal{G}amma(\rho_m, \rho_m)
Where
M
is the number of states and \beta_m
and \rho_m
are parameters 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.
The overdispersion parameters have a prior with the following form:
f(\rho_me,f,g) \propto \rho^{e1}(\rho + g)^{(e+f)}
The model is simulated via blocked Gibbs conditonal on the states.
The \beta
being simulated via the auxiliary mixture sampling
method of FuerhwirthSchanetter et al. (2009). The \rho
is
updated via slice sampling. The \nu_i
are updated their
(conjugate) full conditional, which is also Gamma. The states are
updated as in Chib (1998)
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
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")}.
Daniel Pemstein, Kevin M. Quinn, and Andrew D. Martin. 2007. Scythe Statistical Library 1.0. http://scythe.wustl.edu.s3websiteuseast1.amazonaws.com/.
Sylvia FruehwirthSchnatter, Rudolf Fruehwirth, Leonhard Held, and Havard Rue. 2009. “Improved auxiliary mixture sampling for hierarchical models of nonGaussian data”, Statistics and Computing 19(4): 479492. <doi:10.1007/s1122200891094>
Matthew Blackwell. 2017. “Game Changers: Detecting Shifts in Overdispersed Count Data,” Political Analysis 26(2), 230239. <doi:10.1017/pan.2017.42>
MCMCpoissonChange
, plotState
,
plotChangepoint
## Not run:
n < 150
reg < 3
true.s < gl(reg, n/reg, n)
rho.true < c(1.5, 0.5, 3)
b0.true < c(1, 3, 1)
b1.true < c(1, 2, 2)
x1 < runif(n, 0, 2)
nu.true < rgamma(n, rho.true[true.s], rho.true[true.s])
mu < nu.true * exp(b0.true[true.s] + x1 * b1.true[true.s])
y < rpois(n, mu)
posterior < MCMCnegbinChange(y ~ x1, m = 2, verbose = 1000,
marginal.likelihood = "Chib95",
e = 2, f = 2, g = 10,
b0 = rep(0, 2), B0 = (1/9) * diag(2),
rho.step = rep(0.75, times = 3),
seed = list(NA, 2))
par(mfrow=c(attr(posterior, "m") + 1, 1), mai=c(0.4, 0.6, 0.3, 0.05))
plotState(posterior, legend.control = c(1, 0.6))
plotChangepoint(posterior, verbose = TRUE, ylab="Density",
start=1, overlay=TRUE)
open.ended < MCMCnegbinChange(y ~ x1, m = 10, verbose = 1000,
fixed.m = FALSE, mcmc = 2000, burnin = 2000,
e = 2, f = 2, g = 10,
a = 100, b = 1,
b0 = rep(0, 2), B0 = (1/9) * diag(2),
rho.step = 0.75,
seed = list(NA, 2))
plotState(open.ended, legend.control = c(1, 0.6))
## End(Not run)
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