MCMCtobit  R Documentation 
This function generates a sample from the posterior distribution of a linear regression model with Gaussian errors using Gibbs sampling (with a multivariate Gaussian prior on the beta vector, and an inverse Gamma prior on the conditional error variance). The dependent variable may be censored from below, from above, or both. 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.
MCMCtobit(
formula,
data = NULL,
below = 0,
above = Inf,
burnin = 1000,
mcmc = 10000,
thin = 1,
verbose = 0,
seed = NA,
beta.start = NA,
b0 = 0,
B0 = 0,
c0 = 0.001,
d0 = 0.001,
...
)
formula 
A model formula. 
data 
A dataframe. 
below 
The point at which the dependent variable is censored from below. The default is zero. To censor from above only, specify that below = Inf. 
above 
The point at which the dependent variable is censored from above. To censor from below only, use the default value of Inf. 
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. 
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 
b0 
The prior mean of 
B0 
The prior precision of 
c0 

d0 

... 
further arguments to be passed 
MCMCtobit
simulates from the posterior distribution using standard
Gibbs sampling (a multivariate Normal draw for the betas, and an inverse
Gamma draw for the conditional error variance). MCMCtobit
differs
from MCMCregress
in that the dependent variable may be censored from
below, from above, or both. The simulation proper is done in compiled C++
code to maximize efficiency. Please consult the coda documentation for a
comprehensive list of functions that can be used to analyze the posterior
sample.
The model takes the following form:
y_i = x_i ' \beta + \varepsilon_{i},
where the errors are assumed to be Gaussian:
\varepsilon_{i} \sim \mathcal{N}(0, \sigma^2).
Let c_1
and c_2
be the two censoring points, and let
y_i^\ast
be the partially observed dependent variable. Then,
y_i = y_i^{\ast} \texttt{ if } c_1 < y_i^{\ast} < c_2,
y_i = c_1 \texttt{ if } c_1 \geq y_i^{\ast},
y_i = c_2 \texttt{ if } c_2 \leq y_i^{\ast}.
We assume standard, semiconjugate priors:
\beta \sim \mathcal{N}(b_0,B_0^{1}),
and:
\sigma^{2} \sim \mathcal{G}amma(c_0/2, d_0/2),
where \beta
and \sigma^{2}
are
assumed a priori independent. Note that only starting
values for \beta
are allowed because simulation is done
using Gibbs sampling with the conditional error variance as the
first block in the sampler.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
Ben Goodrich, goodrich.ben@gmail.com
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/.
Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2006. “Output Analysis and Diagnostics for MCMC (CODA)”, R News. 6(1): 711. https://CRAN.Rproject.org/doc/Rnews/Rnews_20061.pdf.
Siddhartha Chib. 1992. “Bayes inference in the Tobit censored regression model." Journal of Econometrics. 51:7999.
James Tobin. 1958. “Estimation of relationships for limited dependent variables." Econometrica. 26:2436.
plot.mcmc
, summary.mcmc
,
survreg
, MCMCregress
## Not run:
library(survival)
example(tobin)
summary(tfit)
tfit.mcmc < MCMCtobit(durable ~ age + quant, data=tobin, mcmc=30000,
verbose=1000)
plot(tfit.mcmc)
raftery.diag(tfit.mcmc)
summary(tfit.mcmc)
## End(Not run)
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