MCMCpoisson | R Documentation |
This function generates a sample from the posterior distribution of a Poisson regression model using a random walk Metropolis algorithm. 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.
MCMCpoisson(
formula,
data = NULL,
burnin = 1000,
mcmc = 10000,
thin = 1,
tune = 1.1,
verbose = 0,
seed = NA,
beta.start = NA,
b0 = 0,
B0 = 0,
marginal.likelihood = c("none", "Laplace"),
...
)
formula |
Model formula. |
data |
Data frame. |
burnin |
The number of burn-in 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. |
tune |
Metropolis tuning parameter. Can be either a positive scalar or
a |
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 |
b0 |
The prior mean of |
B0 |
The prior precision of |
marginal.likelihood |
How should the marginal likelihood be calculated?
Options are: |
... |
further arguments to be passed. |
MCMCpoisson
simulates from the posterior distribution of a Poisson
regression model using a random walk Metropolis algorithm. 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 \sim \mathcal{P}oisson(\mu_i)
Where the inverse link function:
\mu_i = \exp(x_i'\beta)
We assume a multivariate Normal prior on \beta
:
\beta \sim \mathcal{N}(b_0,B_0^{-1})
The Metropois proposal distribution is centered at the current value of
\theta
and has variance-covariance V = T (B_0 + C^{-1})^{-1} T
where T
is a the diagonal positive definite matrix formed from the
tune
, B_0
is the prior precision, and C
is the
large sample variance-covariance matrix of the MLEs. This last calculation
is done via an initial call to glm
.
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): 1-21. \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.s3-website-us-east-1.amazonaws.com/.
Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2006. “Output Analysis and Diagnostics for MCMC (CODA)”, R News. 6(1): 7-11. https://CRAN.R-project.org/doc/Rnews/Rnews_2006-1.pdf.
plot.mcmc
,summary.mcmc
,
glm
## Not run:
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
posterior <- MCMCpoisson(counts ~ outcome + treatment)
plot(posterior)
summary(posterior)
## End(Not run)
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