MCMCpoisson {MCMCpack} | R Documentation |
This function generates a posterior density sample from a Poisson regression model using a random walk Metropolis algorithm. The user supplies data and priors, and a sample from the posterior density is returned as an mcmc object, which can be subsequently analyzed with functions provided in the coda package.
MCMCpoisson(formula, data = list(), burnin = 1000, mcmc = 10000, thin = 5, tune = 1.1, verbose = FALSE, seed = 0, beta.start = NA, b0 = 0, B0 = 0.001, ...)
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. Make sure that the acceptance rate is satisfactory before using the posterior density sample for inference. |
verbose |
A switch which determines whether or not the progress of the sampler is printed to the screen. If TRUE, the iteration number and the beta is printed to the screen every 500 iterations. |
seed |
The seed for the random number generator. The code uses the Mersenne Twister, which requires an integer as an input. If nothing is provided, the Scythe default seed is used. |
beta.start |
The starting value for the beta vector. This can either be a scalar or a column vector with dimension equal to the number of betas. If this takes a scalar value, then that value will serve as the starting value for all of the betas. The default value of NA will use the maximum likelihood estimate of beta as the starting value. |
b0 |
The prior mean of beta. This can either be a scalar or a column vector with dimension equal to the number of betas. If this takes a scalar value, then that value will serve as the prior mean for all of the betas. |
B0 |
The prior precision of beta. This can either be a scalar or a square matrix with dimensions equal to the number of betas. If this takes a scalar value, then that value times an identity matrix serves as the prior precision of beta. |
... |
further arguments to be passed |
MCMCpoisson
simulates from the posterior density 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 density sample.
The model takes the following form:
y_i ~ Poisson(mu_i)
Where the inverse link function:
mu_i = exp(x_i'beta)
We assume a multivariate Normal prior on beta:
beta ~ N(b0,B0^(-1))
The candidate generating density is a multivariate Normal density centered at the current value of beta with variance-covariance matrix that is an approximation of the posterior based on the maximum likelihood estimates and the prior precision multiplied by the tuning parameter squared.
An mcmc object that contains the posterior density sample. This object can be summarized by functions provided by the coda package.
Andrew D. Martin, Kevin M. Quinn, and Daniel Pemstein. 2003. Scythe Statistical Library 0.4. http://scythe.wustl.edu.
Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2002. Output Analysis and Diagnostics for MCMC (CODA). http://www-fis.iarc.fr/coda/.
## 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)