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 = parent.frame(), burnin = 1000, mcmc = 10000, thin = 1, tune = 1.1, verbose = FALSE, seed = NA, beta.start = NA, b0 = 0, B0 = 0, ...)

`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 k-vector, where k is the length of
beta.Make sure that the
acceptance rate is satisfactory (typically between 0.20 and 0.5)
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, the current beta vector, and the Metropolis acceptance rate are printed to the screen every 500 iterations. |

`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 `rep(12345,6)` is used). The second element of
list is a positive substream number. See the MCMCpack
specification for more details. |

`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. Default value of 0 is
equivalent to an improper uniform prior for 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 Metropois proposal distribution is centered at the current value of
*theta* and has variance-covariance *V = T (B0 + C^{-1})^{-1} T*, where
*T* is a the diagonal positive definite matrix formed from the
`tune`

, *B0* 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 density sample. This object can be summarized by functions provided by the coda package.

Andrew D. Martin, Kevin M. Quinn, and Daniel Pemstein. 2004.
*Scythe Statistical Library 1.0.* 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)

[Package *MCMCpack* version 0.5-2 Index]