MCMCregress {MCMCpack} | R Documentation |

This function generates a posterior density sample from 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 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.

MCMCregress(formula, data = parent.frame(), burnin = 1000, mcmc = 10000, thin = 1, verbose = FALSE, seed = NA, beta.start = NA, b0 = 0, B0 = 0, c0 = 0.001, d0 = 0.001, ...)

`formula` |
Model formula. |

`data` |
Data frame. |

`burnin` |
The number of burn-in 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 TRUE, the iteration number, the
beta vector, and the conditional error variance is 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 values for the beta vector.
This can either be a scalar or a
column vector with dimension equal to the number of betas.
The default value of of NA will use the OLS
estimate of beta as the starting value. If this is a
scalar, that value will serve as the starting value
mean for all of the betas. |

`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. |

`c0` |
c0/2 is the shape parameter for the inverse
Gamma prior on sigma^2 (the variance of the
disturbances). The amount of information in the inverse Gamma prior
is something like that from c0 pseudo-observations. |

`d0` |
d0/2 is the scale parameter for the
inverse Gamma prior on sigma^2 (the variance of the
disturbances). In constructing the inverse Gamma prior,
d0 acts like the sum of squared errors from the
c0 pseudo-observations. |

`...` |
further arguments to be passed |

`MCMCregress`

simulates from the posterior density using
standard Gibbs sampling (a multivariate Normal draw for the betas, and an
inverse Gamma draw for the conditional error variance). 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 = x_i'beta + epsilon_i*

Where the errors are assumed to be Gaussian:

*epsilon_i ~ N(0,
sigma^2)*

We assume standard, semi-conjugate priors:

*beta ~ N(b0,B0^(-1))*

And:

*sigma^(-2) ~
Gamma(c0/2, d0/2)*

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 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: line <- list(X = c(-2,-1,0,1,2), Y = c(1,3,3,3,5)) posterior <- MCMCregress(Y~X, data=line, verbose=TRUE) plot(posterior) raftery.diag(posterior) summary(posterior) ## End(Not run)

[Package *MCMCpack* version 0.5-2 Index]