MCMCpanel {MCMCpack} | R Documentation |

MCMCpanel generates a posterior density sample from a General Linear Panel Model using Algorithm 2 of Chib and Carlin (1999). This model uses a multivariate Normal prior for the fixed effects parameters, a Wishart prior on the random effects precision matrix, and a Gamma prior on the conditional error precision. 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.

MCMCpanel(obs, Y, X, W, burnin = 1000, mcmc = 10000, thin = 5, verbose = FALSE, seed = NA, sigma2.start = NA, D.start = NA, b0 = 0, B0 = 1, eta0, R0, nu0 = 0.001, delta0 = 0.001, ...)

`obs` |
An (nk * 1) vector that contains unique
observation numbers for each subject. |

`Y` |
An (nk * 1) vector of response variables,
stacked across all subjects. |

`X` |
An (nk * p) matrix of fixed effects
covariates, stacked across all subjects. |

`W` |
An (nk * q) matrix of random effects
covariates, stacked across all subjects. |

`burnin` |
The number of burnin iterations for the sampler. |

`mcmc` |
The number of Gibbs iterations for the sampler. |

`thin` |
The thinning interval used in the simulation. The number of mcmc iterations must be divisible by this value. |

`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. |

`verbose` |
A switch which determines whether or not the progress of the sampler is printed to the screen. If TRUE, the iteration number and parameters are printed to the screen. |

`sigma2.start` |
The starting value for the conditional error variance. Default value of NA uses the least squares estimates. |

`D.start` |
The starting value for precision matrix of the random
effects. This can either be a scalar or square matrix with dimension
equal to the number of random effects. If this takes a scalar value, then
that value multiplied by an identity matrix will be the starting
value. Default value of NA uses an identity matrix multiplied by 0.5
the OLS sigma2 estimate. |

`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. |

`eta0` |
The shape parameter for the Wishart prior on precision matrix for the random effects. |

`R0` |
The scale matrix for the Wishart prior on precision matrix for the random effects. |

`nu0` |
The shape parameter for the Gamma prior on the conditional error precision. |

`delta0` |
The scale parameter for the Gamma prior on the conditional error precision. |

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

`MCMCpanel`

simulates from the posterior density sample using
the blocked Gibbs sampler of Chib and Carlin (1999), Algorithm 2.
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 + W_i *
b_i + epsilon_i*

Where the random effects:

*b_i ~ N_q(0,D)*

And the errors:

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

We assume standard, conjugate priors:

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

And:

*sigma^(-2) ~
Gamma(nu0/2, delta0/2)*

And:

*D^-1 ~ Wishart(eta0,
R0^-1)*

See Chib and Carlin (1999) or Martin and Saunders (2002) for more details.

*NOTE: Unlike most models in MCMCpack, we do not provide default
parameters for the priors on the precision matrix for the random effects.*
When fitting one of these models, it is of utmost importance to choose a
prior that reflects your prior beliefs about the random effects. Using the
`dwish`

and `rwish`

functions might be useful in choosing these
values. Also, the user is not allowed to specify a starting value
for the *beta* parameters, as they are simulated in the
first block of the sampler.

An mcmc object that contains the posterior density sample. This object can be summarized by functions provided by the coda package.

Siddhartha Chib and Bradley P. Carlin. 1999. ``On MCMC Sampling in
Hierarchical Longitudinal Models." *Statistics and Computing.* 9:
17-26.

Andrew D. Martin, Kevin M. Quinn, and Daniel Pemstein. 2004. *Scythe
Statistical Library 1.0.* http://scythe.wustl.edu.

Andrew D. Martin and Kyle L. Saunders. 2002. ``Bayesian Inference for Political Science Panel Data.'' Paper presented at the 2002 Annual Meeting of the American Political Science Association.

Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2002.
*Output Analysis and Diagnostics for MCMC (CODA)*.
http://www-fis.iarc.fr/coda/.

[Package *MCMCpack* version 0.5-2 Index]