MCMCoprobit {MCMCpack} | R Documentation |

This function generates a posterior density sample from an ordered probit regression model using the data augmentation approach of Cowles (1996). 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.

MCMCoprobit(formula, data = parent.frame(), burnin = 1000, mcmc = 10000, thin=1, tune = NA, 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 MCMC iterations for the sampler. |

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

`tune` |
The tuning parameter for the Metropolis-Hastings step. Default of NA corresponds to a choice of 0.05 divided by the number of categories in the response variable. |

`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 Metropolis-Hastings 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 rescaled estimates from an ordered
logit model. |

`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 on
beta. |

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

`MCMCoprobit`

simulates from the posterior density of a ordered probit
regression model using data augmentation. 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 observed variable *y_i* is ordinal with a total of *C*
categories, with distribution
governed by a latent variable:

*z_i = x_i'beta + epsilon_i*

The errors are assumed to be from a standard Normal distribution. The
probabilities of observing each outcome is governed by this latent
variable and *C-1* estimable cutpoints, which are denoted
*gamma_c*. The probability that individual *i*
is in category *c* is computed by:

*pi_ic = Phi(gamma_c - x_i'beta) - Phi(gamma_(c-1) - x_i'beta)
*

These probabilities are used to form the multinomial distribution that defines the likelihoods.

The algorithm employed is discussed in depth by Cowles (1996). Note that
the model does include a constant in the data matrix. Thus, the first
element *gamma_1* is normalized to zero, and is not
returned in the mcmc object.

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

M. K. Cowles. 1996. ``Accelerating Monte Carlo Markov Chain Convergence for
Cumulative-link Generalized Linear Models." *Statistics and Computing.*
6: 101-110.

Valen E. Johnson and James H. Albert. 1999. ``Ordinal Data Modeling." Springer: New York.

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: x1 <- rnorm(100); x2 <- rnorm(100); z <- 1.0 + x1*0.1 - x2*0.5 + rnorm(100); y <- z; y[z < 0] <- 0; y[z >= 0 & z < 1] <- 1; y[z >= 1 & z < 1.5] <- 2; y[z >= 1.5] <- 3; posterior <- MCMCoprobit(y ~ x1 + x2, tune=0.3, mcmc=20000) plot(posterior) summary(posterior) ## End(Not run)

[Package *MCMCpack* version 0.5-2 Index]