MCMChierEI {MCMCpack} | R Documentation |

`MCMChierEI' is used to fit Wakefield's hierarchical ecological inference model for partially observed 2 x 2 contingency tables.

MCMChierEI(r0, r1, c0, c1, burnin=5000, mcmc=50000, thin=1, verbose=FALSE, seed=NA, m0=0, M0=2.287656, m1=0, M1=2.287656, a0=0.825, b0=0.0105, a1=0.825, b1=0.0105, ...)

`r0` |
(ntables * 1) vector of row
sums from row 0. |

`r1` |
(ntables * 1) vector of row
sums from row 1. |

`c0` |
(ntables * 1) vector of
column sums from column 0. |

`c1` |
(ntables * 1) vector of
column sums from column 1. |

`burnin` |
The number of burn-in scans for the sampler. |

`mcmc` |
The number of mcmc scans to be saved. |

`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. Information is printed if TRUE. |

`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. |

`m0` |
Prior mean of the mu0 parameter. |

`M0` |
Prior variance of the mu0 parameter. |

`m1` |
Prior mean of the mu1 parameter. |

`M1` |
Prior variance of the mu1 parameter. |

`a0` |
`a0/2` is the shape parameter for the inverse-gamma
prior on the sigma^2_0 parameter. |

`b0` |
`b0/2` is the scale parameter for the inverse-gamma
prior on the sigma^2_0 parameter. |

`a1` |
`a1/2` is the shape parameter for the inverse-gamma
prior on the sigma^2_1 parameter. |

`b1` |
`b1/2` is the scale parameter for the inverse-gamma
prior on the sigma^2_1 parameter. |

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

Consider the following partially observed 2 by 2 contingency table for
unit *t* where *t=1,...,ntables*:

| Y=0 | | Y=1 | | | |

- - - - - | - - - - - | - - - - - | - - - - - |

X=0 | | Y0[t] | | | |r0[t] |

- - - - - | - - - - - | - - - - - | - - - - - |

X=1 | | Y1[t] | | | | r1[t] |

- - - - - | - - - - - | - - - - - | - - - - - |

| c0[t] | | c1[t] | | N[t] |

Where *r0[t]*, *r1[t]*,
*c0[t]*, *c1[t]*, and
*N[t]* are non-negative integers that are
observed. The interior cell entries are not observed. It is
assumed that *Y0[t]|r0[t] ~ Binomial(r0[t], p0[t])* and
*Y1[t]|r1[t] ~
Binomial(r1[t],p1[t])*. Let *theta0[t] = log(p0[t]/(1-p0[t]))*,
and *theta1[t] =
log(p1[t]/(1-p1[t]))*.

The following prior distributions are
assumed: *theta0[t] ~ Normal(mu0, sigma^2_0)*,
*theta1[t] ~ Normal(mu1, sigma^2_1)*.
*theta0[t]* is assumed to be a priori independent of
*theta1[t]* for all t.
In addition, we assume the
following hyperpriors:
*mu0 ~ Normal(m0, M0)*,
*mu1 ~ Normal(m1,
M1)*,
*σ^2_0 ~
InvGamma(a0/2, b0/2)*, and
*σ^2_1 ~
InvGamma(a1/2, b1/2)*.

The default priors have been chosen to make the implied prior
distribution for *p0* and *p1*
*approximately* uniform on (0,1).

Inference centers on *p0*, *p1*, *mu0*,
*mu1*, *sigma^2_0*, and
*sigma^2_1*.
Univariate slice sampling (Neal, 2003) along with Gibbs sampling is
used to sample from the posterior density.

See Section 5.4 of Wakefield (2003) for discussion of the priors used
here. `MCMChierEI`

departs from the Wakefield model in that the
`mu0`

and `mu1`

are here assumed to be drawn from
independent normal distributions whereas Wakefield assumes they are
drawn from logistic distributions.

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

Jonathan C. Wakefield. 2003. ``Ecological inference for 2x2 tables." Read before the Royal Statistical Society, on November 12th, 2003.

Radford Neal. 2003. ``Slice Sampling" (with discussion). *Annals of
Statistics*, 31: 705-767.

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/.

`MCMCdynamicEI`

,
`plot.mcmc`

,`summary.mcmc`

## Not run: ## simulated data example set.seed(3920) n <- 100 r0 <- round(runif(n, 400, 1500)) r1 <- round(runif(n, 100, 4000)) p0.true <- pnorm(rnorm(n, m=0.5, s=0.25)) p1.true <- pnorm(rnorm(n, m=0.0, s=0.10)) y0 <- rbinom(n, r0, p0.true) y1 <- rbinom(n, r1, p1.true) c0 <- y0 + y1 c1 <- (r0+r1) - c0 ## plot data tomogplot(r0, r1, c0, c1) ## fit exchangeable hierarchical model post <- MCMChierEI(r0,r1,c0,c1, mcmc=40000, thin=5, verbose=TRUE, seed=list(NA, 1)) p0meanHier <- colMeans(post)[1:n] p1meanHier <- colMeans(post)[(n+1):(2*n)] ## plot truth and posterior means pairs(cbind(p0.true, p0meanHier, p1.true, p1meanHier)) ## End(Not run)

[Package *MCMCpack* version 0.5-2 Index]