dirichlet.o {bspmma}

Mixture of Ordinary Dirichlet Model

Description

MCMC generation of posterior distributions for the usual (unconditional) Dirichlet mixing distribution model, using an m+1-cycle Gibbs sampler

Usage

dirichlet.o(data, ncycles=10, M=1,d=c(.1,.1,0,1000),
            start=NULL,K=100)

Arguments

data

is a two-column matrix with a row for each study in the meta-analysis. The first column is the log of estimate of relative risk, often a log(odds ratio). The second column is the true or estimated standard error of the log(odds ratio).

ncycles

is the number of cycles of the Markov chain.

M

is the precision parameter of the Dirichlet process prior.

d

is a vector of length four with the values of the hyperparameters, in order, the location and scale of the Gamma inverse prior, mean and variance multiplier for the normal prior on mu.

start

is an optional vector containing starting values for the parameters, \psi_i, i=1, \ldots, m where m is the number of studies in the meta-analysis, \mu and \tau.

K

is the number of summands to include when one uses Sethuraman's (1994) representation for getting the parameter \eta = mean(F). If you do not intend to use this parameter, then take K small, say K=10.

Details

This function generates MCMC output for the posterior distribution for the parameters \psi_i, i=1,...,m where m is the number of studies in the meta-analysis, \mu, \tau, and \eta in the ordinary Dirichlet mixing model for random-effects meta-analysis. Notation is taken from Burr (2012), Model 2 and 3.

The MCMC algorithm for estimating the posterior under this model is given in Burr and Doss (2005). The chain is a (m+1)-cycle Gibbs sampler which cycles through the vector of \psi_i's and the triple \mu, \tau, \eta, and the main part of the computational burden is in the first part of the cycle, the generation of the vector of \psi_i's.

Value

call

the call that resulted in this object

ncycles

the number of cycles in the Markov chain

M

the value of the precision parameter for the conditional Dirichlet model

prior

the vector length four of hyperparameters

chain

A matrix with ncycles +1 rows and m+3 columns, where m is the number of studies in the meta-analysis. The rows hold output from the Markov chain runs (the first row is the initial values). Columns 1 through m hold the individual study parameters, the \psi_i's. The next two columns hold the mean and standard deviation parameters of the centering normal distribution of the Dirichlet prior, \mu and \tau, and the final column holds the parameter \eta. In the ordinary Dirichlet mixing model, the parameter \mu does not equal the mean of the distribution F of the \psi_i's; we denote this mean \eta and estimate it by Sethuraman's (1994) method.

start.user

logical, TRUE if the user supplied initial values of the parameter vector, FALSE if input argument start was not specified by the user.

start

vector of initial parameter values, whether default or user-supplied

References

Burr, Deborah (2012). “bspmma: An R package for Bayesian semi-parametric models for meta-analysis.” Journal of Statistical Software 50(4), 1–23. http://www.jstatsoft.org/v50/i04/.

Burr, D. and Doss, H. (2005). “A Bayesian semiparametric model for random-effects meta-analysis.” Journal of the American Statistical Association 100 242–251.

Sethuraman, J. (1994). “A constructive definition of Dirichlet priors.” Statistica Sinica 4, 639–650.

Examples

## Not run: 
data(breast.17) # the dataset
breast.data <- as.matrix(breast.17) # put data in matrix object
set.seed(1) # initialize the seed at 1 
diro <- dirichlet.o(breast.data, ncycles=4000, M=5)

## a short description of the model and Markov chain
print(diro1)

## the last mcmc cycle
diro$mcmc[4001,]

## End(Not run)