Reduced.Binary {GLMMarp}R Documentation

Reduced MCMC by Fixing Part of the Parameters

Description

This function generates a sample from the reduced Markov Chain Monte Carlo simulation for computing the Bayes factor for model comparison. The sample cannot be used for inferences about the parameters, but only used for the Bayes factor calculation. The function is based on the reduced form of the GLMM-AR(p) model. It is not necessary to check convergence on the sample.

Usage

Reduced.Binary(Y,X, W, S, unit.id, time.id, m=1000, burnin=500, mcmc.pos,
               beta0,B0, D0, d0, E0, e0, nlag,tracking,
               monitor=c("rho","q.rho", "beta", "bi", "ct", "D", "E", "ystar", "u"), 
               fixed="NULL")

Arguments

Y A vector of the dichotomous response variable taking values of 0 and 1.
X A matrix of covariates with fixed effects at all levels.
W A matrix of covariates with subject-varying effects.
S A matrix of covariates with time-varying effects.
unit.id A vector of subject index, i.e., the i's. Note: the number of observations of each unit should be larger than the lag order, nlag. Those units which have fewer than or equal to nlag observations should be taken out of the sample in order to use the function.
time.id A vector of time index, i.e., the t's. Note: no missing observations in the middle of the sample time periods of a unit are allowed. In other words, unbalanced data structures are allowed, but no broken data structure.
m The number of iterations after burn-in and to be returned.
burnin The number of burn-in iterations for the sampler.
mcmc.pos The MCMC output generated by the full MCMC by using the function of GLMMARp.Binary.
beta0 The prior mean of beta. This should be a vector with dimension equal to the number of fixed-effect parameters in the reduced form. Since the dimension is difficult for the user to compute when the model contains multiple random coefficients and multiple group-level predictors, the function will provide the correct dimension in the error message if the dimension of beta0 is incorrectly specified, and the user can respecify beta0 with this information and recall the function.
B0 The prior covariance matrix of beta. This should be a positive definite matrix with dimension equal to the number of betas in the reduced form of GLMM-AR(p).
d0, D0 The degree of freedom and scale matrix of the Wishart prior on b_i which are the subject-level residuals. D0 should not be too defuse, otherwise it may takes a long time for the chain to converge. Recommended values is a*I, where a is between 1.67 and 10. No default is provided.
e0, E0 The degree of freedom and scale matrix of the Wishart prior on c_t which are the time-level residuals. E0 should not be too defuse, otherwise it may takes a long time for the chain to converge. Recommended values is a*I, where a is between 1.67 and 10. No default is provided. All the priors put into this function should be the same as those used in the full MCMC.
nlag A scalar of the lag order p, which should be an integer equal to or greater than 1. At this stage, the function does not support the GLMM-AR(0) moel, which can be estimated by using BUGs or JAGs.
tracking The tracking interval in the simulation. Every "tracking" iterations, the function will return the information about how many iterations in total have been done. The default is 0 and no tracking information will be given during the simulation.
monitor A string contains the names of parameters whose MCMC output are to be returned. The string has to be a subset of ("rho", "beta", "bi", "ct", "D", "E", "ystar", "u") which is also the default.
fixed A string specifying which parameters are fixed in the reduced simulation.

Details

ReducedMCMC.Binary is a funtion for conducting reduced runs for empirically integration in the process of computing the Bayes factor. The partition of the parameters is set by the function, and the user is not given the option of re-partitioning those parameters.

Value

A list that contains the posterior sample. The same format as the sample returned by GLMMARp.Binary().

References

Albert, James A. and Siddhartha Chib. 1993. "Bayesian Analysis of Binary and Polychotomous Response Data." Journal of the American Statistical Association. 88: 669-679.

Chib, Siddhartha. 1995. "Marginal Likelihood from the Gibbs Output." Journal of the American Statistical Association. 90: 1313-1321.

Chib, Siddhartha, and Ivan Jeliazkov. 2001. "Marginal Likelihood from the Metropolis-Hastings Output." Journal of the American Statistical Association. 96: 270-281.

Examples

   ## Not run: 

   ## End(Not run)

[Package GLMMarp version 0.1-1 Index]