hybrid.lcm {lca}R Documentation

Hybrid Sampling from posterior of Latent Class Model

Description

Use a hybrid of Metropolis-Hastings and pure Gibbs sampling to explore the posterior distribution of a Latent Class Model with Dirichlet prior distributions. The general Metropolis-Hastings steps are designed to prevent the sampler becoming ‘stuck’ in local modes in the posterior surface. The position of these modes must be specified.

Usage

hybrid.lcm(dat, H, modes, prop.mh = 0.1, N = 10000, n.thin = 1, n.burn = 1000, prior.theta = rep(1/H, H), prior.eta = NULL, start.theta = NULL, start.eta = NULL, na.ignore = FALSE, lls = TRUE, mode.weights, verbose = TRUE)

Arguments

dat object of class freq.table containing observations.
H number of latent classes.
modes matrix of Dirichlet parameters containing mode locations.
prop.mh proportion of iterations to use general Metropolis-Hastings step.
N total number of iterations in the main run.
n.thin thinning factor for main run - used to save memory for large N.
n.burn number of iterations during burn-in.
prior.theta numeric vector of length H containing Dirichlet prior parameters for latent class proportions.
prior.eta array containing Dirichlet prior parameters on other parameters.
start.theta numeric vector of length H containing initial parameter values for latent class proportions.
start.eta numeric array containing initial parameter values for other parameters.
na.ignore logical - should missing values be ignored?
lls logical - should log-likelihood at each iteration be recorded?
mode.weights numeric vector containing proportion of attempted MH jumps to each mode.
verbose logical - should progress be sent to stdout?

Details

The MCMC sampling works as follows: at each step, a general Metropolis Hastings (MH) step is chosen with probability prop.mh, otherwise a Gibbs sampling step is selected. The MH step selects from a proposal distribution which is a mixture based upon the locations of the modes in the posterior. The proposals are independent of the current parameter estimates.

Specifically, each mode is approximated using a product of Dirichlet distributions (one for each set of parameters constrained to sum to 1) whose parameters are given in modes. To ensure irreducibility, the mixture includes a proposal which is uniform in the whole parameter space.

Value

An object of class lcm.hybrid

[[1]] a numeric matrix containing parameter estimates at each iteration. Each row represents a single saved iteration, and each column a parameter, thus there are N/n.thin rows in total.
H H.
J the number of items.
K a numeric vector containing the number of possible responses to each item.
dat dat.
ll a list containing the value of the log-likelihood at each iteration.
modes.visited
moved logical vector explaining whether a proposed MH step was accepted. Gibbs steps coded as NA.

Author(s)

Robin Evans

References

Tierney, L. (1994) - Markov Chains for Exploring Posterior Distributions

See Also

gibbs.lcm


[Package lca version 0.2 Index]