gibbsPLMIX {PLMIX}

Gibbs sampling for a Bayesian mixture of Plackett-Luce models

Description

Perform Gibbs sampling simulation for a Bayesian mixture of Plackett-Luce models fitted to partial orderings.

Usage

gibbsPLMIX(pi_inv, K, G, init = list(z = NULL, p = NULL),
  n_iter = 1000, n_burn = 500, hyper = list(shape0 = matrix(1, nrow =
  G, ncol = K), rate0 = rep(0.001, G), alpha0 = rep(1, G)),
  centered_start = FALSE)

Arguments

pi_inv

An object of class top_ordering, collecting the numeric N\timesK data matrix of partial orderings, or an object that can be coerced with as.top_ordering.

K

Number of possible items.

G

Number of mixture components.

init

List of named objects with initialization values: z is a numeric N\timesG matrix of binary mixture component memberships; p is a numeric G\timesK matrix of component-specific support parameters. If starting values are not supplied (NULL), they are randomly generated with a uniform distribution. Default is NULL.

n_iter

Total number of MCMC iterations.

n_burn

Number of initial burn-in drawings removed from the returned MCMC sample.

hyper

List of named objects with hyperparameter values for the conjugate prior specification: shape0 is a numeric G\timesK matrix of shape hyperparameters; rate0 is a numeric vector of G rate hyperparameters; alpha0 is a numeric vector of G Dirichlet hyperparameters. Default is vague prior setting.

centered_start

Logical: whether a random start whose support parameters and weights should be centered around the observed relative frequency that each item has been ranked top. Default is FALSE. Ignored when init is not NULL.

Details

The size L of the final MCMC sample is equal to n_iter-n_burn.

Value

A list of S3 class gsPLMIX with named elements:

W

Numeric L\timesG matrix with MCMC samples of the mixture weights.

P

Numeric L\times(G*K) matrix with MCMC samples of the component-specific support parameters.

log_lik

Numeric vector of L posterior log-likelihood values.

deviance

Numeric vector of L posterior deviance values (-2 * log_lik).

objective

Numeric vector of L objective function values (that is the kernel of the log-posterior distribution).

call

The matched call.

Author(s)

Cristina Mollica and Luca Tardella

References

Mollica, C. and Tardella, L. (2017). Bayesian Plackett-Luce mixture models for partially ranked data. Psychometrika, 82(2), pages 442–458, ISSN: 0033-3123, DOI: 10.1007/s11336-016-9530-0.

Examples

data(d_carconf)
GIBBS <- gibbsPLMIX(pi_inv=d_carconf, K=ncol(d_carconf), G=3, n_iter=30, n_burn=10)
str(GIBBS)
GIBBS$P
GIBBS$W