gibbsPLMIX function

Gibbs sampling for a Bayesian mixture of Plackett-Luce models

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

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$$x$$K 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$$x$$G matrix of binary mixture component memberships; p is a numeric G$$x$$K 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$$x$$K 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.

Returns

A list of S3 class gsPLMIX with named elements:

• W: Numeric L$$x$$G matrix with MCMC samples of the mixture weights.

• P: Numeric L$$x$$(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.

Details

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

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

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.

Author(s)

Cristina Mollica and Luca Tardella