gibbsPLMIX_with_norm: Gibbs sampling for a Bayesian mixture of Plackett-Luce models

In lucatardella/PLMIX: Bayesian Analysis of Finite Mixture of Plackett-Luce Models

Description

Perform Gibbs sampling simulation for a Bayesian mixture of Plackett-Luce models fitted to partial orderings. Differently from the gibbsPLMIX function it contains a normalization step for the support parameters which should be proven to be equivalent to the case where the normalization step is skipped and the support parameter space is unidentified up to a proportionality constant.

Usage

gibbsPLMIX_with_norm(
  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 NxK 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 NxG matrix of binary mixture component memberships; p is a numeric GxK 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 GxK 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 LxG matrix with MCMC samples of the mixture weights.
P	Numeric Lx(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_with_norm(pi_inv=d_carconf, K=ncol(d_carconf), G=3, n_iter=30, n_burn=10)
str(GIBBS)
GIBBS$P
GIBBS$W

lucatardella/PLMIX documentation built on Jan. 1, 2021, 8:25 a.m.