label_switchPLMIX function

Label switching adjustment of the Gibbs sampling simulations for Bayesian mixtures of Plackett-Luce models

Remove the label switching phenomenon from the MCMC samples of Bayesian mixtures of Plackett-Luce models with $G>1$ components.

label_switchPLMIX(pi_inv, seq_G, MCMCsampleP, MCMCsampleW, MAPestP,
  MAPestW, parallel = 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.
• seq_G: Numeric vector with the number of components of the Plackett-Luce mixtures to be assessed.
• MCMCsampleP: List of size length(seq_G), whose generic element is a numeric L$$x$$(G*K) matrix with the MCMC samples of the component-specific support parameters to be processed.
• MCMCsampleW: List of size length(seq_G), whose generic element is a numeric L$$x$$G matrix with the MCMC samples of the mixture weights to be processed.
• MAPestP: List of size length(seq_G), whose generic element is a numeric G$$x$$K matrix with the MAP estimates of the component-specific support parameters to be used as a pivot in the PRA method (see 'Details').
• MAPestW: List of size length(seq_G), whose generic element is a numeric vector with the MAP estimates of the $G$ mixture weights to be used as a pivot in the PRA method (see 'Details').
• parallel: Logical: whether parallelization should be used. Default is FALSE.

Returns

A list of named objects:

• final_sampleP: List of size length(seq_G), whose generic element is a numeric G$$x$$K$$x$$L array with the MCMC samples of the component-specific support parameters adjusted for label switching.

• final_sampleW: List of size length(seq_G), whose generic element is a numeric L$$x$$G matrix with the MCMC samples of the mixture weights adjusted for label switching.

Details

The label_switchPLMIX function performs the label switching adjustment of the MCMC samples via the Pivotal Reordering Algorithm (PRA) described in Marin et al (2005), by recalling the pra function from the label.switching package.

Examples

data(d_carconf)
K <- ncol(d_carconf)

## Fit 1- and 2-component PL mixtures via MAP estimation
MAP_1 <- mapPLMIX_multistart(pi_inv=d_carconf, K=K, G=1, 
                             n_start=2, n_iter=400*1)

MAP_2 <- mapPLMIX_multistart(pi_inv=d_carconf, K=K, G=2, 
                             n_start=2, n_iter=400*2)
                                   
MAP_3 <- mapPLMIX_multistart(pi_inv=d_carconf, K=K, G=3, 
                             n_start=2, n_iter=400*3)
                                   
mcmc_iter <- 30
burnin <- 10

## Fit 1- and 2-component PL mixtures via Gibbs sampling procedure
GIBBS_1 <- gibbsPLMIX(pi_inv=d_carconf, K=K, G=1, n_iter=mcmc_iter, 
                      n_burn=burnin, init=list(p=MAP_1$mod$P_map,
                      z=binary_group_ind(MAP_1$mod$class_map,G=1)))
GIBBS_2 <- gibbsPLMIX(pi_inv=d_carconf, K=K, G=2, n_iter=mcmc_iter, 
                      n_burn=burnin, init=list(p=MAP_2$mod$P_map,
                      z=binary_group_ind(MAP_2$mod$class_map,G=2)))
GIBBS_3 <- gibbsPLMIX(pi_inv=d_carconf, K=K, G=3, n_iter=mcmc_iter, 
                      n_burn=burnin, init=list(p=MAP_3$mod$P_map,
                      z=binary_group_ind(MAP_3$mod$class_map,G=3)))
                            
## Adjusting the MCMC samples for label switching
LS <- label_switchPLMIX(pi_inv=d_carconf, seq_G=1:3, 
                   MCMCsampleP=list(GIBBS_1$P, GIBBS_2$P, GIBBS_3$P), 
                   MCMCsampleW=list(GIBBS_1$W, GIBBS_2$W, GIBBS_3$W), 
                   MAPestP=list(MAP_1$mod$P_map, MAP_2$mod$P_map, MAP_3$mod$P_map), 
                   MAPestW=list(MAP_1$mod$W_map, MAP_2$mod$W_map, MAP_3$mod$W_map))
str(LS)

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.

Papastamoulis, P. (2016). label.switching: An R Package for Dealing with the Label Switching Problem in MCMC Outputs. Journal of Statistical Software, 69 (1), pages 1--24, DOI: 10.18637/jss.v069.c01.

Marin, J. M., Mengersen, K. and Robert, C.P. (2005). Bayesian modelling and inference on mixtures of distributions. Handbook of Statistics (25), D. Dey and C.R. Rao (eds). Elsevier-Sciences.

See Also

pra

Author(s)

Cristina Mollica and Luca Tardella