# 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. ```r 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 ```r 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

label_switchPLMIX function