selectPLMIX_single: Bayesian selection criteria for mixtures of Plackett-Luce...

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

Bayesian selection criteria for mixtures of Plackett-Luce models

Description

Compute Bayesian comparison criteria for mixtures of Plackett-Luce models with a different number of components.

Usage

selectPLMIX_single(
  pi_inv,
  G,
  MCMCsampleP = NULL,
  MCMCsampleW = NULL,
  MAPestP,
  MAPestW,
  deviance,
  post_est = "mean"
)

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.
G	Number of mixture components.
MCMCsampleP	Numeric L\timesG*K matrix with the MCMC samples of the component-specific support parameters.
MCMCsampleW	Numeric L\timesG matrix with the MCMC samples of the mixture weights.
MAPestP	Numeric G\timesK matrix of MAP component-specific support parameter estimates.
MAPestW	Numeric vector of the G MAP estimates of the mixture weights.
deviance	Numeric vector of posterior deviance values.
post_est	Character string indicating the point estimates of the Plackett-Luce mixture parameters to be computed from the MCMC sample. This argument is ignored when MAP estimates are supplied in the MAPestP and MAPestW arguments. Default is "mean". Alternatively, one can choose "median".

Details

Two versions of DIC and BPIC are returned corresponding to two alternative ways of computing the penalty term: the former was proposed by Spiegelhalter et al. (2002) and is denoted with pD, whereas the latter was proposed by Gelman et al. (2004) and is denoted with pV. DIC2 coincides with AICM, that is, the Bayesian counterpart of AIC introduced by Raftery et al. (2007).

Value

A list of named objects:

point_estP	Numeric G\times(K+1) matrix with the point estimates of the Plackett-Luce mixture parameters. The (K+1)-th column contains estimates of the mixture weights.
point_estW	Numeric G\times(K+1) matrix with the point estimates of the Plackett-Luce mixture parameters. The (K+1)-th column contains estimates of the mixture weights.
D_bar	Posterior expected deviance.
D_hat	Deviance function evaluated at point_est.
pD	Effective number of parameters computed as D_bar-D_hat.
pV	Effective number of parameters computed as half the posterior variance of the deviance.
DIC1	Deviance Information Criterion with penalty term equal to pD.
DIC2	Deviance Information Criterion with penalty term equal to pV.
BPIC1	Bayesian Predictive Information Criterion obtained from DIC1 by doubling its penalty term.
BPIC2	Bayesian Predictive Information Criterion obtained from DIC2 by doubling its penalty term.
BICM1	Bayesian Information Criterion-Monte Carlo.
BICM2	Bayesian Information Criterion-Monte Carlo based on the actual MAP estimate given in the MAPestP and MAPestW arguments (unlike BICM1, no approximation of the MAP estimate from the MCMC sample).

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>.

Ando, T. (2007). Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. Biometrika, 94(2), pages 443–458.

Raftery, A. E, Satagopan, J. M., Newton M. A. and Krivitsky, P. N. (2007). BAYESIAN STATISTICS 8. Proceedings of the eighth Valencia International Meeting 2006, pages 371–416. Oxford University Press.

Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian data analysis. Chapman & Hall/CRC, Second Edition, ISBN: 1-58488-388-X. New York.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), pages 583–639.

PLMIX documentation built on July 1, 2025, 1:12 a.m.