bicPLMIX: BIC for the MLE of a mixture of Plackett-Luce models
In PLMIX: Bayesian Analysis of Finite Mixtures of Plackett-Luce Models for Partial Rankings/Orderings

Description Usage Arguments Details Value Author(s) References See Also Examples

Compute BIC value for the MLE of a mixture of Plackett-Luce models fitted to partial orderings.

1	bicPLMIX(max_log_lik, pi_inv, G, ref_known = TRUE, ref_vary = FALSE)

`max_log_lik`	Maximized log-likelihood value.
`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`.
`G`	Number of mixture components.
`ref_known`	Logical: whether the component-specific reference orders are known (not to be estimated). Default is `TRUE`.
`ref_vary`	Logical: whether the reference orders vary across mixture components. Default is `FALSE`.

The max_log_lik and the BIC values can be straightforwardly obtained from the output of the mapPLMIX and mapPLMIX_multistart functions when the default noninformative priors are adopted in the MAP procedure. So, the bicPLMIX function is especially useful to compute the BIC value from the output of alternative MLE methods for mixtures of Plackett-Luce models implemented, for example, with other softwares.

The ref_known and ref_vary arguments accommodate for the more general mixture of Extended Plackett-Luce models (EPL), involving the additional reference order parameters (Mollica and Tardella 2014). Since the Plackett-Luce model is a special instance of the EPL with the reference order equal to the identity permutation (1,…,K), the default values of ref_known and ref_vary are set equal, respectively, to TRUE and FALSE.

A list of two named objects:

`max_log_lik`	The `max_log_lik` argument.
`bic`	BIC value.

Cristina Mollica and Luca Tardella

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.

Mollica, C. and Tardella, L. (2014). Epitope profiling via mixture modeling for ranked data. Statistics in Medicine, 33(21), pages 3738–3758, ISSN: 0277-6715, DOI: 10.1002/sim.6224.

Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist., 6(2), pages 461–464, ISSN: 0090-5364, DOI: 10.1002/sim.6224.

mapPLMIX and mapPLMIX_multistart

data(d_carconf)
K <- ncol(d_carconf)
MAP_mult <- mapPLMIX_multistart(pi_inv=d_carconf, K=K, G=3, n_start=2, n_iter=400*3)
bicPLMIX(max_log_lik=MAP_mult$mod$max_objective, pi_inv=d_carconf, G=3)$bic

## Equivalently
MAP_mult$mod$bic