bicPLMIX {PLMIX}

BIC for the MLE of a mixture of Plackett-Luce models

Description

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

Usage

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

Arguments

max_log_lik

Maximized log-likelihood value.

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.

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.

Details

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,\dots,K), the default values of ref_known and ref_vary are set equal, respectively, to TRUE and FALSE.

Value

A list of two named objects:

max_log_lik

The max_log_lik argument.

bic

BIC value.

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.

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.

See Also

mapPLMIX and mapPLMIX_multistart

Examples

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