Compute the consensus ranking using either cumulative
probability (CP) or maximum a posteriori (MAP) consensus
(Vitelli et al. 2018)
. For mixture models, the consensus
is given for each mixture. Consensus of augmented ranks can also be
computed for each assessor, by setting parameter = "Rtilde".
Arguments
- model_fit
A model fit.
- ...
Other arguments passed on to other methods. Currently not used.
- type
Character string specifying which consensus to compute. Either
"CP"or"MAP". Defaults to"CP".- parameter
Character string defining the parameter for which to compute the consensus. Defaults to
"rho". Available options are"rho"and"Rtilde", with the latter giving consensus rankings for augmented ranks.- assessors
When
parameter = "rho", this integer vector is used to define the assessors for which to compute the augmented ranking. Defaults to1L, which yields augmented rankings for assessor 1.
References
Vitelli V, Sørensen, Crispino M, Arjas E, Frigessi A (2018). “Probabilistic Preference Learning with the Mallows Rank Model.” Journal of Machine Learning Research, 18(1), 1–49. https://jmlr.org/papers/v18/15-481.html.
See also
Other posterior quantities:
assign_cluster(),
compute_posterior_intervals(),
get_acceptance_ratios(),
heat_plot(),
plot.BayesMallows(),
plot.SMCMallows(),
plot_elbow(),
plot_top_k(),
predict_top_k(),
print.BayesMallows()
Examples
# The example datasets potato_visual and potato_weighing contain complete
# rankings of 20 items, by 12 assessors. We first analyse these using the
# Mallows model:
model_fit <- compute_mallows(setup_rank_data(potato_visual))
# Se the documentation to compute_mallows for how to assess the convergence of
# the algorithm. Having chosen burin = 1000, we compute posterior intervals
burnin(model_fit) <- 1000
# We then compute the CP consensus.
compute_consensus(model_fit, type = "CP")
#> cluster ranking item cumprob
#> 1 Cluster 1 1 P12 1.000
#> 2 Cluster 1 2 P13 1.000
#> 3 Cluster 1 3 P9 0.978
#> 4 Cluster 1 4 P10 0.973
#> 5 Cluster 1 5 P17 0.879
#> 6 Cluster 1 6 P7 0.917
#> 7 Cluster 1 7 P14 1.000
#> 8 Cluster 1 8 P16 1.000
#> 9 Cluster 1 9 P1 0.540
#> 10 Cluster 1 10 P5 0.657
#> 11 Cluster 1 11 P11 1.000
#> 12 Cluster 1 12 P19 1.000
#> 13 Cluster 1 13 P20 0.568
#> 14 Cluster 1 14 P18 1.000
#> 15 Cluster 1 15 P6 0.977
#> 16 Cluster 1 16 P4 0.621
#> 17 Cluster 1 17 P2 0.908
#> 18 Cluster 1 18 P15 1.000
#> 19 Cluster 1 19 P3 1.000
#> 20 Cluster 1 20 P8 1.000
# And we compute the MAP consensus
compute_consensus(model_fit, type = "MAP")
#> cluster map_ranking item probability
#> 1 Cluster 1 1 P12 0.154
#> 2 Cluster 1 2 P13 0.154
#> 3 Cluster 1 3 P9 0.154
#> 4 Cluster 1 4 P10 0.154
#> 5 Cluster 1 5 P17 0.154
#> 6 Cluster 1 6 P7 0.154
#> 7 Cluster 1 7 P14 0.154
#> 8 Cluster 1 8 P16 0.154
#> 9 Cluster 1 9 P1 0.154
#> 10 Cluster 1 10 P5 0.154
#> 11 Cluster 1 11 P11 0.154
#> 12 Cluster 1 12 P19 0.154
#> 13 Cluster 1 13 P20 0.154
#> 14 Cluster 1 14 P18 0.154
#> 15 Cluster 1 15 P6 0.154
#> 16 Cluster 1 16 P4 0.154
#> 17 Cluster 1 17 P2 0.154
#> 18 Cluster 1 18 P15 0.154
#> 19 Cluster 1 19 P3 0.154
#> 20 Cluster 1 20 P8 0.154
if (FALSE) { # \dontrun{
# CLUSTERWISE CONSENSUS
# We can run a mixture of Mallows models, using the n_clusters argument
# We use the sushi example data. See the documentation of compute_mallows for
# a more elaborate example
model_fit <- compute_mallows(
setup_rank_data(sushi_rankings),
model_options = set_model_options(n_clusters = 5))
# Keeping the burnin at 1000, we can compute the consensus ranking per cluster
burnin(model_fit) <- 1000
cp_consensus_df <- compute_consensus(model_fit, type = "CP")
# We can now make a table which shows the ranking in each cluster:
cp_consensus_df$cumprob <- NULL
stats::reshape(cp_consensus_df, direction = "wide", idvar = "ranking",
timevar = "cluster",
varying = list(sort(unique(cp_consensus_df$cluster))))
} # }
if (FALSE) { # \dontrun{
# MAP CONSENSUS FOR PAIRWISE PREFENCE DATA
# We use the example dataset with beach preferences.
model_fit <- compute_mallows(setup_rank_data(preferences = beach_preferences))
# We set burnin = 1000
burnin(model_fit) <- 1000
# We now compute the MAP consensus
map_consensus_df <- compute_consensus(model_fit, type = "MAP")
# CP CONSENSUS FOR AUGMENTED RANKINGS
# We use the example dataset with beach preferences.
model_fit <- compute_mallows(
setup_rank_data(preferences = beach_preferences),
compute_options = set_compute_options(save_aug = TRUE, aug_thinning = 2))
# We set burnin = 1000
burnin(model_fit) <- 1000
# We now compute the CP consensus of augmented ranks for assessors 1 and 3
cp_consensus_df <- compute_consensus(
model_fit, type = "CP", parameter = "Rtilde", assessors = c(1L, 3L))
# We can also compute the MAP consensus for assessor 2
map_consensus_df <- compute_consensus(
model_fit, type = "MAP", parameter = "Rtilde", assessors = 2L)
# Caution!
# With very sparse data or with too few iterations, there may be ties in the
# MAP consensus. This is illustrated below for the case of only 5 post-burnin
# iterations. Two MAP rankings are equally likely in this case (and for this
# seed).
model_fit <- compute_mallows(
setup_rank_data(preferences = beach_preferences),
compute_options = set_compute_options(
nmc = 1005, save_aug = TRUE, aug_thinning = 1))
burnin(model_fit) <- 1000
compute_consensus(model_fit, type = "MAP", parameter = "Rtilde",
assessors = 2L)
} # }