confintMSmix {MSmix}

Hessian-based confidence intervals for mixtures of Mallows models with Spearman distance

Description

Return the Hessian-based confidence intervals of the continuous parameters of a mixture of Mallow models with Spearman distance fitted to full rankings, namely the component-specific precisions and weights.

Usage

confintMSmix(
  object,
  sample_size = (if (length(object$mod$theta) > 1) NULL),
  conf_level = 0.95
)

Arguments

object

An object of class "emMSmix" returned by fitMSmix.

sample_size

Number of rankings in the observed sample. Needed only when the estimated mixture has a single (G=1) component.

conf_level

Value in the interval (0,1) indicating the desired confidence level of the interval estimates. Defaults to 0.95.

Details

The current implementation of the hessian-based confidence intervals assumes that the observed rankings are complete.

Value

A list with the following named components:

ci_theta

The confidence intervals for the precision parameters.

ci_weights

The confidence intervals for the mixture weights. Returned when G>1.

References

Crispino M, Mollica C, Modugno L, Casadio Tarabusi E, and Tardella L (2024+). MSmix: An R Package for clustering partial rankings via mixtures of Mallows Models with Spearman distance. (submitted)

Marden JI (1995). Analyzing and modeling rank data. Monographs on Statistics and Applied Probability (64). Chapman & Hall, ISSN: 0-412-99521-2. London.

Mclachlan G and Peel D (2000). Finite Mixture Models. Vol. 299. New York: Wiley.

Examples

## Example 1. Simulate rankings from a 2-component mixture of Mallow models
## with Spearman distance.
set.seed(123)
d_sim <- rMSmix(sample_size = 75, n_items = 8, n_clust = 2)
rankings <- d_sim$samples
# Fit the basic Mallows model with Spearman distance.
set.seed(123)
fit1 <- fitMSmix(rankings = rankings, n_clust = 1, n_start = 10)
# Compute the hessian-based confidence intervals for the MLEs of the precision.
confintMSmix(object = fit1, sample_size=nrow(rankings))
# Fit the true model.
set.seed(123)
fit2 <- fitMSmix(rankings = rankings, n_clust = 2, n_start = 10)
# Compute the hessian-based confidence intervals for the MLEs of the weights and precisions.
confintMSmix(object = fit2)