confintMSmix function

Asymptotic confidence intervals for the fitted mixture of Mallows models with Spearman distance

Return the asymptotic confidence intervals of the continuous parameters (component-specific precisions and weights) of a mixture of Mallows models with Spearman distance fitted to full rankings.

print method for class "ciMSmix".

confintMSmix(object, conf_level = 0.95)

## S3 method for class 'ciMSmix'
print(x, ...)

Arguments

• object: An object of class "emMSmix" returned by fitMSmix.
• conf_level: Numeric: value in the interval (0,1] indicating the desired confidence level of the interval estimates. Defaults to 0.95.
• x: An object of class "ciMSmix" returned by confintMSmix.
• ...: Further arguments passed to or from other methods (not used).

Returns

An object of class "ciMSmix", namely a list with the following named components:

• ci_theta: Numeric G$$x$$2 matrix with the confidence intervals of the component-specific precision parameters in each row.
• ci_weights: Numeric G$$x$$2 matrix with the confidence intervals of the mixture weights in each row (when $G>1$), otherwise NULL.

Details

The current implementation of the asymptotic confidence intervals assumes that the observed rankings are complete.

Examples

## Example 1. Simulate rankings from a 2-component mixture of Mallows 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 asymptotic confidence intervals for the MLEs of the precision.
ci95_fit1 <- confintMSmix(object = fit1)
print(ci95_fit1)
# Fit the true model.
set.seed(123)
fit2 <- fitMSmix(rankings = rankings, n_clust = 2, n_start = 10)
# Compute the asymptotic confidence intervals for the MLEs of the weights and precisions.
ci95_fit2 <- confintMSmix(object = fit2)
print(ci95_fit2)

References

Crispino M, Mollica C and Modugno L (2025+). 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. Wiley Series in Probability and Statistics, John Wiley & Sons.