Analysis of Interval DAta

Tools for the analysis of interval-valued data, including construction, visualization, and statistical modeling. The package provides the 'intData' class for representing interval-valued data, along with functions to aggregate microdata and to estimate parameters of latent distributions. Barycenter and covariance matrix estimation is implemented based on the Mallows distance (Oliveira et al. (2025) ). Robust estimation of the symbolic covariance matrix is implemented via the Interval Minimum Covariance Determinant (IMCD) estimator, enabling outlier detection based on the robust squared Interval-Mahalanobis distance, as proposed by Loureiro et al. (2026b) . Explainable outlier detection is supported through Shapley value based decomposition of the squared robust Interval-Mahalanobis distance, allowing assessment of variable contributions to outlyingness (Loureiro et al. (2026a) ). Shapley interaction indices are also implemented, along with visualization tools to support interpretation of the results.

AIDA: Analysis of Interval DAta

Overview

AIDA provides tools for the analysis of interval-valued data, including construction, visualization, robust estimation, and outlier detection. The R package is built around the intData class and is designed to support methodological research and applied workflows involving interval-valued data.

AIDA currently includes functionality for:

• Construction of interval-valued datasets
• Interval-valued covariance estimation based on Mallows distance
• Interval Minimum Covariance Determinant (IMCD) estimator
• Robust squared Interval-Mahalanobis distance
• Outlier detection based on robust distances
• Explainable outlier detection using Shapley values
• Visualization tools for interval data

Installation

You can install the development version from GitHub:

# install.packages("pak")
pak::pak("catarinaploureiro/AIDA")

Minimal Example

library(AIDA)
#> 
#> Attaching package: 'AIDA'
#> The following object is masked from 'package:base':
#> 
#>     rbind

# Create an intData object from the iris dataset, using the Species column as 
# grouping variable. We also specify the latent distribution as "General" to 
# estimate the parameters based on the microdata.
data(iris)
iris_int <- micro2intData(iris[,1:4], iris$Species, LatentCase = "General")

# Check the parameters of the latent distribution
iris_int@LatentParam
#> [[1]]
#>           [,1]      [,2]      [,3]      [,4]
#> [1,] 0.1835903 0.1554921 0.1660354 0.1990067
#> [2,] 0.1554921 0.1381013 0.1461729 0.1683492
#> [3,] 0.1660354 0.1461729 0.1627440 0.1828199
#> [4,] 0.1990067 0.1683492 0.1828199 0.2704900
#> 
#> [[2]]
#>            [,1]       [,2]       [,3]       [,4]
#> [1,] 0.01851852 0.00000000 0.00000000  0.0000000
#> [2,] 0.00000000 0.04199507 0.00000000  0.0000000
#> [3,] 0.00000000 0.00000000 0.02913753  0.0000000
#> [4,] 0.00000000 0.00000000 0.00000000 -0.1802821

# Compute the classical covariance and correlation matrices
iris_cov <- int_cov(iris_int)
iris_corr <- cov2cor(iris_cov)

# Pairs plot, the lower triangular shows scatter plots of the four variables, 
# while the upper triangular shows the interval correlation matrix.
plot_pairs_int(iris_int, corr = iris_corr, labels = colnames(iris_int))

Vignettes

For a full introduction about the intData class (Oliveira, Pinheiro, and Oliveira (2025)), see:

vignette("intData_examples", package = "AIDA")

For examples on the IMCD estimator and outlier detection based on the robust squared Interval-Mahalanobis distance (Loureiro et al. (2026b)), see:

vignette("IMCD_examples", package = "AIDA")

For examples on explainable outlier detection using Shapley values (Loureiro et al. (2026a)), see:

vignette("Shapley_examples", package = "AIDA")

References