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Sample Correlation Matrix for Interval-valued Data

Source: R/int_cov.r
int_cor.Rd

Calculate the sample correlation matrix based on the covariance matrix.

Usage

int_cor(
  data = NULL,
  sigma_cc = NULL,
  sigma_rr = NULL,
  sigma_cr = NULL,
  LatentParam = NULL,
  LatentCase = c("U_id_symmetric", "U_id", "General"),
  cov = NULL
)

Arguments

data

An intData object containing the macrodata/interval data. If cov is not provided but data is provided, the covariance matrix is calculated based on the the sample covariance of the centers and ranges and the sample covariance between centers and ranges, and the parameters of the latent variables contained in the intData object. If cov and data are not provided, the covariance matrix is calculated based on sigma_cc, sigma_rr, sigma_cr, LatentParam, and LatentCase.

sigma_cc

Covariance matrix of the centers.

sigma_rr

Covariance matrix of the ranges.

sigma_cr

Covariance matrix between the centers and ranges.

LatentParam

A list with the parameters of the latent variables. Expects a list with a single number if LatentCase is "U_id_symmetric", a list of two numbers if LatentCase is "U_id", and a list of two matrices if LatentCase is "General", as in:

  • "U_id_symmetric": The latent variables are identically distributed and symmetric, so its parameters are:

    • \(\delta=\mathbb{E}(U^2)/4\)

  • "U_id": The latent variables are identically distributed, so its parameters are:

    • \(\delta=\mathbb{E}(U^2)/4\)

    • \(\mathbb{E}(U)\)

  • "General": The latent variables do not have any nice properties, so its parameters are:

    • \([\boldsymbol{\mathfrak{E}}_{UU}]_{j\ell}=\mathcal{E}(U_j,U_\ell)\), \(j\neq \ell\), with \(\mathcal{E}(U_j,U_\ell)=\int_0^1 F_{U_j}^{-1}(t) F_{U_\ell}^{-1}(t) \, dt\), and \([\boldsymbol{\mathfrak{E}}_{UU}]_{jj}=\mathbb{E}(U_j^2)\), \(j,\ell=1,\dots,p\)

    • \(\boldsymbol{\Psi}=\text{Diag}(\mathbb{E}(U_1),\dots,\mathbb{E}(U_p))\)

LatentCase

A string specifying which of the three scenarios applies to the latent variables:

  • "U_id_symmetric": The case where the latent variables are identically distributed and symmetric.

  • "U_id": The case where the latent variables are identically distributed.

  • "General": The case where the latent variables do not have any nice properties.

Defaults to "U_id_symmetric".

cov

Covariance matrix of the interval-valued data. If cov is provided, the correlation matrix is calculated based on it. If cov is not provided, the correlation matrix is calculated based on the data or the covariance matrices of the centers and ranges.

Value

The symbolic correlation matrix.

Details

This function calculates the correlation matrix based on the covariance matrix using the cov2cor function. The correlation matrix can be calculated either based on the data, the symbolic covariance matrix, or the covariance matrices of the centers and ranges. For more details, see int_cov.

References

Oliveira, M. R., Pinheiro, D., & Oliveira, L. (2025). Location and association measures for interval-valued data based on Mallows' distance. arXiv preprint arXiv:2407.05105. https://arxiv.org/abs/2407.05105

Examples

data(creditcard)
credit_card_cor <- int_cor(creditcard$intData)