In wtagr/dbicc: Generalized reliability based on distances

A brief guide to the dbicc package

This package implements a new approach to reliability, extending the classical intraclass correlation coefficient (ICC) to a new measure based on arbitrary distances among observations (Xu et al., 2020).

The key function dm2icc computes the reliability (distance-based ICC, or dbICC) for a given matrix of distances among observations, while dm2icc.bt gives boostrap confidence intervals for the dbICC value.

The dataset dt2v3 is the fMRI data set analyzed by Xu et al. (2020). plotdmat visualizes the associated distance matrix.

Please feel free to contact Meng Xu [e-mail] with questions and bug reports.

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Installation

This package can be installed from GitHub, and loaded, as follows:

# devtools::install_github("wtagr/dbicc", force = TRUE)
library(dbicc)

Distance matrix computation

The package does not include functions to compute the distance matrix, but the following function performs this step for our application. It inputs a list object and outputs a distance matrix determined by the method argument: method = 'f' yields the Frobenius norm, method = 'r' the $\sqrt{1-r}$ distance, and method = 'l1' the $\ell_1$ distance (sum of absolute differences).

mdist <- function(datalist, method=c("f")) {
    dmat<-matrix(0,length(datalist),length(datalist))
    for (i in 2:length(datalist)) for (j in 1:(i-1)){
        if (method=="r"){
            v1<-datalist[[i]][lower.tri(datalist[[i]], diag = FALSE)]
            v2<-datalist[[j]][lower.tri(datalist[[j]], diag = FALSE)]
            r<-cor(v1,v2)
            dmat[i,j]=dmat[j,i]=sqrt(1-r)
        } else if (method=='l1'){
            dmat[i,j]=dmat[j,i]=sum(abs(datalist[[i]]-datalist[[j]]))
        } else {
            dmat[i,j]=dmat[j,i]=norm(datalist[[i]]-datalist[[j]],type=method)
        }
    }
    return(dmat)
}

dt2v3 contains fMRI time series for 25 individuals with 2 scans each, grouped by individual. Here we compute a matrix of distances among the correlation matrices resulting from these multivariate time series:

data(dt2v3)

# compute correlation matrices
cor2v3 <- lapply(dt2v3,cor)

# compute the matrix of distances among the correlation matrices
distmat <- mdist(cor2v3)

# visualize
plotdmat(distmat, 25, 2)

Compute the reliability

We can then input the distance matrix to dm2icc, to compute the dbICC:

dm2icc(distmat,25,2)

Obtain confidence interval for the dbICC, based on 100 boostrap replicates (a larger number of replicates is recommended in practice):

dm2icc.bt(distmat,25,2, nB=100)

Reference

Xu, M., Reiss, P. T., and Cribben, I. (2020). Generalized reliability based on distances. Biometrics, to appear.

wtagr/dbicc documentation built on April 8, 2020, 7:18 p.m.