rankICC {rankICC}

Rank ICC with two hierarchies

Description

rankICC computes the rank intraclass correlation coefficient (ICC) of a two-level hierarchical distribution. It can be used with any orderable variable, including continuous and discrete variables. Different weighting methods are provided, including methods assigning equal weights to observations or to clusters.

Usage

rankICC(
  x,
  cluster,
  weights = c("obs", "clusters", "ess", "combination"),
  conf.int = 0.95,
  fisher = FALSE,
  na.rm = FALSE,
  ...
)

Arguments

x

a numeric or factor vector.

cluster

a vector of cluster index corresponding to x.

weights

a character string indicating which weighting method is used. Or an optional vector of user-defined weights to be used. Should be one of the strings "obs", "clusters", "ess", "combination", or a numeric vector. Default is "obs". See Details.

conf.int

numeric specifying confidence interval level.

fisher

logical, indicating whether to apply Fisher transformation to compute confidence intervals.

na.rm

logical. Should missing values be removed?

...

additional arguments to be passed to the iteration function if weights is "ess" or "combination". Specifying the tolerance via "tol" and the maximum iteration times via "maxIter".

Details

"obs" assigns equal weights to observations; p_{ij} = 1/N, where N is the total number of observations. "clusters" assigns equal weights to clusters; p_{ij} = 1/(nk_i), where n is the total number of clusters and k_i is the cluster size. "ess" and "combination" implement iterations until convergence; p_{ij}(\gamma_I)=1/(1+k_i\gamma_I)/\{\sum_{j=1}^n k_j/(1+k_j\gamma_I)\} for "ess", p_{ij}(\gamma_I)=(1-\gamma_I)/N+\gamma_I/(nk_i) for "combination".

Value

a vector with following components.

rankICC	the rank ICC.
SE	the standard error.
Lower, Upper	the lower and upper bound of the confidence interval.

References

Tu, S., Li, C., Zeng, D., and Shepherd, B. E. (2023). Rank intraclass correlation for clustered data. Statistics in Medicine 42, 4333-4348.

Examples

k <- 50; m <- 5
sigma.u <- 1; sigma.e <- 2
u <- rnorm(k, 5, sigma.u)
x1 <- matrix(NA, k, m)
for (i in 1:k){
x1[i,] <- u[i] + rnorm(5, 0, sigma.e)
}
x <- as.vector(t(x1))
cluster <- rep(1:k, each=5)
rankICC(x, cluster, weights = "clusters")
rankICC(x, cluster, weights = "ess", tol = 1e-4, maxIter = 10)