rankICC3levels {rankICC}

Rank ICC with three hierarchies

Description

rankICC3levels computes the rank intraclass correlation coefficient (ICC) with three hierarchies. Starting from the innermost level, the three levels are named level 1, level 2, and level 3. The rank ICC at level 2 evaluates the rank correlation between a random pair from the same level-2 unit. The rank ICC at level 3 evaluates the rank correlation between a random pair from the same level-3 unit but different level-2 units.

Usage

rankICC3levels(
  x,
  level2,
  level3,
  weights = c("level1", "level2", "level3"),
  conf.int = 0.95,
  fisher = FALSE,
  na.rm = FALSE
)

Arguments

x

a numeric or factor vector.

level2

a vector indicating level-2 membership.

level3

a vector indicating level-3 membership.

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 "level1", "level2", "level3", or a numeric vector. Default is "level1". 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?

Details

"level1" assigns equal weights to level-1 units; p_{ijk}=1/(\sum_{i=1}^n\sum_{j=1}^{n_i}m_{ij}), where n is the total number of level-3 units, n_i is the number of level-2 units in the ith level-3 unit, and m_{ij} is the number of level-1 units in the jth level-2 unit and the ith level-3 unit. "level2" assigns equal weights to level-2 units; p_{ijk}=1/(m_{ij}\sum_{i=1}^n n_{i}). "level3" assigns equal weights to level-3 units; p_{ijk}=1/(nn_{i}m_{ij}).

Value

a matrix with two rows. The first row is for rank ICC at level 2 and the second row is for rank ICC at level 3. Each row has the 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))
level2 <- rep(1:k, each=5)
level3 <- round(level2 / 10)
rankICC3levels(x, level2, level3, weights = "level2")