iccTraj (version 1.0.4)

interval: Computes the confidence interval for the ICC

Description

Computes the confidence interval for the ICC

Usage

interval(x, conf = 0.95, method = c("EB", "AN", "ZT"))

Value

A vector with the two boundaries of the confidence interval.

Arguments

x

An object of class "iccTraj"

conf

Numeric. Level of confidence. Default is set to 0.95.

method

String. Method used to estimate the confidence interval. Accepted values are **EB** for Empirical Bootstrap, **AN** for asymptotic Normal, and **ZT** for asymptotic Normal using the Z-transformation.

Details

Let \(\hat{\theta}\) denote the ICC sample estimate and \(\theta_i^{B}\) denote the ICC bootstrap estimates with \(i=1,\ldots,B\). Let \(\delta_{\alpha/2}^{B}\) and \(\delta_{1-\alpha/2}^{B}\) be the \(\frac{\alpha}{2}\) and \(1-\frac{\alpha}{2}\) percentiles of \(\delta_{i}^{B}=\theta_i^{B}-\hat{\theta}\). The empirical bootstrap confidence interval is then estimated as \(\hat{\theta}+\delta_{\alpha/2}^{B},\hat{\theta}+\delta_{1-\alpha/2}^{B}\).

Asymptotic Normal (AN) interval is obtained as \(\hat{\theta} \pm Z_{1-\alpha/2}*SE_B\) where \(SE_B\) denotes the standard deviation of \(\theta_i^{B}\), and \(Z_{1-\alpha/2}\) stands for the \(1-\alpha/2\) quantile of the standard Normal distribution.

In the ZT approach, the ICC is transformed using Fisher's Z-transformation. Then, the AN approach is applied to the transformed ICC.

Examples

# \donttest{
# Using median Hausdorff distance
Hd<-iccTraj(gull_data,"ID","trip","LONG","LAT","triptime", parallel=FALSE, distance="H")
Hd$est
interval(Hd)
# }