interval {iccTraj}

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"))

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.

Value

A vector with the two boundaries of the confidence interval.

Examples

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