What is Tau?
The tau parameters are the unknown joinpoints in the joinpoint regression model described by Kim et al. (2000). For fitted models with one or more joinpoints, the Joinpoint software displays the estimates of the tau parameters and estimates of other joinpoint model parameters
Confidence Intervals - Empirical Quantile Method
For a more detailed description of the Empirical Quantile methodology, please go here.
Confidence Intervals - Parametric Method
If k > 0 then the output lists the estimated joinpoints. The associated confidence intervals (CI) come from Lerman (1980) equation 6 using C2α. Explicitly, the100(1-α)% confidence interval for the jth of k joinpoints includes all values of x from the grid such that Qx,j,k ≤ C2α, where
\(C_2^\alpha =\ Q_k \left( 1 +\ \frac{k}{n-p} \right) F_{k,n-p}^{-1} \left( 1 - \alpha \right)\)