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APC/AAPC/Tau Confidence Intervals

A description of the methods used for calculating APC, AAPC, and Tau Confidence Intervals.

Relevant FAQ's:

 

Empirical Quantile

Motivated by a conservative tendency of the asymptotic confidence interval for the true AAPC, a new method called the empirical quantile method was introduced as an improved confidence interval. The idea of the empirical quantile method is to generate resampled data by (i) generating resampled residuals as the inverse function values of the uniform random numbers over (0,1) where the function is the empirical distribution function of the original residuals and then (ii) adding resampled residuals to the original fit. For each resampled data set, the model is fit and the AAPCs are estimated. Then, the 100(α/2)th and 100(1-α/2)th percentiles of the resampled AAPC values are obtained as the lower and upper limits of the 100(1-α)% empirical quantile confidence interval for the true AAPC.  For details regarding this method please see the Improved Confidence Interval for Average Annual Percent Change in Trend Analysis article.

For a more detailed description of the Empirical Quantile methodology, please go here.

This method is also available for the APC and Tau Confidence Intervals.

Final Selected Model Only

Because the Empirical Quantile method is computationally intensive, applying it to each Joinpoint model can increase job execution times.  To decrease the job times, Joinpoint provides the "Final Selected Model Only" option.  When that option is selected, The Empirical Quantile method will only be used for the final selected model.  All other models will use the Parametric method.

# of Resamples

This parameter can be set to control the number of resampled data sets used to compute the Empirical Quantile confidence intervals.   This parameter is defaulted to the recommended value of 10,000.

Parametric

In the Joinpoint software, the parametric confidence interval for the true AAPC is based on the normal distribution, and the APC confidence interval is based on a t distribution. If an AAPC lies entirely within a single joinpoint segment, the AAPC is equal to the APC for that segment. To obtain consistency between the APC and AAPC confidence intervals in this situation, the confidence interval for the AAPC has been modified to be identical to that used for the APC using the t distribution instead of the normal distribution.

More Information:

    Alpha Levels: To learn how to adjust the alpha levels for any of the confidence intervals, please go to the Preferences help section .