### Answer:

As with many statistical models, if you add more parameters you get a better fit. The same is true with joinpoint models. What the program does is to try to choose the smallest number of joinpoints such that if one more joinpoint is added, the improvement is not statistically significant. Thus, in the final model you may interpret each of the joinpoints and its corresponding changes in trend as significant.

Joinpoint selects the final model using two different methods: Permutation Test and Bayesian Information Criterion (BIC). First, the user specifies MIN as the minimum number of joinpoints and MAX as the maximum number of joinpoints on the **Method and Parameters** tab.

Then the program uses a sequence of permutation tests to select the final model. Each one of the permutation tests performs a test of the null hypothesis H_{0}: number of joinpoints = *k _{a}* against the alternative H

_{a}: number of joinpoints=k

_{b}where K

_{a}< K

_{b}. The procedure begins with

*k*= MIN and

_{a}*k*= MAX. If the null is rejected, then increase

_{b}*k*by 1; otherwise, decrease

_{a}*k*by 1. The procedure continues until

_{b}*k*=

_{a}*k*and the final value of is the selected number of joinpoints.

_{b}The second method is based on the Bayesian Information Criterion (BIC). The value of BIC is the loglikelihood value penalized by the cost of extra parameters. The model with the minimum value of BIC is selected as the optimal model.