Selecting the Final Model

Why doesn't the joinpoint program give me the best possible fit? I can see other models with more joinpoints that would fit better. Exactly how does the program decide which tests to perform and which joinpoint model is the final model?

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 H0: number of joinpoints = ka against the alternative Ha: number of joinpoints=kb where Ka < Kb. The procedure begins with ka = MIN and kb = MAX. If the null is rejected, then increase ka by 1; otherwise, decrease kb by 1. The procedure continues until ka = kb and the final value of \^k = k_a = k_b is the selected number of joinpoints.

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.