Bayesian Information Criterion (BIC) Details

What is the Bayesian Information Criterion method for selecting the best model?

Answer:

Permutation test (PT) and BIC are two different approaches to selecting the optimal number of joinpoints. The Permutation test approach uses a sequence of permutation tests to determine the best number of joinpoints. The PT approach controls the error probability of selecting the wrong model at a certain level (i.e. 0.05), whereas the BIC approach finds the model with the best fit by penalizing the cost of extra parameters. The models picked by BIC tend to fit the data well but are less parsimonious. The applications have shown that the PT approach worked well for cancer incidence and mortality data.

The equation for computing the BIC for a k-joinpoint model is:

BIC(k) = ln{SSE(k)/#Obs} + {#Parm(k) /#Obs} * ln(#Obs),

where SSE(k) is the sum of squared errors of the k-joinpoint regression model, #Parm(k)=2*(k+1) is the number of parameters of the k-joinpoint model and #Obs is the number of observations.

The k-joinpoint model with the minimum value of BIC(k) is selected as the final model.