BIC3 uses a harsher penalty than the traditional Bayesian Information Criterion (BIC). The equation for computing the BIC3 for a k-joinpoint model is:

BIC3(k) = ln{SSE(k) / #Obs} + {PenaltyCoefficient(k) / #Obs} * ln(#Obs),

where SSE is the sum of squared errors of the k-joinpoint regression model, PenaltyCoefficient(k) = 3k + 2 is the penalty coefficient of the k-joinpoint model, and #Obs is the number of observations. The k-joinpoint model with the minimum value of BIC3(k) is selected as the final model.