A Study Onjoinpoint Regression Model Using Log-Likelihood And Information Criterion
The traditional research about a joinpoint regression modelhas been established under the concept of minimizing residual sum of squares. Hence, any errors on segmented lines have been assumed to have same variance, namely, homoscedastic errors. Then, the number of lines has been determined using permutation tests in the traditional research. Permutation tests consume a huge of time since many data sets are generated by randomly shuffling all errors. Additionally, it is not necessarily practical that any errors on segmented lines have same variance. Hence, this paper deals with a joinpoint regression model without the assumption that any errors on segmented lines have same variance, namely, heteroscedastic errors. In this case, we construct a joinpoint regression model using likelihood theory. Then, a procedure for determining the number of lines is established using information criterion, which is closely related to likelihood theory.
Index Terms - dynamic programming, information criterion, joinpoint regression, maximum log-likelihood.