An Exact Algorithm for Estimating Breakpoints in Segmented Generalized Linear Models

We consider the problem of estimating the unknown breakpoints in segmented generalized linear models. Exact algorithms for calculating maximum likelihood estimators are derived for different types of models. After discussing the case of a GLM with a single covariate having one breakpoint a new algorithm is presented when further covariates are included in the model. The essential idea of this approach is then used for the case of more than one breakpoint. As further extension an algorithm for the situation of two regressors each having a breakpoint is proposed. These techniques are applied for analyzing the data of the Munich rental table. It can be seen that these algorithms are easy to handle without too much computational effort. The algorithms are available as GAUSS-programs