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 analysing 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.