Mixtures of regressions with changepoints

We introduce an extension to the mixture of linear regressions model where changepoints are present. Such a model provides greater flexibility over a standard changepoint regression model if the data are believed to not only have changepoints present, but are also believed to belong to two or more unobservable categories. This model can provide additional insight into data that are already modeled using mixtures of regressions, but where the presence of changepoints has not yet been investigated. After discussing the mixture of regressions with changepoints model, we then develop an Expectation/Conditional Maximization (ECM) algorithm for maximum likelihood estimation. Two simulation studies illustrate the performance of our ECM algorithm and we analyze a real dataset.