Flexible Detection of Groups in Data

Observations often come from a heterogeneous population which consists of different groups. However, the information from which group each observation stems is not observed. This occurs either due to difficulties in the measurement of the group indicator or because not a single characteristic could be identified that captures the grouping. In statistical modeling finite mixtures have been used for more than 100 years as a flexible model class to describe this kind of data and determine the group memberships of the given observations as well as the group sizes and a group-specific statistical model. The areas of application consist of astronomy, biology, economics, marketing and medicine. The usefulness of the application of finite mixture models often suffers from the fact that a-priori knowledge about certain characteristics of the grouping is available, but cannot be easily included in the model. This project aims at overcoming this drawback by offering a suitable approach for fitting a finite mixture model while also taking this additional information into account. Especially the possibility to include information on which observations are likely to be in the same group or should rather end up in different groups will be considered. A possible area of application for this newly developed approach is market segmentation. In market segmentation the aim is to partition the market into sub-markets. Segments are often defined to consist of consumers with similar behavior. However, the possibility to implement a successful marketing strategy is only ensured if these segments do not only differ in their behavior, but also with respect to socio-demographic characteristics. A combined approach taking all requirements on the segments directly into account will ease the statistical analysis and improve the finally derived solution. In addition the rigorous application of advanced mixtures of regression models will be i