Identification and Estimation of Finite Mixture Models

Finite mixture models have been used for more than 100 years, but have seen a real boost in popularity over the last decade due to the tremendous increase in available computing prwer. Applications in disjoint scientific communities have led to the development of a lot of variants and extensions for special cases without proper analysis of many structural and statistical properties of the general model cases. The EM algorithm provides a unifying framework for maximum likelihood estimation of parameters. However; the identification of these models was only considered for special cases and a thorough investigation of recent extensions and variants, as, e.g., mixtures of generalized linear models, is still missing. One major goal of this project is to develop a general theory for the identification of mixture models in a top-down approach. In addition to the theoretical investigations we will develop an open-source reference implementation within R, an environment for statistical computing and graphics. State of the art estimation techniques will be made available through a uniform and convenient user interface. Automatic model selection, diagnostic tools and checlcing of identifiability constraints for a specified model caass and a given data set will be implemented, all of which are almost completely missing in existing software packages. The ultimate goal is a comprehensive methodological and computational toolbox for identification and estimation of finite mixture models.