Modelling unobserved heterogeneity with mixtures

Finite mixture models are a popular technique for modelling unobserved heterogeneity. Areas of application include for example marketing and market segmentation. There exist several extensions and variations of the basic model class. Due to the flexibility of the most common estimation methods, such as the Expectation-Maximization (EM) algorithm for Maximum Likelihood estimation or Gibbs sampling and Markov Chain Monte Carlo (MCMC) methods for Bayesian estimation, nearly arbitrary component specific models can be included. This project aims at extending the general model class by using generalized additive models (GAMs) for the components. GAMs extend generalized linear models by allowing for smooth terms as independent variables and thus to determine the relationship between the independent and dependent variables in a data-driven way. Identification, estimation and application of finite mixtures of GAMs will be investigated. Model estimation with the EM algorithm will be improved by investigating and developing different initialization strategies. Available initialization methods have often been only developed and validated for special kinds of mixture models. The applicability of these methods for general mixture models, especially those also including independent variables in a regression setting, has to be verified. In addition methods to automatically assess the difficulty of the estimation problem are investigated. The results of these investigations will enable the development of an adaptive estimation procedure which takes the difficulty and the specific characteristics of the problem into regard. Given the wide range of different possible mixture models tools for model selection and diagnostics will be investigated in order to enable the user to select the most appropriate model. The developed methods will be made available in an open-source reference implementation using R, an environment for statistical computing and graphics. The implementation will aim at flexibility, extensibility and user friendliness in order to allow for the easy and quick addition of new model extensions and ensure the applicability of the estimation techniques, diagnostic tools and visualization methods for new variants.