Finite Mixture Models
Overview
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 power. 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
class.
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 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
checking of identifiability constraints for a specified model class
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.
CI Project Members
R Packages
- FlexMix: Flexible Mixture Modeling
A general framework for finite mixtures of regression models using
the EM algorithm. FlexMix provides the E-step and all data handling,
while the M-step can be supplied by the user to easily define new
models. Existing drivers implement mixtures of standard linear
models, generalized linear models, and model-based clustering.
- BayesMix
Bayesian Mixture Models with JAGS
Publications
-
Bettina Grün and Friedrich Leisch.
Fitting Finite Mixtures of Generalized Linear Regressions in R.
Computational Statistics and Data Analysis, 51(11), 5247-5252, 2007.
[ bib |
.pdf ]
-
Bettina Grün and Friedrich Leisch.
FlexMix: An R package for finite mixture modelling.
R News, 7(1), 8-13, 1007.
[ bib |
.pdf ]
-
Friedrich Leisch and Bettina Grün.
Extending standard cluster algorithms to allow for group constraints.
In Alfredo Rizzi and Maurizio Vichi, editors, Compstat
2006-Proceedings in Computational Statistics, pages 885-892. Physica
Verlag, Heidelberg, Germany, 2006.
[ bib |
.pdf ]
- Bettina Grün and Friedrich Leisch.
Fitting finite mixtures of linear regression models with varying &
fixed effects in R.
In Alfredo Rizzi and Maurizio Vichi, editors, Compstat
2006-Proceedings in Computational Statistics, pages 853-860. Physica
Verlag, Heidelberg, Germany, 2006.
[ bib |
.pdf ]
- Bettina Grün and Friedrich Leisch.
Finite mixture model diagnostics using the parametric bootstrap.
In Wilfried Elmenreich and Hans Kaiser, editors, Proceedings of
the Junior Scientist Conference 2006, pages 301-302, Vienna, Austria, April
2006. Vienna University of Technology.
[ bib |
.pdf ]
- Friedrich Leisch.
FlexMix: A general framework for finite mixture models and latent
class regression in R.
Journal of Statistical Software, 11(8), 2004.
[ bib |
http ]
-
Bettina Grün and Friedrich Leisch.
Bootstrapping finite mixture models.
In Compstat 2004 - Proceedings in Computational Statistics,
pages 1115-1122. Physika Verlag, Heidelberg, Germany, 2004.
ISBN 3-7908-1554-3.
[ bib |
.pdf ]
-
Friedrich Leisch.
Exploring the structure of mixture model components.
In Jaromir Antoch, editor, Compstat 2004 - Proceedings in
Computational Statistics, pages 1405-1412. Physika Verlag, Heidelberg,
Germany, 2004.
ISBN 3-7908-1554-3.
[ bib |
.pdf ]