
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
topdown approach.
In addition to the theoretical investigations we develop an
opensource 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.
AASC Project Members
R Packages
 FlexMix: Flexible Mixture Modeling
A general framework for finite mixtures of regression models using
the EM algorithm. FlexMix provides the Estep and all data handling,
while the Mstep can be supplied by the user to easily define new
models. Existing drivers implement mixtures of standard linear
models, generalized linear models, and modelbased clustering.
 BayesMix
Bayesian Mixture Models with JAGS
Funding
 Austrian Research Foundation (FWF)
 Standalone Project "Identification and Estimation of Finite Mixture Models" (P17382, 20042008)
 HerthaFirnberg Project "Modelling Unobserved Heterogeneity with Mixtures" (T351, 20072010)
 Austrian Academy of Sciences (ÖAW)
 DOCFFORTE scholarship (20052006)
Publications

Bettina Grün and Friedrich Leisch.
Dealing with label switching in mixture models under genuine
multimodality.
Journal of Multivariate Analysis, 100(5):851861, May 2009.
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DOI 
preprint ]

Bettina Grün and Friedrich Leisch.
Identifiability of finite mixtures of multinomial logit models with
varying and fixed effects.
Journal of Classification, 25(2):225247, November 2008.
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DOI 
preprint ]

Bettina Grün and Friedrich Leisch.
Flexmix version 2: Finite mixtures with concomitant variables and
varying and constant parameters.
Journal of Statistical Software, 28(4):135, September 2008.
[ bib 
http ]

Bettina Grün.
Fitting finite mixtures of linear mixed models with the EM
algorithm.
In Paula Brito, editor, Compstat 2008Proceedings in
Computational Statistics, volume II, pages 165173. Physica Verlag,
Heidelberg, Germany, 2008.
[ bib ]

Bettina Grün and Friedrich Leisch.
Finite mixtures of generalized linear regression models.
In Shalabh and Christian Heumann, editors, Recent Advances In
Linear Models and Related Areas, pages 205230. Springer, 2008.
[ bib 
DOI 
preprint ]

Friedrich Leisch.
Visualizing cluster analysis and finite mixture models.
In Chun houh Chen, Wolfgang Härdle, and Antony Unwin, editors,
Handbook of Data Visualization, Springer Handbooks of Computational
Statistics. Springer Verlag, 2008.
[ bib ]

Bettina Grün and Friedrich Leisch.
Fitting Finite Mixtures of Generalized Linear Regressions in R.
Computational Statistics and Data Analysis, 51(11), 52475252, 2007.
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.pdf ]

Bettina Grün and Friedrich Leisch.
FlexMix: An R package for finite mixture modelling.
R News, 7(1), 813, 2007.
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Friedrich Leisch and Bettina Grün.
Extending standard cluster algorithms to allow for group constraints.
In Alfredo Rizzi and Maurizio Vichi, editors, Compstat
2006Proceedings in Computational Statistics, pages 885892. 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
2006Proceedings in Computational Statistics, pages 853860. 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 301302, Vienna, Austria, April
2006. Vienna University of Technology.
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 Friedrich Leisch.
FlexMix: A general framework for finite mixture models and latent
class regression in R.
Journal of Statistical Software, 11(8), 2004.
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http ]

Bettina Grün and Friedrich Leisch.
Bootstrapping finite mixture models.
In Compstat 2004  Proceedings in Computational Statistics,
pages 11151122. Physika Verlag, Heidelberg, Germany, 2004.
ISBN 3790815543.
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Friedrich Leisch.
Exploring the structure of mixture model components.
In Jaromir Antoch, editor, Compstat 2004  Proceedings in
Computational Statistics, pages 14051412. Physika Verlag, Heidelberg,
Germany, 2004.
ISBN 3790815543.
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.pdf ]
