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Fast estimation of Gaussian Mixture Copula Models

The GMCM package (Bilgrau et. al., 2016) offers R functions that perform high-dimensional meta-analysis (Li et. al., 2011) and general unsupervised cluster analysis (Tewari et. al., 2011) using Gaussian Copula Mixture Models in a very fast manner. Online documentation is available here.

Gaussian copula mixture models (GMCMs) are a very flexible alternative to Gaussian mixture models in unsupervised cluster analysis for continuous data where non-Gaussian clusters are present. GMCMs model the ranks of the observed data and are thus invariant to monotone increasing transformations of the data, i.e. they are semi-parametric and only the ordering of the data is important. Alternatively, a special-case of the GMCMs can be used for a novel meta-analysis approach in high-dimensional settings. In this context, the model tries to cluster results which agree and do not agree on statistical evidence into a reproducible and irreproducible group.

The optimization of the complicated likelihood function is difficult, however. GMCM utilizes Rcpp and RcppArmadillo to evaluate the likelihood function quickly and arrive at a parameter estimate using either standard numerical optimization routines or an pseudo EM algorithm.

Additional information, documentation, help, and examples can be found by here or by running ?GMCM in R. The paper [1] is also found as a vignette by vignette("GMCM-JStatSoft"). The core user functions of GMCM are fit.full.GMCM and fit.meta.GMCM.


The released and tested version of GMCM is available at CRAN (Comprehensive R Archive Network). It can be installed from within R by running


If you wish to install the latest version of GMCM directly from the master branch at GitHub, run

#install.packages("remotes")  # Install remotes if needed

Note, that this version is in development and is likely different from the version at CRAN. As such, it may be unstable. Be sure that you have the package development prerequisites if you wish to install the package from the source.

When installed, run GMCM::runGMCM() to launch a local instance of the GMCM shiny application also available online at Run news(package = "GMCM") to view the latest changes of GMCM or visit here.

For previous versions of GMCM, visit the old releases at GitHub or the archive at CRAN.


  1. Anders Ellern Bilgrau, Poul Svante Eriksen, Jakob Gulddahl Rasmussen, Hans Erik Johnsen, Karen Dybkaer, Martin Boegsted (2016). GMCM: Unsupervised Clustering and Meta-Analysis Using Gaussian Mixture Copula Models. Journal of Statistical Software, 70(2), 1-23. doi:10.18637/jss.v070.i02