ManlyMix: An R Package for Manly Mixture Modeling
Xuwen Zhu, Volodymyr Melnykov · The R Journal · 2017
Model-based clustering is a popular technique for grouping objects based on a finite mixture model.It has countless applications in different fields of study.The R package ManlyMix implements the Manly mixture model that allows modeling skewness within data groups and performs cluster analysis.ManlyMix is a powerful diagnostics tool that is capable of conducting investigation concerning the normality of variables upon fitting of a Manly forward or backward model.Theoretical foundations as well as description of functions are provided.All features of the package are illustrated with examples in great detail.The analysis of real-life datasets demonstrates the flexibility and usefulness of the package.• providing an alternative approach to modeling heterogeneous skewed data;• calling core functions from C for speed;• providing excellent model interpretability through output of skewness parameters;• preventing overfitting of the data by implementing model selection algorithms;• offering effective assessment of mixture characteristics through the overlap calculation and variability assessment.This paper is organized in the following way.A brief introduction to the Expectation-Maximization (EM) algorithm for Manly mixture models as well as the classification Expectation-Maximization (CEM) algorithm for Manly K-means is provided in the second section.In section "Package functionality and illustrative examples", a comprehensive description of all functions in ManlyMix is given along with the analysis of two real-life datasets.All features of the package are illustrated in great detail.Demo examples are constructed in section four for users to conduct further investigation of ManlyMix.In the last section, we provide a brief summary for the paper. Methodological and algorithmic details Manly mixture modelConsider a dataset X 1 , . . ., X n of size n, where X i 's are p-variate independent observations that are identically distributed.The exponential (Manly) transformation to near normality is defined by