On the number of components in a Gaussian mixture model

McLachlan, Geoffrey J.; Rathnayake, Suren I.

doi:10.1002/widm.1135

Cited by 165 publications

(103 citation statements)

References 97 publications

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“…The selection of the order of the mixture, i.e. the number of mixture components or clusters, can be also performed by formal hypothesis testing; for a recent review see McLachlan and Rathnayake (2014).…”

Section: Model Selectionmentioning

confidence: 99%

mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models

et al. 2016

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Finite mixture models are being used increasingly to model a wide variety of random phenomena for clustering, classification and density estimation. mclust is a powerful and popular package which allows modelling of data as a Gaussian finite mixture with different covariance structures and different numbers of mixture components, for a variety of purposes of analysis. Recently, version 5 of the package has been made available on CRAN. This updated version adds new covariance structures, dimension reduction capabilities for visualisation, model selection criteria, initialisation strategies for the EM algorithm, and bootstrap-based inference, making it a full-featured R package for data analysis via finite mixture modelling.

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Section: Model Selectionmentioning

confidence: 99%

mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models

et al. 2016

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“…Gail and Simon proposed to use a likelihood ratio test (LRT) to evaluate the treatment efficacy among different subgroups of patients in clinical trials. In this paper, we apply the LRT to test the hypothesis that the sampled patients are from a single population …”

Section: Introductionmentioning

confidence: 99%

“…As mentioned, it is useful to learn the underlying subgroup structure and whether there are subgroups prior to subgroup selection. We apply the LRT for testing homogeneity among the patient population. The null hypothesis is that the sampled patients are from a single population and the alternative hypothesis is that the sampled patients are from a mixture of 2 distributions.…”

Section: Introductionmentioning

confidence: 99%

Development of predictive signatures for treatment selection in precision medicine with survival outcomes

Chen

Lee

Tsai

et al. 2018

Pharmaceutical Statistics

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For survival endpoints in subgroup selection, a score conversion model is often used to convert the set of biomarkers for each patient into a univariate score and using the median of the univariate scores to divide the patients into biomarker-positive and biomarker-negative subgroups. However, this may lead to bias in patient subgroup identification regarding the 2 issues: (1) treatment is equally effective for all patients and/or there is no subgroup difference; (2) the median value of the univariate scores as a cutoff may be inappropriate if the sizes of the 2 subgroups are differ substantially. We utilize a univariate composite score method to convert the set of patient's candidate biomarkers to a univariate response score. We propose applying the likelihood ratio test (LRT) to assess homogeneity of the sampled patients to address the first issue. In the context of identification of the subgroup of responders in adaptive design to demonstrate improvement of treatment efficacy (adaptive power), we suggest that subgroup selection is carried out if the LRT is significant. For the second issue, we utilize a likelihood-based change-point algorithm to find an optimal cutoff. Our simulation study shows that type I error generally is controlled, while the overall adaptive power to detect treatment effects sacrifices approximately 4.5% for the simulation designs considered by performing the LRT; furthermore, the change-point algorithm outperforms the median cutoff considerably when the subgroup sizes differ substantially.

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“…6), and significance must be assessed by resampling approaches. For a recent review, see McLachlan and Rathnayake (), and for an implementation in the mclust software see Scrucca et al. ().…”

Section: Finite Mixture Modelingmentioning

confidence: 99%

A transformation‐based approach to Gaussian mixture density estimation for bounded data

Scrucca

2019

Biometrical J

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Finite mixture of Gaussian distributions provide a flexible semiparametric methodology for density estimation when the continuous variables under investigation have no boundaries. However, in practical applications, variables may be partially bounded (e.g., taking nonnegative values) or completely bounded (e.g., taking values in the unit interval). In this case, the standard Gaussian finite mixture model assigns nonzero densities to any possible values, even to those outside the ranges where the variables are defined, hence resulting in potentially severe bias. In this paper, we propose a transformation‐based approach for Gaussian mixture modeling in case of bounded variables. The basic idea is to carry out density estimation not on the original data but on appropriately transformed data. Then, the density for the original data can be obtained by a change of variables. Both the transformation parameters and the parameters of the Gaussian mixture are jointly estimated by the expectation‐maximization (EM) algorithm. The methodology for partially and completely bounded data is illustrated using both simulated data and real data applications.

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On the number of components in a Gaussian mixture model

Cited by 165 publications

References 97 publications

mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models

mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models

Development of predictive signatures for treatment selection in precision medicine with survival outcomes

A transformation‐based approach to Gaussian mixture density estimation for bounded data

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