Manly transformation in finite mixture modeling

Zhu, Xuwen; Melnykov, Volodymyr

doi:10.1016/j.csda.2016.01.015

Cited by 35 publications

(20 citation statements)

References 42 publications

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“…This is substantially more excellent informative and more robust to response variable outliers than Ordinary Least Squares (OLS) for inference (Eide & Showalter, 1998;Levin, 2001). FMM, both fixed and varying weight parameter models, assume a linear relationship of the probability distributions, generally defined components (Park, Lord, & Wu, 2016;Zhu & Melnykov, 2018). With this feature, FMM has been used in many different areas before; the effect of job loss on drinking (Deb, Gallo, Ayyagari, Fletcher, & Sindelar, 2011), the analysis of medical data (Schlattmann, 2009), flow cytometry data (Pyne et al, 2009) and vehicle crash data (Park & Lord, 2009 (1)…”

Section: Instrument and Proceduresmentioning

confidence: 99%

Determination of the Factors Affecting Students’ Science Achievement Level in Turkey and Singapore: An Application of Quantile Regression Mixture Model

Depren

2020

JBSE

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In the last decade, the usage of advanced statistical models is growing rapidly in many different disciplines. However, the Quantile Regression Mixture Model (QRMIX), which is a developed approach of the Finite Mixture Model (FMM), is an applicable new method in the educational literature. The aim of the proposed study was to determine factors affecting students' science achievement using the QRMIX approach. To reach this aim, data of the Programme for International Student Assessment (PISA) survey, which has been conducted by the Organization Economic for Co-Operation and Development (OECD) every 3 years, was used. Dataset used in the research is composed of 6,115 students from Singapore, which is the top-performer country among the participant countries, and 5,895 students from Turkey. The results showed that the factors affecting students' science achievement and its importance on the achievement differentiated according to the achievement levels of the students. In conclusion, it was revealed that Turkish students with the lowest science achievement level should be supported with home possessions, perceived feedback, and environmental awareness and Singaporean students with the lowest achievement level should be supported with perceived feedback, enjoyment of science, and epistemological beliefs.

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Section: Instrument and Proceduresmentioning

confidence: 99%

Determination of the Factors Affecting Students’ Science Achievement Level in Turkey and Singapore: An Application of Quantile Regression Mixture Model

Depren

2020

JBSE

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“…As this can be very helpful for modelling purposes it can be misleading when dealing with clustering/classification applications as one cluster may be represented by more than one mixture component just because it has, in fact, a non‐elliptical distribution. A first possible route to continue to use our approach also in the presence of conditional non‐elliptical distributions for each cluster, consists in considering transformations so as to make the components as elliptical as possible (Schork & Schork, ; Zhu & Melnykov, ). Although such a treatment is very convenient to use the achievement of joint ellipticality is rarely satisfied and the transformed variables become more difficult to be interpreted.…”

Section: Discussionmentioning

confidence: 99%

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

2016

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This article proposes the elliptical multivariate leptokurtic‐normal (MLN) distribution to fit data with excess kurtosis. The MLN distribution is a multivariate Gram–Charlier expansion of the multivariate normal (MN) distribution and has a closed‐form representation characterized by one additional parameter denoting the excess kurtosis. It is obtained from the elliptical representation of the MN distribution, by reshaping its generating variate with the associated orthogonal polynomials. The strength of this approach for obtaining the MLN distribution lies in its general applicability as it can be applied to any multivariate elliptical law to get a suitable distribution to fit data. Maximum likelihood is discussed as a parameter estimation technique for the MLN distribution. Mixtures of MLN distributions are also proposed for robust model‐based clustering. An EM algorithm is presented to obtain estimates of the mixture parameters. Benchmark real data are used to show the usefulness of mixtures of MLN distributions. The Canadian Journal of Statistics 45: 95–119; 2017 © 2016 Statistical Society of Canada

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“…While this can be very helpful for modeling purposes, it can be misleading when dealing with clustering/classification applications since one state may be represented by more than one mixture component just because it has, in fact, a non-elliptical distribution. A first possible route to continue to use our approach also in the presence of conditional non-elliptical distributions for each state, consists in considering transformations so as to make the components as elliptical as possible (Schork andSchork, 1988 andZhu andMelnykov, 2016). Although such a treatment is very convenient to use, the achievement of joint ellipticity is rarely satisfied and the transformed variables become more difficult to be interpreted.…”

Section: Discussionmentioning

confidence: 99%

Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers

Maruotti

Punzo

2017

Computational Statistics & Data Analysis

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A class of multivariate linear models under the longitudinal setting, in which unobserved heterogeneity may evolve over time, is introduced. A latent structure is considered to model heterogeneity, having a discrete support and following a first-order Markov chain. Heavy-tailed multivariate distributions are introduced to deal with outliers. Maximum likelihood estimation is performed to estimate parameters by using expectation-maximization and expectation-conditional-maximization algorithms. Notes on model identifiability and robustness are provided, along with all computational details needed to implement the proposal. Three applications on artificial and real data are illustrated. These focus on the potential effects of outliers on clustering and their identification.

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Manly transformation in finite mixture modeling

Cited by 35 publications

References 42 publications

Determination of the Factors Affecting Students’ Science Achievement Level in Turkey and Singapore: An Application of Quantile Regression Mixture Model

Determination of the Factors Affecting Students’ Science Achievement Level in Turkey and Singapore: An Application of Quantile Regression Mixture Model

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers

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