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A new Bayesian approach for determining the number of components in a finite mixture

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A new Bayesian approach for determining the number of components in a finite mixture. / Aitkin, Murray; Vu, Duy; Francis, Brian.

In: Metron, Vol. 73, No. 2, 21.08.2015, p. 155-175.

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Aitkin, Murray ; Vu, Duy ; Francis, Brian. / A new Bayesian approach for determining the number of components in a finite mixture. In: Metron. 2015 ; Vol. 73, No. 2. pp. 155-175.

Bibtex

@article{8e052d1031ac4dc9a512b519694973ec,
title = "A new Bayesian approach for determining the number of components in a finite mixture",
abstract = "This article evaluates a new Bayesian approach to determining the number of components in a finite mixture. We evaluate through simulation studies mixtures of normals and latent class mixtures of Bernoulli responses. For normal mixtures we use a “gold standard” set of population models based on a well-known “testbed” data set – the galaxy recession velocity data set of Roeder (1990). For Bernoulli latent class mixtures we consider models for psychiatric diagnosis (Berkhof, van Mechelen and Gelman 2003). The new approach is based on comparing models with different numbers of components through their posterior deviance distributions, based on non-informative or diffuse priors.Simulations show that even large numbers of closely spaced normal components can be identified with sufficiently large samples, while for atent classes with Bernoulli responses identification is more complex, though it again improves with increasing sample size.",
keywords = "finite mixture models, number of groups, Bayesian, latent class analysis, Number of components, Deviance distribution",
author = "Murray Aitkin and Duy Vu and Brian Francis",
note = " (included in attached document) The final publication is available at Springer via http://dx.doi.org/10.1007/s40300-015-0068-1",
year = "2015",
month = aug,
day = "21",
doi = "10.1007/s40300-015-0068-1",
language = "English",
volume = "73",
pages = "155--175",
journal = "Metron",
issn = "0026-1424",
publisher = "Universita di Roma {"}La Sapienza{"}",
number = "2",

}

RIS

TY - JOUR

T1 - A new Bayesian approach for determining the number of components in a finite mixture

AU - Aitkin, Murray

AU - Vu, Duy

AU - Francis, Brian

N1 - (included in attached document) The final publication is available at Springer via http://dx.doi.org/10.1007/s40300-015-0068-1

PY - 2015/8/21

Y1 - 2015/8/21

N2 - This article evaluates a new Bayesian approach to determining the number of components in a finite mixture. We evaluate through simulation studies mixtures of normals and latent class mixtures of Bernoulli responses. For normal mixtures we use a “gold standard” set of population models based on a well-known “testbed” data set – the galaxy recession velocity data set of Roeder (1990). For Bernoulli latent class mixtures we consider models for psychiatric diagnosis (Berkhof, van Mechelen and Gelman 2003). The new approach is based on comparing models with different numbers of components through their posterior deviance distributions, based on non-informative or diffuse priors.Simulations show that even large numbers of closely spaced normal components can be identified with sufficiently large samples, while for atent classes with Bernoulli responses identification is more complex, though it again improves with increasing sample size.

AB - This article evaluates a new Bayesian approach to determining the number of components in a finite mixture. We evaluate through simulation studies mixtures of normals and latent class mixtures of Bernoulli responses. For normal mixtures we use a “gold standard” set of population models based on a well-known “testbed” data set – the galaxy recession velocity data set of Roeder (1990). For Bernoulli latent class mixtures we consider models for psychiatric diagnosis (Berkhof, van Mechelen and Gelman 2003). The new approach is based on comparing models with different numbers of components through their posterior deviance distributions, based on non-informative or diffuse priors.Simulations show that even large numbers of closely spaced normal components can be identified with sufficiently large samples, while for atent classes with Bernoulli responses identification is more complex, though it again improves with increasing sample size.

KW - finite mixture models

KW - number of groups

KW - Bayesian

KW - latent class analysis

KW - Number of components

KW - Deviance distribution

U2 - 10.1007/s40300-015-0068-1

DO - 10.1007/s40300-015-0068-1

M3 - Journal article

VL - 73

SP - 155

EP - 175

JO - Metron

JF - Metron

SN - 0026-1424

IS - 2

ER -