A Modified Likelihood Ratio Test for Homogeneity in Finite Mixture Models

Chen, Hanfeng; Chen, Jiahua; Kalbfleisch, John D.

doi:10.1111/1467-9868.00273

Cited by 200 publications

(173 citation statements)

References 15 publications

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“…In practice this method has three drawbacks: (i) the likelihood ratio test does not have a simple approximate limiting distribution for tail probabilities; (ii) the likelihood surface may possess multiple modes, and without a careful choice of starting values, a standard optimization routine may fail to find the global maximum; and (iii), an arbitrary lower bound on the missing weights is required and it requires some care to implement correctly. Chen et al [2001] offer an alternative solution that also attempts to circumvent the dif-ficulties encountered when conducting a likelihood ratio test for mixture models. Their solution involves utilizing a penalized likelihood approach.…”

Section: Discussionmentioning

confidence: 99%

Mixture models for linkage analysis of affected sibling pairs and covariates

Devlin

Jones

Bacanu

et al. 2001

Genetic Epidemiology

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To determine the genetic etiology of complex diseases, a common study design is to recruit affected sib/relative pairs (ASP/ARP) and evaluate their genome-wide distribution of identical by descent (IBD)-sharing using a set of highly polymorphic markers. Other attributes or environmental exposures of the ASP/ARP, which are thought to affect liability to disease, are sometimes collected. Conceivably these covariates could refine the linkage analysis. Most published methods for ASP/ARP linkage with covariates can be conceptualized as logistic models in which IBD-status of the ASP is predicted by pair-specific covariates. We develop a different approach to the problem of ASP analysis in the presence of covariates, one that extends naturally to ARP under certain conditions. For ASP linkage analysis, we formulate a mixture model in which a disease mutation is segregating in only a fraction « of the sibships, with ½ « sibships being unlinked. Covariate information is used to predict membership within groups; in this report, the two groups correspond to the linked and unlinked sibships. feature of our conceptualization of ASP linkage analysis, with covariates, is that it is apparent how data analysts might evaluate covariates prior to the linkage analysis, thus avoiding the loss of power described by Leal and Ott [2000] when data are stratified.

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Section: Discussionmentioning

confidence: 99%

Mixture models for linkage analysis of affected sibling pairs and covariates

Devlin

Jones

Bacanu

et al. 2001

Genetic Epidemiology

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“…Chen et al (followed by Qin et al) proposed a simple and clever idea to avoid the degeneracy problems: they add a penalization to the log-likelihood with a factor increasing to infinity as the parameters tend to values where degeneracy occurs. They consequently obtain convex combination of chi-square for the asymptotic distribution of the modified testing statistic, see [8,9,38,39].…”

Section: Motivations and Aimsmentioning

confidence: 99%

The likelihood ratio test for general mixture models with or without structural parameter

2009

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Abstract. This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations in a finite mixture with or without structural parameter.Résumé. Nousétudions le test du rapport de vraisemblance (TRV) pour des hypothèses sur la mesure mélangeante dans un mélange en présenceéventuelle d'un paramètre structurel, et ce dans toutes les situations possibles. Le résultat principal donne la distribution asymptotique du TRV sous des hypothèses qui ne sont pas loin d'être nécessaires. Nous donnons une solution détaillée pour le test d'une simple distribution contre un mélange avec application aux lois Gaussiennes, Poisson et binomiales, ainsi que pour le test du nombre de populations dans un mélange fini avec un paramètre structurel.Mathematics Subject Classification. 62F05, 62F12, 62H10, 62H30.

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“…Neste caso, na distribuição de renda per capita cross-section, os componentes correspondem a grupos com diferentes níveis de renda per capita. Chen et al (2001Chen et al ( , 2004 sugerem aplicar um teste modificado de razão de probabilidades (likelihood ratio test, LRT) para determinar o número de componentes do modelo de misturas finitas. Deve ser mencionado que este teste não é alterado sob transformação monotônica dos dados, sendo o resultado completamente consistente quando as variáveis são testadas em log.…”

Section: Distribuição De Misturas Finitas: Definição E Teste Lr Para unclassified

Convergência, para onde? Uma análise da dinâmica de distribuição de renda per capita a partir do modelo de misturas finitas

Catela¹,

Gonçalves²

2009

Econ. Apl.

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ResumoDiferentes teorias de crescimento implicam em diferentes padrões de distribuição de níveis de renda per capita entre as economias mundiais. A validação empírica de tais teorias pressupõe propriedades nos processos estocásticos nem sempre verificadas nos exercícios empíricos tradicionais de regressões de crescimento. Este trabalho busca estas propriedades e discute a existência de clubes de renda na economia mundial analisando a distribuição da renda per capita em 134 países durante o período 1970-2003. As conclusões mostram uma estratificação em três grupos, com path dependence sem lock in, isto é existe uma alta probabilidade de permanên-cia do status quo. Palavras-chave: Crescimento, Misturas Finitas, Convergência em ClubesAbstract Different growth theories implies in different patterns of per capita income distribution between countries. The empirical validation to these theories assumes some non-commonly verified stochastic processes properties. This paper seeks for theseis properties and discusses the existence of per capita income clubs in the world economy by analyzing the distribution of per capita income in 134 countries during the period 1970-2003. The conclusions show stratification in three groups, with path dependence and no lock in, that is, there is a high probability of maintenance of the status quo, while there exists a small probability of migration between groups.

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A Modified Likelihood Ratio Test for Homogeneity in Finite Mixture Models

Cited by 200 publications

References 15 publications

Mixture models for linkage analysis of affected sibling pairs and covariates

Mixture models for linkage analysis of affected sibling pairs and covariates

The likelihood ratio test for general mixture models with or without structural parameter

Convergência, para onde? Uma análise da dinâmica de distribuição de renda per capita a partir do modelo de misturas finitas

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