Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects

Grün, Bettina; Leisch, Friedrich

doi:10.1007/s00357-008-9022-8

Cited by 56 publications

(50 citation statements)

References 23 publications

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“…The proof is straight-forward given the previous results for finite mixtures of standard linear regression models by Hennig (2000) and finite mixtures of GLMs and multinomial logit models with varying and fixed effects in the regression coefficients by Grün (2006); .…”

Section: Generic Identifiabilitymentioning

confidence: 88%

Finite Mixtures of Generalized Linear Regression Models

Grün

Leisch²

2008

Recent Advances in Linear Models and Related Areas

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Summary. Generalized linear models have become a standard technique in the statistical modelling toolbox for investigating relationships between variables. The assumption of homogeneity of regression coefficients over all observations can be relaxed by incorporating generalized linear models into the finite mixture framework.The model class consisting of finite mixtures of generalized linear models is presented. Model identification is discussed given that difficulties might be encountered due to trivial and generic identifiability problems. These problems have already been observed for mixtures of distributions, but the extension to mixtures of regression models introduces additional identifiability problems. Details on model estimation are given and the application is illustrated on several examples.

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Section: Generic Identifiabilitymentioning

confidence: 88%

Finite Mixtures of Generalized Linear Regression Models

Grün

Leisch²

2008

Recent Advances in Linear Models and Related Areas

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“…This grouping is specified in R by adding | Center to the formula similar to the notation used in nlme (Pinheiro and Bates 2000). Under the assumption of homogeneity within centers identifiability of the model class can be ensured as induced by the sufficient conditions for identifability given in Follmann and Lambert (1991) for binomial logit models with varying intercepts and Grün and Leisch (2008) for multinomial logit models with varying and constant parameters. In order to determine the suitable number of components, the mixture is fitted with different numbers of components.…”

Section: Beta-blockers Datasetmentioning

confidence: 99%

“…, V : k ∈ K v }. The nesting structure of the component specific parameters is also described in Grün and Leisch (2006). Different concomitant variable models are possible to determine the component weights (Dayton and Macready 1988).…”

Section: Model Specification and Estimationmentioning

confidence: 99%

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FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters

Grün¹,

Leisch²

2008

J. Stat. Soft.

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340

249

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flexmix provides infrastructure for flexible fitting of finite mixture models in R using the expectation-maximization (EM) algorithm or one of its variants. The functionality of the package was enhanced. Now concomitant variable models as well as varying and constant parameters for the component specific generalized linear regression models can be fitted. The application of the package is demonstrated on several examples, the implementation described and examples given to illustrate how new drivers for the component specific models and the concomitant variable models can be defined.

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“…Alternative approaches to finite mixtures for ordinal data have been advanced by Wedel and DeSarbo (1995); Greene and Hensher (2003); Grün and Leisch (2008); Breen and Luijkx (2010), among others. These authors propose convex combinations of probability distributions belonging to the same class of models and assume the existence of subgroups whose responses should be differently modelled.…”

Section: Introductionmentioning

confidence: 99%

Mixture models for ordinal responses to account for uncertainty of choice

Tutz

Schneider

Iannario

et al. 2016

Adv Data Anal Classif

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In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The deliberate choice can in particular be determined by classical ordinal response models as the cumulative and adjacent categories model. Then one obtains the traditional and flexible models as special cases when the uncertainty component is irrelevant. It is shown that the effect of explanatory variables is underestimated if the uncertainty component is neglected in a cumulative type mixture model. Visualization tools for the effects of variables are proposed and the modelling strategies are evaluated by use of real data sets. It is demonstrated that the extended class of models frequently yields better fit than classical ordinal response models without an uncertainty component.

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Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects

Cited by 56 publications

References 23 publications

Finite Mixtures of Generalized Linear Regression Models

Finite Mixtures of Generalized Linear Regression Models

FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters

Mixture models for ordinal responses to account for uncertainty of choice

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