A maximum likelihood methodology for clusterwise linear regression

DeSarbo, Wayne S.; Cron, William L.

doi:10.1007/bf01897167

Cited by 418 publications

(235 citation statements)

References 51 publications

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“…The mixture likelihood approach proposed simultaneously estimates the membership of the observations in an (initially specified) number of classes and the parameters of the generalized linear model that relates the dependent to the independent variables within each class, accommodating a large number of possible distributions for the dependent variable. This paper generalizes the McCullagh and Nelder (1989) work to a latent class framework, as well as previously published models (e.g., DeSarbo and Cron 1988;De Soete and DeSarbo 1991;Kamakura and Russell 1989;) to accommodate any distribution from the exponential family (as well as others) and provides a simple and unifying estimation approach. The EM-algorithm proposed for the estimation of the model has the advantages of being computationally attractive, of being easy to program, and of convergence being ensured.…”

Section: Discussionmentioning

confidence: 92%

“…Cramrr 1946;Redner and Walker 1984;DeSarbo and Cron 1988). The asymptotic covariance matrix of the estimates of 13 i, conditional upon Class i can be calculated from the inverse of the observed Fisher information matrix (e.g., McLachlan and Basford 1988;Louis 1982):…”

Section: Standard Errors Of the Estimatesmentioning

confidence: 99%

“…Whereas in these "unconditional" approaches for finite mixtures of normal distributions the mean and variance of the underlying densities are estimated, "conditional" mixture models allow for the simultaneous probabilistic classification of observations and the estimation of regression models relating covariates to the expectations of the dependent variable within latent classes. DeSarbo and Cron (1988) propose a "conditional" mixture model which enables the estimation of separate regression functions (and corresponding object memberships) in a number of classes using maximum likelihood. The model specifies a finite mixture of univariate normal densities in which the expectations of these densities are specified as linear functions of a set of explanatory variables.…”

Section: Introductionmentioning

confidence: 99%

“…As such, the model generalizes the Quandt (1972), Hosmer (1974), and Quandt and Ramsey (1978) stochastic switching regression models to more than two classes, and uses maximum likelihood rather than method of moments estimators. DeSarbo and Cron (1988) use an EM algorithm to estimate their conditional mixture model. A large number of mixture regression models has now been developed (see Wedel and DeSarbo 1994, for a review).…”

Section: Introductionmentioning

confidence: 99%

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A mixture likelihood approach for generalized linear models

Wedel

DeSarbo

1995

Journal of Classification

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252

155

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A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.

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Section: Discussionmentioning

confidence: 92%

Section: Standard Errors Of the Estimatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A mixture likelihood approach for generalized linear models

Wedel

DeSarbo

1995

Journal of Classification

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252

155

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“…Different types of functional models have been used to for such data. Among them polynomial and spline regression are the most commonly used models [3] and have been successfully applied to a number of diverse applications, ranging from gene clustering in bioinformatics to clustering of cyclone trajectories, see for example [4] [5], [6] and [7].…”

Section: Introductionmentioning

confidence: 99%

A Sparse Regression Mixture Model for Clustering Time-Series

Blekas

Galatsanos

Likas

Artificial Intelligence: Theories, Models and Applications

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Abstract. In this study we present a new sparse polynomial regression mixture model for fitting time series. The contribution of this work is the introduction of a smoothing prior over component regression coefficients through a Bayesian framework. This is done by using an appropriate Student-t distribution. The advantages of the sparsity-favouring prior is to make model more robust, less independent on order p of polynomials and improve the clustering procedure. The whole framework is converted into a maximum a posteriori (MAP) approach, where the known EM algorithm can be applied offering update equations for the model parameters in closed forms. The efficiency of the proposed sparse mixture model is experimentally shown by applying it on various real benchmarks and by comparing it with the typical regression mixture and the K-means algorithm. The results are very promising.

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Unsupervised Learning

Giovanni¹

2018

Wiley Encyclopedia of Electrical and Electronics Engineering

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This article presents a review of traditional and current methods of classification in the framework of unsupervised learning. Focus is placed on cluster analysis and self‐organizing neural networks: two vector quantization methods aiming at minimizing the distance between an input vector and its representation. The learning is unsupervised as no predefined cluster structure of the input data is assumed. The review of cluster analysis methods covers (i) hard clustering, hierarchical and nonhierarchical, whose aim is to assign exact units (objects) to clusters (i.e., with membership degree equal to 1); (ii) fuzzy clustering, where the membership degree of a unit to a cluster is in the range [0; 1]; and (iii) mixture clustering, a model‐based clustering consisting in fitting a mixture model to data and identifying each cluster with one of its components. These clustering methods are reviewed in all the variants related to the presence of complex and/or big data structures and to the presence of outliers. The self‐organizing maps are also presented as artificial neural network, the cells (neurons) of which become specifically tuned to various input data patterns or classes of patterns through an unsupervised learning process.

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A maximum likelihood methodology for clusterwise linear regression

Abstract: Cluster analysis, Multiple regression, Maximum likelihood estimation, E-M algorithm, Marketing trade shows,

Cited by 418 publications

References 51 publications

A mixture likelihood approach for generalized linear models

A mixture likelihood approach for generalized linear models

A Sparse Regression Mixture Model for Clustering Time-Series

Unsupervised Learning

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