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AbstractThe logistic regression model is one of the most powerful statistical methods for the analysis of binary data. Logistic regression allows using a set of covariates to explain the binary responses. A mixture of logistic regression models is used to fit heterogeneous populations using an unsupervised learning approach. The multicollinearity problem is one of the most common problems in logistic and a mixture of logistic regressions, where the covariates are highly correlated. This problem results in unreliable maximum likelihood estimates for the regression coefficients. This research develops shrinkage methods to deal with the multicollinearity in a mixture of logistic regression models. These shrinkage methods include ridge and Liu-type estimators. Through extensive numerical studies, we show that the developed methods provide more reliable results in estimating the coefficients of the mixture. Finally, we applied shrinkage methods to analyze the status of bone disorders in women aged 50 and older. [ABSTRACT FROM AUTHOR]

In this paper we study point processes on the complex plane and illustrate their uses in several statistical areas, where the quantities of interest requiring estimation involve Fourier expansions. In particular, for any problem where we can describe a quantity in terms of its Fourier expansion, we propose modeling the coefficients of the expansion using a point process on the complex plane. We utilize the Poisson complex point process and model its intensity function using log-linear and mixture models. The proposed models are exemplified via applications to general density approximation, via modeling of the characteristic function, and time series analysis, via modeling of the spectral density. [ABSTRACT FROM AUTHOR]

Abstract Mixture models and designs are used in situations where the response depends on the proportions of the factors (components). Optimum designs were derived for mixture models with fixed regression parameters under homoscedastic error variance by several authors. In this paper, an attempt has been made to find D- and A-optimum designs for the estimation of model parameters with heteroscedastic error variance. It is assumed that the error variance has constant value for all points equidistant from the center of the design. Equivalence theorem plays an important role in this investigation. Robustness of the standard optimum designs in the homoscedastic case under changes in the error variances has also been studied. [ABSTRACT FROM AUTHOR]

We propose a variant of the bootstrap to assess the variability of posterior probabilities arising from Gaussian model-based clustering. The bootstrap variant uses predictions based on out-of-bootstrap-sample observations and then constructs confidence intervals for the posterior probabilities using the percentile method. The methodology outperforms the multivariate Delta method approach when comparing empirical coverage probabilities on simulated data. The proposed and multivariate Delta methods are also illustrated on the well-known Iris data set. [ABSTRACT FROM AUTHOR]

Recent research in the area of univariate mixture modeling indicated that the finite mixture models based on Burr and Inverse Burr component distributions perform well in the modeling of heavy-tail insurance data. Mixture models are able to capture the multimodality which is quite a common characteristic of insurance losses. Through an extensive simulation study, we assess the performance of three different methods in building the confidence intervals for high quantiles of the mixtures of Burr and Inverse Burr distributions. First, we provide mathematical justification for linking the tail of the k-Burr and k-Inverse Burr mixtures to the maximum domain of attraction of the Fréchet distribution which allows us to employ the Generalized Pareto Distribution (GPD) in the estimation of high quantiles and their corresponding confidence intervals. Then, we compare these results to those obtained using order statistics and the bootstrap methods. We also modified the existing Peak Over Threshold (POT) algorithm for the efficient computation of the confidence intervals in the upper tail of these mixture models. A real data set on Danish Fire Losses is used to illustrate the application of these methods in practice. [ABSTRACT FROM AUTHOR]

This paper investigates the data generating structure which can be represented as a mixture of single-index panel data model with heterogeneous link function. The switching between the states is governed by a hidden variable. We also offer an Expectation Maximization (EM) algorithm for estimating parameters numerically. The ability of the proposed mixture model will be illustrated with both the simulated performance and the empirical applications. [ABSTRACT FROM AUTHOR]

The Riesz probability distribution was introduced in 2001 as an extension of the Wishart one. Although the Wishart distribution was investigated in many engineering applications, the Riesz applicability seems to be forsaken. This can be explained by the lack of studies offering statistical models and algorithms dealing with this distribution. Within this framework, we extend the Bartlett decomposition to the Riesz and inverse Riesz probability distributions. We prove that they can be generated easily using gamma and Gaussian independent variates adequately parameterized. Then we develop an Expectation-Maximization algorithm to estimate the parameters of the Riesz mixture model, along with the inverse Riesz mixture. Finally, some simulations are conducted and show a good estimation of the mixture parameters and clusters number. [ABSTRACT FROM AUTHOR]

Mixture models are frequently used for modeling complex data. An extension of the EM algorithm, here called ECME, is proposed to compute the maximum likelihood estimate of parameters of symmetric-stable mixture model (SSMM). Comprehensive simulation studies are performed to show the performance of the proposed ECME algorithm. The robustness of the SSMM is investigated by simulations when it is used to model data generated from mixture of exponential power andtdistributions. Both proposed ECME and Bayesian approaches are applied to three sets of real data, which shows that the proposed ECME algorithm outperforms the Bayesian paradigm for all three sets. Also, the SSMM is compared with the mixture of normal, skew normal,t, and skewtdistributions for modeling four sets of real data. It turns out that the SSMM works as well as or better than above models. This can be considered as SSMM capability in robust mixture modeling. [ABSTRACT FROM PUBLISHER]

The analysis of human perceptions is often carried out by resorting to surveys and questionnaires, where respondents are asked to express ratings about the objects being evaluated. A class of mixture models, called CUB (Combination of Uniform and shifted Binomial), has been recently proposed in this context. This article focuses on a model of this class, the Nonlinear CUB, and investigates some computational issues concerning parameter estimation, which is performed by Maximum Likelihood. More specifically, we consider two main approaches to optimize the log-likelihood: the classical numerical methods of optimization and the EM algorithm. The classical numerical methods comprise the widely used algorithms Nelder–Mead, Newton–Raphson, Broyden–Fletcher–Goldfarb–Shanno (BFGS), Berndt–Hall–Hall–Hausman (BHHH), Simulated Annealing, Conjugate Gradients and usually have the advantage of a fast convergence. On the other hand, the EM algorithm deserves consideration for some optimality properties in the case of mixture models, but it is slower. This article has a twofold aim: first we show how to obtain explicit formulas for the implementation of the EM algorithm in nonlinear CUB models and we formally derive the asymptotic variance–covariance matrix of the Maximum Likelihood estimator; second, we discuss and compare the performance of the two above mentioned approaches to the log-likelihood maximization. [ABSTRACT FROM AUTHOR]

Mixtures of factor analyzers (MFAs) have been popularly used to cluster the high-dimensional data. However, the traditional estimation method is based on the normality assumptions of random terms and thus is sensitive to outliers. In this article, we introduce a robust estimation procedure of MFAs using the trimmed likelihood estimator. We use a simulation study and a real data application to demonstrate the robustness of the trimmed estimation procedure and compare it with the traditional normality-based maximum likelihood estimate. [ABSTRACT FROM PUBLISHER]

In 2009 a survey was performed in Veneto, a region in the north-east of Italy, to study the demand for wine and specifically for Passito, a typical Italian wine. The main goal of the study consisted in analyzing how the preferences and consumption habits of Passito vary depending on consumers’ characteristics. Specifically two kinds of statistical methods were applied:Covariate Uniform Binomial (CUB)model, a statistical approach for ordinal data to study the feeling toward Passito and the uncertainty of the respondents; classical logistic regression analysis, to describe how the attitude toward passito can be modeled as function of consumers’ covariates. Gender and residence were the most important covariates, useful in defining segments of consumers with significant differences in terms of Passito's preferences and consumption behavior. The logistic regression analysis allowed to complete the statistical analysis based on CUB models validating the results of the CUB model and estimating a model useful to predict the attitude toward the considered product for specific sub-groups of consumers. [ABSTRACT FROM PUBLISHER]

The use of mixture models for clustering purposes has been considerably increased the last years primarily due to the existence of efficient computational methods that facilitate estimation. Nowadays, there are several clustering procedures based on mixtures for certain types of data. On the other hand, copulas are becoming very popular models to model dependencies as one of their appealing properties is the separation of the marginal properties of the data from the dependence properties. The purpose of this article is to put together the two distinct ideas, namely mixtures and copulas, so as to use mixtures of copulas aiming at using them for clustering with respect to the dependence properties of the data. This is accomplished by considering finite mixture of different copulas to represent different dependence structures. We provide properties of the derived models along with the description of an estimation method using an EM algorithm based on the standard approach for mixture models. Using daily returns from major stock markets, we illustrate the potential of our method. [ABSTRACT FROM PUBLISHER]

This article enlarges the covariance configurations, on which the classical linear discriminant analysis is based, by considering the four models arising from the spectral decomposition when eigenvalues and/or eigenvectors matrices are allowed to vary or not between groups. As in the classical approach, the assessment of these configurations is accomplished via a test on the training set. The discrimination rule is then built upon the configuration provided by the test, considering or not the unlabeled data. Numerical experiments, on simulated and real data, have been performed to evaluate the gain of our proposal with respect to the linear discriminant analysis. [ABSTRACT FROM PUBLISHER]

In this article, the approaches for exploiting mixtures of mixtures are expanded by using the Multiresolution family of probability density functions (MR pdf). The flexibility and the properties of local analysis of the MR pdf facilitate the location of subpopulations into a given population. In order to do this, two algorithms are provided. The MR model is more flexible in adapting to the different subpopulations than the traditional mixtures. In addition, the problems of identification of mixtures distributions and the label-switching do not appear in the MR pdf context. [ABSTRACT FROM PUBLISHER]

A developmental trajectory describes the course of behavior over time. Identifying multiple trajectories within an overall developmental process permits a focus on subgroups of particular interest. We introduce a framework for identifying trajectories by using the Expectation-Maximization (EM) algorithm to fit semiparametric mixtures of logistic distributions to longitudinal binary data. For performance comparison, we consider full maximization algorithms (PROC TRAJ in SAS), standard EM, and two other EM-based algorithms for speeding up convergence. Simulation shows that EM methods produce more accurate parameter estimates. The EM methodology is illustrated with a longitudinal dataset involving adolescents smoking behaviors. [ABSTRACT FROM AUTHOR]

The label-switching problem is one of the fundamental problems in Bayesian mixture analysis. Using all the Markov chain Monte Carlo samples as the initials for the expectation-maximization (EM) algorithm, we propose to label the samples based on the modes they converge to. Our method is based on the assumption that the samples converged to the same mode have the same labels. If a relative noninformative prior is used or the sample size is large, the posterior will be close to the likelihood and then the posterior modes can be located approximately by the EM algorithm for mixture likelihood, without assuming the availability of the closed form of the posterior. In order to speed up the computation of this labeling method, we also propose to first cluster the samples byK-means with a large number of clustersK. Then, by assuming that the samples within each cluster have the same labels, we only need to find one converged mode for each cluster. Using a Monte Carlo simulation study and a real dataset, we demonstrate the success of our new method in dealing with the label-switching problem. [ABSTRACT FROM AUTHOR]

A model-based classification technique is developed, based on mixtures of multivariate t-factor analyzers. Specifically, two related mixture models are developed and their classification efficacy studied. An AECM algorithm is used for parameter estimation, and convergence of these algorithms is determined using Aitken's acceleration. Two different techniques are proposed for model selection: the BIC and the ICL. Our classification technique is applied to data on red wine samples from Italy and to fatty acid measurements on Italian olive oils. These results are discussed and compared to more established classification techniques; under this comparison, our mixture models give excellent classification performance. [ABSTRACT FROM PUBLISHER]

In this article we propose mixture of distributions belonging to the biparametric exponential family, considering joint modeling of the mean and variance (or dispersion) parameters. As special cases we consider mixtures of normal and gamma distributions. A novel Bayesian methodology, using Markov Chain Monte Carlo (MCMC) methods, is proposed to obtain the posterior summaries of interest. We include simulations and real data examples to illustrate de performance of the proposal. [ABSTRACT FROM PUBLISHER]

The aim of this article is to discuss homogeneity testing of the exponential distribution. We introduce the exact likelihood ratio test of homogeneity in the subpopulation model, ELR, and the exact likelihood ratio test of homogeneity against the two-components subpopulation alternative, ELR2. The ELR test is asymptotically optimal in the Bahadur sense when the alternative consists of sampling from a fixed number of components. Thus, in some setups the ELR is superior to frequently used tests for exponential homogeneity which are based on the EM algorithm (like the MLRT, ADDS, and D-tests). One important example of superiority of ELR and ELR2 tests is the case of lower contamination. We demonstrate this fact by both theoretical comparisons and simulations. [ABSTRACT FROM AUTHOR]

This article addresses the use of different biweight functions in high breakdown mixture discriminant analysis approach of Bashir and Carter (2005). The translated biweight S function of Rocke (1996) is used in the robust estimation of the mixture distributions parameters. As in discriminant analysis, the main purpose is to classify the test observations with greater accuracy, so the estimators producing smaller errors of misclassification are preferred. In the simulation studies, the use of Tukey's biweight function was proved to be more effective in producing better classification results as compared to the translated biweight function. [ABSTRACT FROM AUTHOR]