Mixture Models And Applications

This book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature. Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection; Present theoretical and practical developments in mixture-based modeling and their importance in different applications; Discusses perspectives and challenging future works related to mixture modeling.

Patients are not alike! This simple truth is often ignored in the analysis of me- cal data, since most of the time results are presented for the “average” patient. As a result, potential variability between patients is ignored when presenting, e.g., the results of a multiple linear regression model. In medicine there are more and more attempts to individualize therapy; thus, from the author’s point of view biostatis- cians should support these efforts. Therefore, one of the tasks of the statistician is to identify heterogeneity of patients and, if possible, to explain part of it with known explanatory covariates. Finite mixture models may be used to aid this purpose. This book tries to show that there are a large range of applications. They include the analysis of gene - pression data, pharmacokinetics, toxicology, and the determinants of beta-carotene plasma levels. Other examples include disease clustering, data from psychophysi- ogy, and meta-analysis of published studies. The book is intended as a resource for those interested in applying these methods.

An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.

Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.

"This is a great overview of the field of model-based clustering and classification by one of its leading developers. McNicholas provides a resource that I am certain will be used by researchers in statistics and related disciplines for quite some time. The discussion of mixtures with heavy tails and asymmetric distributions will place this text as the authoritative, modern reference in the mixture modeling literature." (Douglas Steinley, University of Missouri) Mixture Model-Based Classification is the first monograph devoted to mixture model-based approaches to clustering and classification. This is both a book for established researchers and newcomers to the field. A history of mixture models as a tool for classification is provided and Gaussian mixtures are considered extensively, including mixtures of factor analyzers and other approaches for high-dimensional data. Non-Gaussian mixtures are considered, from mixtures with components that parameterize skewness and/or concentration, right up to mixtures of multiple scaled distributions. Several other important topics are considered, including mixture approaches for clustering and classification of longitudinal data as well as discussion about how to define a cluster Paul D. McNicholas is the Canada Research Chair in Computational Statistics at McMaster University, where he is a Professor in the Department of Mathematics and Statistics. His research focuses on the use of mixture model-based approaches for classification, with particular attention to clustering applications, and he has published extensively within the field. He is an associate editor for several journals and has served as a guest editor for a number of special issues on mixture models.

This book examines extensions of the Rasch model, one of the most researched and applied models in educational research and social science. This collection contains 22 chapters by some of the most renowned international experts in the field. They cover topics ranging from general model extensions to applications in fields as diverse as cognition, personality, organizational and sports psychology, and health sciences and education.

This practical introduction to second-order and growth mixture models using Mplus introduces simple and complex techniques through incremental steps. The authors extend latent growth curves to second-order growth curve and mixture models and then combine the two. To maximize understanding, each model is presented with basic structural equations, figures with associated syntax that highlight what the statistics mean, Mplus applications, and an interpretation of results. Examples from a variety of disciplines demonstrate the use of the models and exercises allow readers to test their understanding of the techniques. A comprehensive introduction to confirmatory factor analysis, latent growth curve modeling, and growth mixture modeling is provided so the book can be used by readers of various skill levels. The book’s datasets are available on the web. Highlights include: -Illustrative examples using Mplus 7.4 include conceptual figures, Mplus program syntax, and an interpretation of results to show readers how to carry out the analyses with actual data. -Exercises with an answer key allow readers to practice the skills they learn. -Applications to a variety of disciplines appeal to those in the behavioral, social, political, educational, occupational, business, and health sciences. -Data files for all the illustrative examples and exercises at www.routledge.com/9781138925151 allow readers to test their understanding of the concepts. -Point to Remember boxes aid in reader comprehension or provide in-depth discussions of key statistical or theoretical concepts. Part 1 introduces basic structural equation modeling (SEM) as well as first- and second-order growth curve modeling. The book opens with the basic concepts from SEM, possible extensions of conventional growth curve models, and the data and measures used throughout the book. The subsequent chapters in part 1 explain the extensions. Chapter 2 introduces conventional modeling of multidimensional panel data, including confirmatory factor analysis (CFA) and growth curve modeling, and its limitations. The logical and theoretical extension of a CFA to a second-order growth curve, known as curve-of-factors model (CFM), are explained in Chapter 3. Chapter 4 illustrates the estimation and interpretation of unconditional and conditional CFMs. Chapter 5 presents the logical and theoretical extension of a parallel process model to a second-order growth curve, known as factor-of-curves model (FCM). Chapter 6 illustrates the estimation and interpretation of unconditional and conditional FCMs. Part 2 reviews growth mixture modeling including unconditional growth mixture modeling (Ch. 7) and conditional growth mixture models (Ch. 8). How to extend second-order growth curves (curve-of-factors and factor-of-curves models) to growth mixture models is highlighted in Chapter 9. Ideal as a supplement for use in graduate courses on (advanced) structural equation, multilevel, longitudinal, or latent variable modeling, latent growth curve and mixture modeling, factor analysis, multivariate statistics, or advanced quantitative techniques (methods) taught in psychology, human development and family studies, business, education, health, and social sciences, this book’s practical approach also appeals to researchers. Prerequisites include a basic knowledge of intermediate statistics and structural equation modeling.