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Multivariate and Mixture Distribution Rasch Models

Multivariate and Mixture Distribution Rasch Models
Author: Matthias Davier
Publisher: Springer Science & Business Media
Total Pages: 400
Release: 2007-12-15
Genre: Social Science
ISBN: 0387498397

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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.


Finite Mixture Models

Finite Mixture Models
Author: Geoffrey McLachlan
Publisher: John Wiley & Sons
Total Pages: 419
Release: 2004-03-22
Genre: Mathematics
ISBN: 047165406X

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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.


Theoretical and Practical Advances in Computer-based Educational Measurement

Theoretical and Practical Advances in Computer-based Educational Measurement
Author: Bernard P. Veldkamp
Publisher: Springer
Total Pages: 399
Release: 2019-07-05
Genre: Education
ISBN: 3030184803

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This open access book presents a large number of innovations in the world of operational testing. It brings together different but related areas and provides insight in their possibilities, their advantages and drawbacks. The book not only addresses improvements in the quality of educational measurement, innovations in (inter)national large scale assessments, but also several advances in psychometrics and improvements in computerized adaptive testing, and it also offers examples on the impact of new technology in assessment. Due to its nature, the book will appeal to a broad audience within the educational measurement community. It contributes to both theoretical knowledge and also pays attention to practical implementation of innovations in testing technology.


Handbook of Item Response Theory

Handbook of Item Response Theory
Author: Wim J. van der Linden
Publisher: CRC Press
Total Pages: 624
Release: 2016-10-14
Genre: Mathematics
ISBN: 1466514426

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Drawing on the work of internationally acclaimed experts in the field, Handbook of Item Response Theory, Volume One: Models presents all major item response models. This first volume in a three-volume set covers many model developments that have occurred in item response theory (IRT) during the last 20 years. It describes models for different response formats or response processes, the need of deeper parameterization due to a multilevel or hierarchical structure of the response data, and other extensions and insights. In Volume One, all chapters have a common format with each chapter focusing on one family of models or modeling approach. An introductory section in every chapter includes some history of the model and a motivation of its relevance. Subsequent sections present the model more formally, treat the estimation of its parameters, show how to evaluate its fit to empirical data, illustrate the use of the model through an empirical example, and discuss further applications and remaining research issues.


Handbook of Mixture Analysis

Handbook of Mixture Analysis
Author: Sylvia Fruhwirth-Schnatter
Publisher: CRC Press
Total Pages: 522
Release: 2019-01-04
Genre: Computers
ISBN: 0429508247

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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.


Cognitive Abilities and Educational Outcomes

Cognitive Abilities and Educational Outcomes
Author: Monica Rosén
Publisher: Springer
Total Pages: 351
Release: 2016-10-03
Genre: Education
ISBN: 331943473X

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This book addresses problems and challenges that face educational measurement at a time when multipurpose usage of observational data from educational assessments, tests and international surveys has become a growing global trend. While the construction of educational measures and use of educational data offer many opportunities, they also require awareness of the numerous threats to validity and methods of reducing such threats. Written by leading international scholars, the book demonstrates the complexity of educational measurement by addressing three broad and interrelated topics. The first part discusses cognitive abilities, including studies on fluid intelligence, its improvement and its links to aptitude tests for admission to higher education. The second part focuses on the effects of school and teacher-related factors on school outcomes at individual and group levels, and uses international studies to analyze causes. The third part presents analytical techniques and measurement methods to improve reliability, for example factor analysis using Bayesian estimators, bi-factor analysis, model misfit and solutions, and discusses balance issues in reporting test results. The book provides examples of state-of-the-art analytical techniques for pursuing fundamental research problems, and the latest advances in measurement methods, with a focus on validity improvement. Eminent researchers discuss and provide insights into questions such as: Is it possible to train individuals to think at a higher level than normal for their age? What determines prospective preschool teachers’ skill to perceive mathematics-related preschool situations? Can international indicator design and instruments be improved to use trends and national context variables more efficiently? Can indicator data at national, school and class levels be compared easier? Are value-added measures of teacher effectiveness valid when it comes to hiring and promoting teachers? Is money better spent on teacher training than on smaller class-size? How do theory and empirical statistical data intertwine in building structures of understanding? This book is inspired by the career and personal influence of the Swedish scholar Professor Jan-Eric Gustafsson, renowned for his research on individual differences, especially the structure of cognitive abilities, and on the effects of education on knowledge and skills.


Statistical Analysis of Questionnaires

Statistical Analysis of Questionnaires
Author: Francesco Bartolucci
Publisher: CRC Press
Total Pages: 324
Release: 2015-07-23
Genre: Mathematics
ISBN: 146656850X

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Statistical Analysis of Questionnaires: A Unified Approach Based on R and Stata presents special statistical methods for analyzing data collected by questionnaires. The book takes an applied approach to testing and measurement tasks, mirroring the growing use of statistical methods and software in education, psychology, sociology, and other fields.


Handbook of Diagnostic Classification Models

Handbook of Diagnostic Classification Models
Author: Matthias von Davier
Publisher: Springer Nature
Total Pages: 656
Release: 2019-10-11
Genre: Education
ISBN: 3030055841

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This handbook provides an overview of major developments around diagnostic classification models (DCMs) with regard to modeling, estimation, model checking, scoring, and applications. It brings together not only the current state of the art, but also the theoretical background and models developed for diagnostic classification. The handbook also offers applications and special topics and practical guidelines how to plan and conduct research studies with the help of DCMs. Commonly used models in educational measurement and psychometrics typically assume a single latent trait or at best a small number of latent variables that are aimed at describing individual differences in observed behavior. While this allows simple rankings of test takers along one or a few dimensions, it does not provide a detailed picture of strengths and weaknesses when assessing complex cognitive skills. DCMs, on the other hand, allow the evaluation of test taker performance relative to a potentially large number of skill domains. Most diagnostic models provide a binary mastery/non-mastery classification for each of the assumed test taker attributes representing these skill domains. Attribute profiles can be used for formative decisions as well as for summative purposes, for example in a multiple cut-off procedure that requires mastery on at least a certain subset of skills. The number of DCMs discussed in the literature and applied to a variety of assessment data has been increasing over the past decades, and their appeal to researchers and practitioners alike continues to grow. These models have been used in English language assessment, international large scale assessments, and for feedback for practice exams in preparation of college admission testing, just to name a few. Nowadays, technology-based assessments provide increasingly rich data on a multitude of skills and allow collection of data with respect to multiple types of behaviors. Diagnostic models can be understood as an ideal match for these types of data collections to provide more in-depth information about test taker skills and behavioral tendencies.