Linear Models For Optimal Test Design
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Linear Models For Optimal Test Design
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Author : W. J. Linden
language : en
Publisher:
Release Date : 2011-03-21
Linear Models For Optimal Test Design written by W. J. Linden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-21 with categories.
Linear Models For Optimal Test Design
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Author : Wim J. van der Linden
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-01
Linear Models For Optimal Test Design written by Wim J. van der Linden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Social Science categories.
Wim van der Linden was just given a lifetime achievement award by the National Council on Measurement in Education. There is no one more prominent in the area of educational testing. There are hundreds of computer-based credentialing exams in areas such as accounting, real estate, nursing, and securities, as well as the well-known admissions exams for college, graduate school, medical school, and law school - there is great need on the theory of testing. This book presents the statistical theory and practice behind constructing good tests e.g., how is the first test item selected, how are the next items selected, and when do you have enough items.
Optimal Experimental Design For Non Linear Models
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Author : Christos P. Kitsos
language : en
Publisher:
Release Date : 2014-01-31
Optimal Experimental Design For Non Linear Models written by Christos P. Kitsos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with categories.
Design Of Experiments For Generalized Linear Models
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Author : Kenneth G. Russell
language : en
Publisher: CRC Press
Release Date : 2018-12-14
Design Of Experiments For Generalized Linear Models written by Kenneth G. Russell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-14 with Mathematics categories.
Generalized Linear Models (GLMs) allow many statistical analyses to be extended to important statistical distributions other than the Normal distribution. While numerous books exist on how to analyse data using a GLM, little information is available on how to collect the data that are to be analysed in this way. This is the first book focusing specifically on the design of experiments for GLMs. Much of the research literature on this topic is at a high mathematical level, and without any information on computation. This book explains the motivation behind various techniques, reduces the difficulty of the mathematics, or moves it to one side if it cannot be avoided, and gives examples of how to write and run computer programs using R. Features The generalisation of the linear model to GLMs Background mathematics, and the use of constrained optimisation in R Coverage of the theory behind the optimality of a design Individual chapters on designs for data that have Binomial or Poisson distributions Bayesian experimental design An online resource contains R programs used in the book This book is aimed at readers who have done elementary differentiation and understand minimal matrix algebra, and have familiarity with R. It equips professional statisticians to read the research literature. Nonstatisticians will be able to design their own experiments by following the examples and using the programs provided.
A First Course In The Design Of Experiments
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Author : John H. Skillings
language : en
Publisher: Routledge
Release Date : 2018-05-08
A First Course In The Design Of Experiments written by John H. Skillings and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with Mathematics categories.
Most texts on experimental design fall into one of two distinct categories. There are theoretical works with few applications and minimal discussion on design, and there are methods books with limited or no discussion of the underlying theory. Furthermore, most of these tend to either treat the analysis of each design separately with little attempt to unify procedures, or they will integrate the analysis for the designs into one general technique. A First Course in the Design of Experiments: A Linear Models Approach stands apart. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. The authors begin with a general introduction then lead students through the theoretical results, the various design models, and the analytical concepts that will enable them to analyze virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. The authors use the SAS software package throughout the book, but also demonstrate how any regression program can be used for analysis. With its balanced presentation of theory, methods, and applications and its highly readable style, A First Course in the Design of Experiments proves ideal as a text for a beginning graduate or upper-level undergraduate course in the design and analysis of experiments.
Statistical Tests For Mixed Linear Models
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Author : André I. Khuri
language : en
Publisher: Wiley-Interscience
Release Date : 1998-01-29
Statistical Tests For Mixed Linear Models written by André I. Khuri and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models at an advanced level. Statistical Tests for Mixed Linear Models: Combines analysis and testing in one self-contained volume. Describes analysis of variance (ANOVA) procedures in balanced and unbalanced data situations. Examines methods for determining the effect of imbalance on data analysis. Explains exact and optimum tests and methods for their derivation. Summarizes test procedures for multivariate mixed and random models. Enables novice readers to skip the derivations and discussions on optimum tests. Offers plentiful examples and exercises, many of which are numerical in flavor. Provides solutions to selected exercises. Statistical Tests for Mixed Linear Models is an accessible reference for researchers in analysis of variance, experimental design, variance component analysis, and linear mixed models. It is also an important text for graduate students interested in mixed models.
Plane Answers To Complex Questions
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Author : Ronald Christensen
language : en
Publisher: Springer
Release Date : 2021-08-26
Plane Answers To Complex Questions written by Ronald Christensen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Mathematics categories.
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.
Design Of Experiments
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Author : Max Morris
language : en
Publisher: CRC Press
Release Date : 2010-07-27
Design Of Experiments written by Max Morris and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-27 with Mathematics categories.
Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experiment
Design Of Experiments For Generalized Linear Models
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Author : Kenneth Graham Russell
language : en
Publisher:
Release Date : 2019
Design Of Experiments For Generalized Linear Models written by Kenneth Graham Russell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with MATHEMATICS categories.
"While there are numerous books on the analysis of Generalized Linear Models (GLMs), there is very little information available on how to design the experiments that will collect the data. This book will describe the theory and methods for designing experiments to collect data that will be analysed by GLMs. It shows that the extensive theory underlying design for linear models does not work for GLMs, and gives practical guidance as to how best to design experiments for GLMs. It includes lots of examples to illustrate the topics, and is supplemented by R code for their implementation"--
Optimization Of Adaptive Test Design Methods For The Determination Of Steady State Data Driven Models In Terms Of Combustion Engine Calibration
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Author : Sandmeier, Nino
language : en
Publisher: Universitätsverlag der TU Berlin
Release Date : 2022-12-01
Optimization Of Adaptive Test Design Methods For The Determination Of Steady State Data Driven Models In Terms Of Combustion Engine Calibration written by Sandmeier, Nino and has been published by Universitätsverlag der TU Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Technology & Engineering categories.
This thesis deals with the development of a model-based adaptive test design strategy with a focus on steady-state combustion engine calibration. The first research topic investigates the question how to handle limits in the input domain during an adaptive test design procedure. The second area of scope aims at identifying the test design method providing the best model quality improvement in terms of overall model prediction error. To consider restricted areas in the input domain, a convex hull-based solution involving a convex cone algorithm is developed, the outcome of which serves as a boundary model for a test point search. A solution is derived to enable the application of the boundary model to high-dimensional problems without calculating the exact convex hull and cones. Furthermore, different data-driven engine modeling methods are compared, resulting in the Gaussian process model as the most suitable one for a model-based calibration. To determine an appropriate test design method for a Gaussian process model application, two new strategies are developed and compared to state-of-the-art methods. A simulation-based study shows the most benefit applying a modified mutual information test design, followed by a newly developed relevance-based test design with less computational effort. The boundary model and the relevance-based test design are integrated into a multicriterial test design strategy that is tailored to match the requirements of combustion engine test bench measurements. A simulation-based study with seven and nine input parameters and four outputs each offered an average model quality improvement of 36 % and an average measured input area volume increase of 65 % compared to a non-adaptive space-filling test design. The multicriterial test design was applied to a test bench measurement with seven inputs for verification. Compared to a space-filling test design measurement, the improvement could be confirmed with an average model quality increase of 17 % over eight outputs and a 34 % larger measured input area. Diese Arbeit befasst sich mit der Entwicklung einer modellbasierten adaptiven Versuchsplanungsstrategie für die Anwendung in der Applikation des Stationärverhaltens von Verbrennungsmotoren. Der erste Forschungsteil untersucht, wie sich Grenzen im Eingangsraum in die Versuchsplanung eines adaptiven Prozesses einbinden lassen. Ein weiterer Fokus liegt auf der Identifikation einer modellbasierten Versuchsplanung, die eine bestmögliche Verbesserung der globalen Modellqualität hinsichtlich des Prädiktionsfehlers ermöglicht. Es wird ein Grenzraummodell auf Basis der konvexen Hülle unter Zuhilfenahme eines Algorithmus zur Bestimmung eines konvexen Konus entwickelt, das als Grundlage für eine Versuchsplanung in beschränkten Eingangsräumen verwendet wird. Um die Anwendbarkeit bei hochdimensionalen Problemstellungen zu gewährleisten, wird ein Verfahren vorgestellt, das eine Berechnung auch ohne die Bestimmung der exakten konvexen Hülle und konvexen Konen ermöglicht. Des Weiteren werden verschiedene Methoden zur datengetriebenen Modellbildung des Verbrennungsmotors verglichen, wobei das Gauß-Prozess Modell als die geeignetste Modellierungsmethode hervorgeht. Um die bestmögliche Versuchsplanungsmethode bei der Anwendung des Gauß-Prozess Modells zu ermitteln, werden zwei neue Strategien entwickelt und mit verfügbaren Methoden aus der Literatur verglichen. Eine simulationsbasierte Studie zeigt, dass eine angepasste Mutual Information Methode die besten Ergebnisse liefert. Ein neu entwickeltes relevanzbasiertes Verfahren erreicht die zweitbesten Ergebnisse, bietet aber einen geringeren Berechnungsaufwand als das Mutual Information Verfahren. Das Grenzmodell und das relevanzbasierte Verfahren werden in einem multikriteriellen Versuchsplanungsverfahren zusammengeführt, das an die Anforderungen von Messungen an einem Verbrennungsmotorenprüfstand angepasst ist. In einer simulationsbasierten Studie mit sieben bzw. neun Eingangsparametern und jeweils vier Ausgängen konnte eine durchschnittliche Modellqualitätsverbesserung von 36 % und eine mittlere Vergrößerung des vermessenen Eingangsraumvolumens von 65 % im Vergleich zu einer nichtadaptiven raumfüllenden Versuchsplanung gezeigt werden. Das multikriterielle Versuchsplanungsverfahren wurde anhand von Prüfstandsmessungen mit sieben Eingangsparametern verifiziert. Im Vergleich zu einer raumfüllenden Versuchsplanung konnte eine mittlere Modellqualitätsverbesserung über alle acht Ausgänge von 17 % und ein um 34 % vergrößertes vermessenes Eingangsraumvolumen erreicht werden, wodurch die Ergebnisse der Simulationen bestätigt werden konnten.