Log Linear Models
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| Author | : Ronald Christensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 498 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387226249 |
The primary focus here is on log-linear models for contingency tables, but in this second edition, greater emphasis has been placed on logistic regression. The book explores topics such as logistic discrimination and generalised linear models, and builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. It also carefully examines the differences in model interpretations and evaluations that occur due to the discrete nature of the data. Sample commands are given for analyses in SAS, BMFP, and GLIM, while numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. Throughoutthe book, the treatment is designed for students with prior knowledge of analysis of variance and regression.
| Author | : Ronald Christensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 420 |
| Release | : 2013-12-14 |
| Genre | : Mathematics |
| ISBN | : 1475741111 |
This book examines log-linear models for contingency tables. Logistic re gression and logistic discrimination are treated as special cases and gener alized linear models (in the GLIM sense) are also discussed. The book is designed to fill a niche between basic introductory books such as Fienberg (1980) and Everitt (1977) and advanced books such as Bishop, Fienberg, and Holland (1975), Haberman (1974), and Santner and Duffy (1989). lt is primarily directed at advanced Masters degree students in Statistics but it can be used at both higher and lower levels. The primary theme of the book is using previous knowledge of analysis of variance and regression to motivate and explicate the use of log-linear models. Of course, both the analogies and the distinctions between the different methods must be kept in mind. The book is written at several levels. A basic introductory course would take material from Chapters I, II (deemphasizing Section II. 4), III, Sec tions IV. 1 through IV. 5 (eliminating the material on graphical models), Section IV. lü, Chapter VII, and Chapter IX. The advanced modeling ma terial at the end of Sections VII. 1, VII. 2, and possibly the material in Section IX. 2 should be deleted in a basic introductory course. For Mas ters degree students in Statistics, all the material in Chapters I through V, VII, IX, and X should be accessible. For an applied Ph. D.
| Author | : Aleksandr Aravkin |
| Publisher | : MIT Press |
| Total Pages | : 215 |
| Release | : 2024-12-03 |
| Genre | : Computers |
| ISBN | : 0262553465 |
Advances in training models with log-linear structures, with topics including variable selection, the geometry of neural nets, and applications. Log-linear models play a key role in modern big data and machine learning applications. From simple binary classification models through partition functions, conditional random fields, and neural nets, log-linear structure is closely related to performance in certain applications and influences fitting techniques used to train models. This volume covers recent advances in training models with log-linear structures, covering the underlying geometry, optimization techniques, and multiple applications. The first chapter shows readers the inner workings of machine learning, providing insights into the geometry of log-linear and neural net models. The other chapters range from introductory material to optimization techniques to involved use cases. The book, which grew out of a NIPS workshop, is suitable for graduate students doing research in machine learning, in particular deep learning, variable selection, and applications to speech recognition. The contributors come from academia and industry, allowing readers to view the field from both perspectives. Contributors Aleksandr Aravkin, Avishy Carmi, Guillermo A. Cecchi, Anna Choromanska, Li Deng, Xinwei Deng, Jean Honorio, Tony Jebara, Huijing Jiang, Dimitri Kanevsky, Brian Kingsbury, Fabrice Lambert, Aurélie C. Lozano, Daniel Moskovich, Yuriy S. Polyakov, Bhuvana Ramabhadran, Irina Rish, Dimitris Samaras, Tara N. Sainath, Hagen Soltau, Serge F. Timashev, Ewout van den Berg
| Author | : Jason W. Osborne |
| Publisher | : SAGE Publications |
| Total Pages | : 489 |
| Release | : 2016-03-24 |
| Genre | : Psychology |
| ISBN | : 1506302750 |
In a conversational tone, Regression & Linear Modeling provides conceptual, user-friendly coverage of the generalized linear model (GLM). Readers will become familiar with applications of ordinary least squares (OLS) regression, binary and multinomial logistic regression, ordinal regression, Poisson regression, and loglinear models. Author Jason W. Osborne returns to certain themes throughout the text, such as testing assumptions, examining data quality, and, where appropriate, nonlinear and non-additive effects modeled within different types of linear models.
| Author | : Randall E. Schumacker |
| Publisher | : SAGE Publications |
| Total Pages | : 648 |
| Release | : 2014-01-28 |
| Genre | : Social Science |
| ISBN | : 148332477X |
Providing easy-to-use R script programs that teach descriptive statistics, graphing, and other statistical methods, Learning Statistics Using R shows readers how to run and utilize R, a free integrated statistical suite that has an extensive library of functions. Randall E. Schumacker’s comprehensive book describes in detail the processing of variables in statistical procedures. Covering a wide range of topics, from probability and sampling distribution to statistical theorems and chi-square, this introductory book helps readers learn not only how to use formulae to calculate statistics, but also how specific statistics fit into the overall research process. Learning Statistics Using R covers data input from vectors, arrays, matrices and data frames, as well as the input of data sets from SPSS, SAS, STATA and other software packages. Schumacker’s text provides the freedom to effectively calculate, manipulate, and graphically display data, using R, on different computer operating systems without the expense of commercial software. Learning Statistics Using R places statistics within the framework of conducting research, where statistical research hypotheses can be directly addressed. Each chapter includes discussion and explanations, tables and graphs, and R functions and outputs to enrich readers′ understanding of statistics through statistical computing and modeling.
| Author | : P. McCullagh |
| Publisher | : Routledge |
| Total Pages | : 536 |
| Release | : 2019-01-22 |
| Genre | : Mathematics |
| ISBN | : 1351445847 |
The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and ot
| Author | : Alexander von Eye |
| Publisher | : Wiley |
| Total Pages | : 472 |
| Release | : 2012-12-17 |
| Genre | : Mathematics |
| ISBN | : 9781118146408 |
An easily accessible introduction to log-linear modeling for non-statisticians Highlighting advances that have lent to the topic's distinct, coherent methodology over the past decade, Log-Linear Modeling: Concepts, Interpretation, and Application provides an essential, introductory treatment of the subject, featuring many new and advanced log-linear methods, models, and applications. The book begins with basic coverage of categorical data, and goes on to describe the basics of hierarchical log-linear models as well as decomposing effects in cross-classifications and goodness-of-fit tests. Additional topics include: The generalized linear model (GLM) along with popular methods of coding such as effect coding and dummy coding Parameter interpretation and how to ensure that the parameters reflect the hypotheses being studied Symmetry, rater agreement, homogeneity of association, logistic regression, and reduced designs models Throughout the book, real-world data illustrate the application of models and understanding of the related results. In addition, each chapter utilizes R, SYSTAT®, and §¤EM software, providing readers with an understanding of these programs in the context of hierarchical log-linear modeling. Log-Linear Modeling is an excellent book for courses on categorical data analysis at the upper-undergraduate and graduate levels. It also serves as an excellent reference for applied researchers in virtually any area of study, from medicine and statistics to the social sciences, who analyze empirical data in their everyday work.
| Author | : Alvin C. Rencher |
| Publisher | : John Wiley & Sons |
| Total Pages | : 690 |
| Release | : 2008-01-07 |
| Genre | : Mathematics |
| ISBN | : 0470192607 |
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
| Author | : Peter K. Dunn |
| Publisher | : Springer |
| Total Pages | : 573 |
| Release | : 2018-11-10 |
| Genre | : Mathematics |
| ISBN | : 1441901183 |
This textbook presents an introduction to generalized linear models, complete with real-world data sets and practice problems, making it applicable for both beginning and advanced students of applied statistics. Generalized linear models (GLMs) are powerful tools in applied statistics that extend the ideas of multiple linear regression and analysis of variance to include response variables that are not normally distributed. As such, GLMs can model a wide variety of data types including counts, proportions, and binary outcomes or positive quantities. The book is designed with the student in mind, making it suitable for self-study or a structured course. Beginning with an introduction to linear regression, the book also devotes time to advanced topics not typically included in introductory textbooks. It features chapter introductions and summaries, clear examples, and many practice problems, all carefully designed to balance theory and practice. The text also provides a working knowledge of applied statistical practice through the extensive use of R, which is integrated into the text. Other features include: • Advanced topics such as power variance functions, saddlepoint approximations, likelihood score tests, modified profile likelihood, small-dispersion asymptotics, and randomized quantile residuals • Nearly 100 data sets in the companion R package GLMsData • Examples that are cross-referenced to the companion data set, allowing readers to load the data and follow the analysis in their own R session
| Author | : Alan Agresti |
| Publisher | : John Wiley & Sons |
| Total Pages | : 471 |
| Release | : 2015-02-23 |
| Genre | : Mathematics |
| ISBN | : 1118730038 |
A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.
