Vector Generalized Linear and Additive Models

Vector Generalized Linear and Additive Models

The methodological contribution of this book stands alone and does not require use of the VGAM package. This book presents a statistical framework that expands generalized linear models (GLMs) for regression modelling.

Author: Thomas W. Yee

Publisher: Springer

ISBN: 9781493928187

Category: Mathematics

Page: 589

View: 110

This book presents a greatly enlarged statistical framework compared to generalized linear models (GLMs) with which to approach regression modelling. Comprising of about half-a-dozen major classes of statistical models, and fortified with necessary infrastructure to make the models more fully operable, the framework allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. However, GLMs are not flexible enough to cope with the demands of practical data analysis. And data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. The methodology here and accompanying software (the extensive VGAM R package) are directed at these limitations and are described comprehensively for the first time in one volume. This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs. The book can be used in senior undergraduate or first-year postgraduate courses on GLMs or categorical data analysis and as a methodology resource for VGAM users. In the second part of the book, the R package VGAM allows readers to grasp immediately applications of the methodology. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences. The methodological contribution of this book stands alone and does not require use of the VGAM package.
Categories: Mathematics

Vector Generalized Linear and Additive Models

Vector Generalized Linear and Additive Models

The methodological contribution of this book stands alone and does not require use of the VGAM package. In the second part of the book, the R package VGAM makes applications of the methodology immediate.

Author: Thomas W. Yee

Publisher:

ISBN: 1493928198

Category:

Page:

View: 860

This book presents a statistical framework that expands generalized linear models (GLMs) for regression modelling. The framework shared in this book allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. This is possible through the approximately half-a-dozen major classes of statistical models included in the book and the software infrastructure component, which makes the models easily operable. The book's methodology and accompanying software (the extensive VGAM R package) are directed at these limitations, and this is the first time the methodology and software are covered comprehensively in one volume. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. The demands of practical data analysis, however, require a flexibility that GLMs do not have. Data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs. The book may be used in senior undergraduate and first-year postgraduate courses on GLMs and regression modeling, including categorical data analysis. It may also serve as a reference on vector generalized linear models and as a methodology resource for VGAM users. The methodological contribution of this book stands alone and does not require use of the VGAM package. In the second part of the book, the R package VGAM makes applications of the methodology immediate. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences.
Categories:

Generalized Additive Models

Generalized Additive Models

Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility.

Author: Simon Wood

Publisher: CRC Press

ISBN: 9781584884743

Category: Mathematics

Page: 410

View: 877

Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.
Categories: Mathematics

Generalized Additive Models

Generalized Additive Models

This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques.

Author: T.J. Hastie

Publisher: CRC Press

ISBN: 0412343908

Category: Mathematics

Page: 352

View: 130

This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.
Categories: Mathematics

COMPSTAT

COMPSTAT

where fi is estimated by a VLPKE and fa by a vector spline. Currently, only s() is ...
Linear smoothers and additive models (with discussion) Ann. Statist., 17, 453-
555. de Boor, ... Nonparametric Regression and Generalized Linear Models.

Author: Jelke G. Bethlehem

Publisher: Springer Science & Business Media

ISBN: 3790813265

Category: Business & Economics

Page: 540

View: 316

This book contains the keynote, invited and full contributed papers presented at COMPSTAT 2000, held in Utrecht. The papers range over all aspects of the link between statistical theory and applied statistics, with special attention for developments in the area of official statistics. The papers have been thoroughly refereed.
Categories: Business & Economics

Data Mining and Statistics for Decision Making

Data Mining and Statistics for Decision Making

decision trees, vector generalized linear model, vector generalized additive
model, neural networks gamma and log- normal regressions Poisson regression,
log-linear model generalized linear models with repeated measures decision
trees, ...

Author: Stéphane Tufféry

Publisher: John Wiley & Sons

ISBN: 0470979283

Category: Computers

Page: 716

View: 484

Data mining is the process of automatically searching large volumes of data for models and patterns using computational techniques from statistics, machine learning and information theory; it is the ideal tool for such an extraction of knowledge. Data mining is usually associated with a business or an organization's need to identify trends and profiles, allowing, for example, retailers to discover patterns on which to base marketing objectives. This book looks at both classical and recent techniques of data mining, such as clustering, discriminant analysis, logistic regression, generalized linear models, regularized regression, PLS regression, decision trees, neural networks, support vector machines, Vapnik theory, naive Bayesian classifier, ensemble learning and detection of association rules. They are discussed along with illustrative examples throughout the book to explain the theory of these methods, as well as their strengths and limitations. Key Features: Presents a comprehensive introduction to all techniques used in data mining and statistical learning, from classical to latest techniques. Starts from basic principles up to advanced concepts. Includes many step-by-step examples with the main software (R, SAS, IBM SPSS) as well as a thorough discussion and comparison of those software. Gives practical tips for data mining implementation to solve real world problems. Looks at a range of tools and applications, such as association rules, web mining and text mining, with a special focus on credit scoring. Supported by an accompanying website hosting datasets and user analysis. Statisticians and business intelligence analysts, students as well as computer science, biology, marketing and financial risk professionals in both commercial and government organizations across all business and industry sectors will benefit from this book.
Categories: Computers

Generalized Additive Models

Generalized Additive Models

Low-rank scale-invariant tensor product smooths for generalized additive mixed
models. Biometrics 62(4) ... Fast stable restricted maximum likelihood and
marginal likelihood estimation of semiparametric generalized linear models.
Journal of the ... Vector generalized linear and additive extreme value models.
Extremes ...

Author: Simon N. Wood

Publisher: CRC Press

ISBN: 9781498728348

Category: Mathematics

Page: 476

View: 763

The first edition of this book has established itself as one of the leading references on generalized additive models (GAMs), and the only book on the topic to be introductory in nature with a wealth of practical examples and software implementation. It is self-contained, providing the necessary background in linear models, linear mixed models, and generalized linear models (GLMs), before presenting a balanced treatment of the theory and applications of GAMs and related models. The author bases his approach on a framework of penalized regression splines, and while firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of R software helps explain the theory and illustrates the practical application of the methodology. Each chapter contains an extensive set of exercises, with solutions in an appendix or in the book’s R data package gamair, to enable use as a course text or for self-study. Simon N. Wood is a professor of Statistical Science at the University of Bristol, UK, and author of the R package mgcv.
Categories: Mathematics

Foundations of Linear and Generalized Linear Models

Foundations of Linear and Generalized Linear Models

Vector generalized additive models. J. R. Stat. Soc. B 58: 481–493. Yule, G.U.
1897. On the theory of correlation. J. Roy. Stat. Soc. 60:812–854. Yule, G.U. 1900
. On the association of attributes in statistics. Philos. Trans. Roy. Soc. London Ser.

Author: Alan Agresti

Publisher: John Wiley & Sons

ISBN: 9781118730058

Category: Mathematics

Page: 480

View: 181

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.
Categories: Mathematics

SAS and R

SAS and R

... for R [93] reshape Flexibly reshape data [195] rjags Bayesian graphical models
using MCMC [131] RMongo MongoDB ... Student t distribution [199] vcd
Visualizing categorical data [118] VGAM Vector generalized linear and additive
models ...

Author: Ken Kleinman

Publisher: CRC Press

ISBN: 9781466584495

Category: Mathematics

Page: 468

View: 865

An Up-to-Date, All-in-One Resource for Using SAS and R to Perform Frequent Tasks The first edition of this popular guide provided a path between SAS and R using an easy-to-understand, dictionary-like approach. Retaining the same accessible format, SAS and R: Data Management, Statistical Analysis, and Graphics, Second Edition explains how to easily perform an analytical task in both SAS and R, without having to navigate through the extensive, idiosyncratic, and sometimes unwieldy software documentation. The book covers many common tasks, such as data management, descriptive summaries, inferential procedures, regression analysis, and graphics, along with more complex applications. New to the Second Edition This edition now covers RStudio, a powerful and easy-to-use interface for R. It incorporates a number of additional topics, including using application program interfaces (APIs), accessing data through database management systems, using reproducible analysis tools, and statistical analysis with Markov chain Monte Carlo (MCMC) methods and finite mixture models. It also includes extended examples of simulations and many new examples. Enables Easy Mobility between the Two Systems Through the extensive indexing and cross-referencing, users can directly find and implement the material they need. SAS users can look up tasks in the SAS index and then find the associated R code while R users can benefit from the R index in a similar manner. Numerous example analyses demonstrate the code in action and facilitate further exploration. The datasets and code are available for download on the book’s website.
Categories: Mathematics

Linear Regression

Linear Regression

The prerequisites for this text are linear algebra and a calculus based course in statistics. This text covers both multiple linear regression and some experimental design models.

Author: David J. Olive

Publisher: Springer

ISBN: 9783319552521

Category: Mathematics

Page: 494

View: 611

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models. This text is for graduates and undergraduates with a strong mathematical background. The prerequisites for this text are linear algebra and a calculus based course in statistics.
Categories: Mathematics

Applied Regression Analysis and Generalized Linear Models

Applied Regression Analysis and Generalized Linear Models

Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book.

Author: John Fox

Publisher: SAGE Publications

ISBN: 9781483321318

Category: Social Science

Page: 816

View: 365

Combining a modern, data-analytic perspective with a focus on applications in the social sciences, the Third Edition of Applied Regression Analysis and Generalized Linear Models provides in-depth coverage of regression analysis, generalized linear models, and closely related methods, such as bootstrapping and missing data. Updated throughout, this Third Edition includes new chapters on mixed-effects models for hierarchical and longitudinal data. Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book.
Categories: Social Science

Journal of the American Statistical Association

Journal of the American Statistical Association

Yee , T . , and Wild , C . ( 1996 ) , “ Vector - Generalized Additive Models , ”
Journal of the Royal Statistical Society , Ser . B , 58 , 481 - 493 . Brent A .
JOHNSON , D . Y . Lin Cottet , Kohn , and Nott : Overdispersed Generalized
Linear Models 671.

Author:

Publisher:

ISBN: UOM:49015003303352

Category: Electronic journals

Page:

View: 418

Categories: Electronic journals

New Developments in Classification and Data Analysis

New Developments in Classification and Data Analysis

In this paper, we propose to constrain bivariate interactions by a bi-additive
model which allows a simple graphical representation in which each category of
every variable is represented by a vector. 1 Introduction Generalized linear
modelling ...

Author: Classification Group of SIS. Meeting

Publisher: Springer Science & Business Media

ISBN: 3540238093

Category: Business & Economics

Page: 369

View: 683

The volume presents new developments in data analysis and classification. Particular attention is devoted to clustering, discrimination, data analysis and statistics, as well as applications in biology, finance and social sciences. The reader will find theory and algorithms on recent technical and methodological developments and many application papers showing the empirical usefulness of the newly developed solutions.
Categories: Business & Economics

COMPSTAT

COMPSTAT

It follows the modelling approach described by Chambers and Hastie ( 1993 ) . 2
Vector Generalized Linear and Additive Models The unifying theory behind this
article is the VGLM / VGAM framework in which the prominant ideas are ...

Author:

Publisher:

ISBN: UOM:39015057319199

Category: Mathematical statistics

Page:

View: 146

Proceedings of symposia held 1974-
Categories: Mathematical statistics

Non Life Insurance Pricing with Generalized Linear Models

Non Life Insurance Pricing with Generalized Linear Models

The book focuses on methods based on GLMs that have been found useful in actuarial practice and provides a set of tools for a tariff analysis.

Author: Esbjörn Ohlsson

Publisher: Springer Science & Business Media

ISBN: 3642107915

Category: Mathematics

Page: 174

View: 143

Non-life insurance pricing is the art of setting the price of an insurance policy, taking into consideration varoius properties of the insured object and the policy holder. Introduced by British actuaries generalized linear models (GLMs) have become today a the standard aproach for tariff analysis. The book focuses on methods based on GLMs that have been found useful in actuarial practice and provides a set of tools for a tariff analysis. Basic theory of GLMs in a tariff analysis setting is presented with useful extensions of standarde GLM theory that are not in common use. The book meets the European Core Syllabus for actuarial education and is written for actuarial students as well as practicing actuaries. To support reader real data of some complexity are provided at www.math.su.se/GLMbook.
Categories: Mathematics

Advances in Statistical Methods for the Health Sciences

Advances in Statistical Methods for the Health Sciences

Therefore, it will still be “close” to a linear model, in the sense that it will be a
simple case of additive model. Another way to enlarge the generalized linear
model ANN (GLM-ANN) is to add a second hidden layer, initialize the training
process so that the ... Each component xi of the predictor vector x serves as input
to a standard ANN whose internal connection weights have to be learned from
the data.

Author: Jean-Louis Auget

Publisher: Springer Science & Business Media

ISBN: 081764542X

Category: Mathematics

Page: 540

View: 487

Statistical methods have become an increasingly important and integral part of research in the health sciences. Many sophisticated methodologies have been developed for specific applications and problems. This self-contained comprehensive volume covers a wide range of topics pertaining to new statistical methods in the health sciences, including epidemiology, pharmacovigilance, quality of life, survival analysis, and genomics. The book will serve the health science community as well as practitioners, researchers, and graduate students in applied probability, statistics, and biostatistics.
Categories: Mathematics

Journal of the Japanese Society of Computational Statistics

Journal of the Japanese Society of Computational Statistics

... ABSTRACT Vector generalized additive models ( VGAMs ) are a multivariate
extension of generalized additive models ... survey vector generalized linear
models ( VGLMs ) , VGAMs and an S - PLUS / R implementation called VGAM
written ...

Author:

Publisher:

ISBN: UOM:39015057351986

Category: Mathematical statistics

Page:

View: 982

Categories: Mathematical statistics

Smoothing and Regression

Smoothing and Regression

Non - and semiparametric alternatives to generalized linear models ,
Computational Statistics , 12 , 173 - 191 . ... Approaches for fitting additive models
with cubic smoothing splines and associated problems , Bulletin of the
International ... Yee , T . W . and Wild , C . J . ( 1994 ) Vector Splines and the
Vector Additive Model .

Author: Michael G. Schimek

Publisher: Wiley-Interscience

ISBN: UOM:39015053114115

Category: Mathematics

Page: 607

View: 155

A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regression Smoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis. Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include: * Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines * A unified, easy-to-follow format * Contributions from more than 25 leading researchers from around the world * More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems * Extensive end-of-chapter references For professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.
Categories: Mathematics

Risk Factors and Surveillance for Arboviruses and Their Vectors in Guatemala and Puerto Rico

Risk Factors and Surveillance for Arboviruses and Their Vectors in Guatemala and Puerto Rico

This dissertation research aimed to identify environmental, geospatial, and sociodemographic risk factors for arboviruses and their vectors in Guatemala, and compare vector and human surveillance strategies to detect local arbovirus ...

Author: Zachary Joseph Madewell

Publisher:

ISBN: OCLC:1141209971

Category:

Page: 154

View: 525

Background: Aedes aegypti-borne diseases, including dengue, chikungunya, and Zika viruses, are increasingly important public health problems. Detecting and monitoring the transmission of arboviruses is critical for prevention and control activities. This dissertation research aimed to identify environmental, geospatial, and sociodemographic risk factors for arboviruses and their vectors in Guatemala, and compare vector and human surveillance strategies to detect local arbovirus transmission in Puerto Rico--sites of recent large arbovirus outbreaks. Methods: This dissertation includes three studies examining arbovirus and vector risk factors and surveillance strategies. Study one was a retrospective case-control study using data from a prospective public health surveillance system in hospitals and clinics in Guatemala and logistic regression to examine whether arboviral infections were associated with indicators of household air pollution. In study two, we used data from human and mosquito surveillance systems in Puerto Rico to develop a simulation model to compare these surveillance systems for detecting and monitoring Zika virus activity. Study three included data from two cross-sectional household surveys in Guatemala and used generalized linear and generalized additive models to assess whether household environmental and geospatial factors were associated with immature mosquito abundance. Results: For study one, arboviral infections were inversely associated with cooking with firewood in the main house, on an open hearth, and ≥5 times per week. In study two, both vector and human surveillance strategies effectively identified transmission in simulated high Zika virus transmission scenarios. In simulated low incidence scenarios, vector surveillance had higher sensitivity than human surveillance and that sensitivity increased with more traps and tests. In study three, proximity to paved roads and other houses/structures was predicted to be associated with greater immature mosquito abundance. Households with low and high household infrastructure had fewer larvae/pupae than households in the middle range. Conclusion: Better understanding of factors defining geographical distribution of arboviral vectors may allow for improved targeting of vector surveillance, prevention, and control measures in areas considered at higher risk for arbovirus transmission. Virological surveillance in mosquitoes may improve sensitivity for arbovirus detection compared to human surveillance, but resource availability is an important factor when considering the most effective approach.
Categories:

Correlated Data Analysis Modeling Analytics and Applications

Correlated Data Analysis  Modeling  Analytics  and Applications

Since the Qstatistic has an additive form and each component in the form uses
different patients or clusters, the ... As far as handling missing values concerns,
vector generalized linear models in Chapter 6 and mixed-effects models in
Chapter ...

Author: Peter X. -K. Song

Publisher: Springer Science & Business Media

ISBN: 9780387713939

Category: Mathematics

Page: 352

View: 312

This book covers recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to cover a broader range of data types than the traditional generalized linear models. The reader is provided with a systematic treatment for the topic of estimating functions, and both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to the discussions on marginal models and mixed-effects models, this book covers new topics on joint regression analysis based on Gaussian copulas.
Categories: Mathematics