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Much social and behavioral research involves hierarchical data structures. The effects of school characteristics on students, how differences in government policies from country to country influence demographic relations within them, and how individuals exposed to different environmental conditions develop over time are a few examples. This introductory text explicates the theory and use of hierarchical linear models through rich illustrative examples and lucid explanations.

"Ecosystem" is an intuitively appealing concept to most ecologists, but, in spite of its widespread use, the term remains diffuse and ambiguous. The authors of this book argue that previous attempts to define the concept have been derived from particular viewpoints to the exclusion of others equally possible. They offer instead a more general line of thought based on hierarchy theory. Their contribution should help to counteract the present separation of subdisciplines in ecology and to bring functional and population/community ecologists closer to a common approach. Developed as a way of understanding highly complex organized systems, hierarchy theory has at its center the idea that organization results from differences in process rates. To the authors the theory suggests an objective way of decomposing ecosystems into their component parts. The results thus obtained offer a rewarding method for integrating various schools of ecology.

Keep Up to Date with the Evolving Landscape of Space and Space-Time Data Analysis and Modeling Since the publication of the first edition, the statistical landscape has substantially changed for analyzing space and space-time data. More than twice the size of its predecessor, Hierarchical Modeling and Analysis for Spatial Data, Second Edition reflects the major growth in spatial statistics as both a research area and an area of application. New to the Second Edition New chapter on spatial point patterns developed primarily from a modeling perspective New chapter on big data that shows how the predictive process handles reasonably large datasets New chapter on spatial and spatiotemporal gradient modeling that incorporates recent developments in spatial boundary analysis and wombling New chapter on the theoretical aspects of geostatistical (point-referenced) modeling Greatly expanded chapters on methods for multivariate and spatiotemporal modeling New special topics sections on data fusion/assimilation and spatial analysis for data on extremes Double the number of exercises Many more color figures integrated throughout the text Updated computational aspects, including the latest version of WinBUGS, the new flexible spBayes software, and assorted R packages The Only Comprehensive Treatment of the Theory, Methods, and Software This second edition continues to provide a complete treatment of the theory, methods, and application of hierarchical modeling for spatial and spatiotemporal data. It tackles current challenges in handling this type of data, with increased emphasis on observational data, big data, and the upsurge of associated software tools. The authors also explore important application domains, including environmental science, forestry, public health, and real estate.

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix.The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition.Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

Popular in the First Edition for its rich, illustrative examples and lucid explanations of the theory and use of hierarchical linear models (HLM), the book has been reorganized into four parts with four completely new chapters. The first two parts, Part I on "The Logic of Hierarchical Linear Modeling" and Part II on "Basic Applications" closely parallel the first nine chapters of the previous edition with significant expansions and technical clarifications, such as: * An intuitive introductory summary of the basic procedures for estimation and inference used with HLM models that only requires a minimal level of mathematical sophistication in Chapter 3* New section on multivariate growth models in Chapter 6 * A discussion of research synthesis or meta-analysis applications in Chapter 7* Data analytic advice on centering of level-1 predictors and new material on plausible value intervals and robust standard estimators

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix.The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition.Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis, or written at a level often inaccessible to those lacking a strong background in mathematical statistics.Hierarchical Modeling and Analysis for Spatial Data is the first accessible, self-contained treatment of hierarchical methods, modeling, and data analysis for spatial and spatio-temporal data. Starting with overviews of the types of spatial data, the data analysis tools appropriate for each, and a brief review of the Bayesian approach to statistics, the authors discuss hierarchical modeling for univariate spatial response data, including Bayesian kriging and lattice (areal data) modeling. They then consider the problem of spatially misaligned data, methods for handling multivariate spatial responses, spatio-temporal models, and spatial survival models. The final chapter explores a variety of special topics, including spatially varying coefficient models.This book provides clear explanations, plentiful illustrations --some in full color--a variety of homework problems, and tutorials and worked examples using some of the field's most popular software packages.. Written by a team of leaders in the field, it will undoubtedly remain the primary textbook and reference on the subject for years to come.

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods.This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures.The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution* abundance models based on many sampling protocols, including distance sampling* capture-recapture models with individual effects* spatial capture-recapture models based on camera trapping and related methods* population and metapopulation dynamic models* models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants)* Development of classical, likelihood-based procedures for inference, as well asBayesian methods of analysis* Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS* Computing support in technical appendices in an online companion web site

Keep Up to Date with the Evolving Landscape of Space and Space-Time Data Analysis and Modeling Since the publication of the first edition, the statistical landscape has substantially changed for analyzing space and space-time data. More than twice the size of its predecessor, Hierarchical Modeling and Analysis for Spatial Data, Second Edition reflects the major growth in spatial statistics as both a research area and an area of application. New to the Second Edition New chapter on spatial point patterns developed primarily from a modeling perspective New chapter on big data that shows how the predictive process handles reasonably large datasets New chapter on spatial and spatiotemporal gradient modeling that incorporates recent developments in spatial boundary analysis and wombling New chapter on the theoretical aspects of geostatistical (point-referenced) modeling Greatly expanded chapters on methods for multivariate and spatiotemporal modeling New special topics sections on data fusion/assimilation and spatial analysis for data on extremes Double the number of exercises Many more color figures integrated throughout the text Updated computational aspects, including the latest version of WinBUGS, the new flexible spBayes software, and assorted R packages The Only Comprehensive Treatment of the Theory, Methods, and Software This second edition continues to provide a complete treatment of the theory, methods, and application of hierarchical modeling for spatial and spatiotemporal data. It tackles current challenges in handling this type of data, with increased emphasis on observational data, big data, and the upsurge of associated software tools. The authors also explore important application domains, including environmental science, forestry, public health, and real estate.

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods.This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures.The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution* abundance models based on many sampling protocols, including distance sampling* capture-recapture models with individual effects* spatial capture-recapture models based on camera trapping and related methods* population and metapopulation dynamic models* models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants)* Development of classical, likelihood-based procedures for inference, as well asBayesian methods of analysis* Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS* Computing support in technical appendices in an online companion web site

Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis, or written at a level often inaccessible to those lacking a strong background in mathematical statistics.Hierarchical Modeling and Analysis for Spatial Data is the first accessible, self-contained treatment of hierarchical methods, modeling, and data analysis for spatial and spatio-temporal data. Starting with overviews of the types of spatial data, the data analysis tools appropriate for each, and a brief review of the Bayesian approach to statistics, the authors discuss hierarchical modeling for univariate spatial response data, including Bayesian kriging and lattice (areal data) modeling. They then consider the problem of spatially misaligned data, methods for handling multivariate spatial responses, spatio-temporal models, and spatial survival models. The final chapter explores a variety of special topics, including spatially varying coefficient models.This book provides clear explanations, plentiful illustrations --some in full color--a variety of homework problems, and tutorials and worked examples using some of the field's most popular software packages.. Written by a team of leaders in the field, it will undoubtedly remain the primary textbook and reference on the subject for years to come.

Seeks to represent the order in nature by discriminating a hierarchical system and defining the logical boundaries of the concepts inherent in this system (such as time, causality, complexity, partitioning, scale, and polarity). This book describes the principles of hierarchical structure.

An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

Applied Hierarchical Modeling in Ecology: Distribution, Abundance, Species Richness offers a new synthesis of the state-of-the-art of hierarchical models for plant and animal distribution, abundance, and community characteristics such as species richness using data collected in metapopulation designs. These types of data are extremely widespread in ecology and its applications in such areas as biodiversity monitoring and fisheries and wildlife management. This first volume explains static models/procedures in the context of hierarchical models that collectively represent a unified approach to ecological research, taking the reader from design, through data collection, and into analyses using a very powerful class of models. Applied Hierarchical Modeling in Ecology, Volume 1 serves as an indispensable manual for practicing field biologists, and as a graduate-level text for students in ecology, conservation biology, fisheries/wildlife management, and related fields.Provides a synthesis of important classes of models about distribution, abundance, and species richness while accommodating imperfect detectionPresents models and methods for identifying unmarked individuals and speciesWritten in a step-by-step approach accessible to non-statisticians and provides fully worked examples that serve as a template for readers' analysesIncludes companion website containing data sets, code, solutions to exercises, and further information

Seeks to represent the order in nature by discriminating a hierarchical system and defining the logical boundaries of the concepts inherent in this system (such as time, causality, complexity, partitioning, scale, and polarity). This book describes the principles of hierarchical structure.

Applied Hierarchical Modeling in Ecology: Distribution, Abundance, Species Richness offers a new synthesis of the state-of-the-art of hierarchical models for plant and animal distribution, abundance, and community characteristics such as species richness using data collected in metapopulation designs. These types of data are extremely widespread in ecology and its applications in such areas as biodiversity monitoring and fisheries and wildlife management. This first volume explains static models/procedures in the context of hierarchical models that collectively represent a unified approach to ecological research, taking the reader from design, through data collection, and into analyses using a very powerful class of models. Applied Hierarchical Modeling in Ecology, Volume 1 serves as an indispensable manual for practicing field biologists, and as a graduate-level text for students in ecology, conservation biology, fisheries/wildlife management, and related fields.Provides a synthesis of important classes of models about distribution, abundance, and species richness while accommodating imperfect detectionPresents models and methods for identifying unmarked individuals and speciesWritten in a step-by-step approach accessible to non-statisticians and provides fully worked examples that serve as a template for readers' analysesIncludes companion website containing data sets, code, solutions to exercises, and further information

An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout. Author resource page: http://www.stat.columbia.edu/~gelman/arm/

Can we live with the God of Ezekiel? Can we relate to a God who has established a multilayered hierarchy that separates the divine from the human, who creates boundaries that segregate people from the temple, the priesthood, and the glory of the Lord? In contrast to those who suggest that Ezekiel should no longer be read as an authoritative part of the canon, the essays in this volume engage Ezekiel’s hierarchical world directly, neither dismissing it out of hand nor accepting it uncritically. By wedding theological interest and reflection with serious biblical exegesis and criticism, this work helps readers to understand Ezekiel’s hierarchical theology—especially the book’s views on creation, priesthood, and land. It thus equips readers to form their own evaluations of the relevance of Ezekiel’s theology for today.

Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout. Author resource page: http://www.stat.columbia.edu/~gelman/arm/