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This textbook presents a unified and rigorous approach to best
linear unbiased estimation and prediction of parameters and random
quantities in linear models, as well as other theory upon which
much of the statistical methodology associated with linear models
is based. The single most unique feature of the book is that each
major concept or result is illustrated with one or more concrete
examples or special cases. Commonly used methodologies based on the
theory are presented in methodological interludes scattered
throughout the book, along with a wealth of exercises that will
benefit students and instructors alike. Generalized inverses are
used throughout, so that the model matrix and various other
matrices are not required to have full rank. Considerably more
emphasis is given to estimability, partitioned analyses of
variance, constrained least squares, effects of model
misspecification, and most especially prediction than in many other
textbooks on linear models. This book is intended for master and
PhD students with a basic grasp of statistical theory, matrix
algebra and applied regression analysis, and for instructors of
linear models courses. Solutions to the book's exercises are
available in the companion volume Linear Model Theory - Exercises
and Solutions by the same author.
In the past, disease pattern mapping depended on census tracts
based on political units, such as states and counties. However,
with the advent of geographic information systems (GIS),
researchers can now achieve a new level of precision and
flexibility in geographic locating. This emerging technology allows
the mapping of many different kinds of geographies, including
disease rates in relation to pollution sources. Geocoding Health
Data presents a state-of-the-art discussion on the current
technical and administrative developments in geographic information
science. In particular, it discusses how geocoded residential
addresses can be used to examine the spatial patterns of cancer
incidence, staging, survival, and mortality. The book begins with
an introduction of various codes and their uses, including census
geographic, health area, and street level codes. It goes on to
describe the specific application of geocodes to cancer, detailing
methods, materials, and technical issues. The text illustrates how
to compile data maps for analysis and addresses issues, such as
mismatch correction and data quality. It describes the current
state of geocoding practices and discusses the use of individually
geocoded cancer incidences in spatial epidemiology, distance
estimation and spatial accessibilities, and tips for handling
non-geocoded cases. Special consideration is given to privacy and
confidentiality issues by focusing on disclosure limitation
methods. With recent disease outbreaks and escalating concerns
about bioterrorism, interest in the application of GIS to
individual data is growing. The fundamental concepts presented by
this book are of great value to anyone trying to understand the
causes, prevention, and control of cancer as well as a variety of
other diseases.
The First Book Dedicated to This Class of Longitudinal Models
Although antedependence models are particularly useful for modeling
longitudinal data that exhibit serial correlation, few books
adequately cover these models. By gathering results scattered
throughout the literature, Antedependence Models for Longitudinal
Data offers a convenient, systematic way to learn about
antedependence models. Illustrated with numerous examples, the book
also covers some important statistical inference procedures
associated with these models. After describing unstructured and
structured antedependence models and their properties, the authors
discuss informal model identification via simple summary statistics
and graphical methods. They then present formal likelihood-based
procedures for normal antedependence models, including maximum
likelihood and residual maximum likelihood estimation of parameters
as well as likelihood ratio tests and penalized likelihood model
selection criteria for the model's covariance structure and mean
structure. The authors also compare the performance of
antedependence models to other models commonly used for
longitudinal data. With this book, readers no longer have to search
across widely scattered journal articles on the subject. The book
provides a thorough treatment of the properties and statistical
inference procedures of various antedependence models.
In the past, disease pattern mapping depended on census tracts
based on political units, such as states and counties. However,
with the advent of geographic information systems (GIS),
researchers can now achieve a new level of precision and
flexibility in geographic locating. This emerging technology allows
the mapping of many different kinds of geographies, including
disease rates in relation to pollution sources. Geocoding Health
Data presents a state-of-the-art discussion on the current
technical and administrative developments in geographic information
science. In particular, it discusses how geocoded residential
addresses can be used to examine the spatial patterns of cancer
incidence, staging, survival, and mortality. The book begins with
an introduction of various codes and their uses, including census
geographic, health area, and street level codes. It goes on to
describe the specific application of geocodes to cancer, detailing
methods, materials, and technical issues. The text illustrates how
to compile data maps for analysis and addresses issues, such as
mismatch correction and data quality. It describes the current
state of geocoding practices and discusses the use of individually
geocoded cancer incidences in spatial epidemiology, distance
estimation and spatial accessibilities, and tips for handling
non-geocoded cases. Special consideration is given to privacy and
confidentiality issues by focusing on disclosure limitation
methods. With recent disease outbreaks and escalating concerns
about bioterrorism, interest in the application of GIS to
individual data is growing. The fundamental concepts presented by
this book are of great value to anyone trying to understand
thecauses, prevention, and control of cancer as well as a variety
of other diseases.
This book contains 296 exercises and solutions covering a wide
variety of topics in linear model theory, including generalized
inverses, estimability, best linear unbiased estimation and
prediction, ANOVA, confidence intervals, simultaneous confidence
intervals, hypothesis testing, and variance component estimation.
The models covered include the Gauss-Markov and Aitken models,
mixed and random effects models, and the general mixed linear
model. Given its content, the book will be useful for students and
instructors alike. Readers can also consult the companion textbook
Linear Model Theory - With Examples and Exercises by the same
author for the theory behind the exercises.
This book contains 296 exercises and solutions covering a wide
variety of topics in linear model theory, including generalized
inverses, estimability, best linear unbiased estimation and
prediction, ANOVA, confidence intervals, simultaneous confidence
intervals, hypothesis testing, and variance component estimation.
The models covered include the Gauss-Markov and Aitken models,
mixed and random effects models, and the general mixed linear
model. Given its content, the book will be useful for students and
instructors alike. Readers can also consult the companion textbook
Linear Model Theory - With Examples and Exercises by the same
author for the theory behind the exercises.
This textbook presents a unified and rigorous approach to best
linear unbiased estimation and prediction of parameters and random
quantities in linear models, as well as other theory upon which
much of the statistical methodology associated with linear models
is based. The single most unique feature of the book is that each
major concept or result is illustrated with one or more concrete
examples or special cases. Commonly used methodologies based on the
theory are presented in methodological interludes scattered
throughout the book, along with a wealth of exercises that will
benefit students and instructors alike. Generalized inverses are
used throughout, so that the model matrix and various other
matrices are not required to have full rank. Considerably more
emphasis is given to estimability, partitioned analyses of
variance, constrained least squares, effects of model
misspecification, and most especially prediction than in many other
textbooks on linear models. This book is intended for master and
PhD students with a basic grasp of statistical theory, matrix
algebra and applied regression analysis, and for instructors of
linear models courses. Solutions to the book's exercises are
available in the companion volume Linear Model Theory - Exercises
and Solutions by the same author.
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