Author

# Donald G. Watts

Bio: Donald G. Watts is an academic researcher from Queen's University. The author has contributed to research in topics: Nonlinear regression & Polynomial regression. The author has an hindex of 18, co-authored 39 publications receiving 4503 citations.

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01 Aug 1988

TL;DR: This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares.

Abstract: Wiley-Interscience Paperback Series The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models ...highly recommend[ed] ...for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." -Technometrics "[This book] provides a good balance of relevant theory and application with many examples ...[and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students." -Mathematical Reviews "[This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition ...[and is] a worthwhile reference for the marketing researcher with a serious interest in linear models. " -Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. The authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. The book also includes pseudocode for computing algorithms.

3,202 citations

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453 citations

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27 May 2008122 citations

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TL;DR: In this article, the individual terms of the parameter effects curvature array are interpreted and local compensation methods are suggested, and a method of computing the parameter-effects array corresponding to a transformed set of parameters is given and discussed how this result could be used to determine reparameterizations which have zero local parameter effects nonlinearity.

Abstract: In a previous paper, it was shown that parameter-effects nonlinearities of a nonlinear regression model-experimental design-parameterization combination can be quantified by means of a parameter-effects curvature array $A$ based on second derivatives of the model function. In this paper, the individual terms of $A$ are interpreted and local compensation methods are suggested. A method of computing the parameter-effects array corresponding to a transformed set of parameters is given and we discuss how this result could be used to determine reparameterizations which have zero local parameter-effects nonlinearity.

92 citations

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TL;DR: In this article, the joint confidence and likelihood regions for the parameters in nonlinear regression models can be defined using the geometric concepts of sample space and solution locus, and it is shown that these inference regions correspond to ellipsoids on the tangent plane at the least squares point.

Abstract: Joint confidence and likelihood regions for the parameters in nonlinear regression models can be defined using the geometric concepts of sample space and solution locus. Using a quadratic approximation to the solution locus, instead of the usual linear approximation, it is shown that these inference regions correspond to ellipsoids on the tangent plane at the least squares point. Accurate approximate inference regions can be obtained by mapping these ellipsoids into the parameter space, and measures of the effect of intrinsic nonlinearity on inference can be based on the difference between the tangent plane ellipsoids and the sphere which would be obtained using a linear approximation.

90 citations

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TL;DR: In this article, a model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms, and the formula and data together determine a numerical representation of the model from which the profiled deviance or the profeatured REML criterion can be evaluated as a function of some of model parameters.

Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

50,607 citations

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TL;DR: In this article, a model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms, and the formula and data together determine a numerical representation of the model from which the profiled deviance or the profeatured REML criterion can be evaluated as a function of some of model parameters.

Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

14,433 citations

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3,494 citations

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27 Jan 2006

TL;DR: In this article, the authors present a detailed case study of R algorithms with publicly available data, and a major section of the book is devoted to fully worked case studies, with a companion website where readers can reproduce every number, figure and table on their own computers.

Abstract: Full four-color book.
Some of the editors created the Bioconductor project and Robert Gentleman is one of the two originators of R.
All methods are illustrated with publicly available data, and a major section of the book is devoted to fully worked case studies.
Code underlying all of the computations that are shown is made available on a companion website, and readers can reproduce every number, figure, and table on their own computers.

2,625 citations