Norman R. Draper

Bio: Norman R. Draper is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topics: Regression analysis & Fractional factorial design. The author has an hindex of 46, co-authored 213 publications receiving 44017 citations. Previous affiliations of Norman R. Draper include University of North Carolina at Chapel Hill & Imperial College London.

Applied Regression Analysis

Abstract: Basic Prerequisite Knowledge. Fitting a Straight Line by Least Squares. Checking the Straight Line Fit. Fitting Straight Lines: Special Topics. Regression in Matrix Terms: Straight Line Case. The General Regression Situation. Extra Sums of Squares and Tests for Several Parameters Being Zero. Serial Correlation in the Residuals and the Durbin--Watson Test. More of Checking Fitted Models. Multiple Regression: Special Topics. Bias in Regression Estimates, and Expected Values of Mean Squares and Sums of Squares. On Worthwhile Regressions, Big F's, and R 2 . Models Containing Functions of the Predictors, Including Polynomial Models. Transformation of the Response Variable. "Dummy" Variables. Selecting the "Best" Regression Equation. Ill--Conditioning in Regression Data. Ridge Regression. Generalized Linear Models (GLIM). Mixture Ingredients as Predictor Variables. The Geometry of Least Squares. More Geometry of Least Squares. Orthogonal Polynomials and Summary Data. Multiple Regression Applied to Analysis of Variance Problems. An Introduction to Nonlinear Estimation. Robust Regression. Resampling Procedures (Bootstrapping). Bibliography. True/False Questions. Answers to Exercises. Tables. Indexes.

Empirical Model-Building and Response Surfaces

Abstract: Introduction to Response Surface Methodology. The Use of Graduating Functions. Least Squares for Response Surface Work. Factorial Designs at Two Levels. Blocking and Fractionating 2 k Factorial Designs. The Use of Steepest Ascent to Achieve System Improvement. Fitting Second--Order Models. Adequacy of Estimation and the Use of Transformation. Exploration of Maxima and Ridge Systems with Second--Order Response Surfaces. Occurrence and Elucidation of Ridge Systems, I. Occurrence and Elucidation of Ridge Systems, II. Links Between Emprirical and Theoretical Models. Design Aspects of Variance, Bias, and Lack of Fit. Variance----Optimal Designs. Practical Choice of a Response Surface Design. Subject Index. Index.

Applied regression analysis 2nd ed.

Abstract: This book brings together a number of procedures developed for regression problems in current use. Since the emphasis is on practical application theoretical results are stated without proofs in many cases. This book provides a standard basic course in multiple linear regression but it also includes material that either has not previously appeared in a textbook or if it has appeared is not generally available. Chapters 1 and 3 together provide a course in fitting a straight line without using matrix algebra at all. If chapter 2 is added the idea of matrix representation of regression problems can be introduced as well. Chapter 4 covers 2 predictor variables and chapter 5 deals with more complicated models. Selecting the best regression equation is discussed in chapter 6. Chapter 7 covers specific problems. Chapters 8 and 9 discuss 1) multiple regression and mathematical model building and 2) multiple regression applied to analysis of variance problems. Chapter 10 contains an introduction to nonlinear estimation. The 2nd edition contains many new regression ideas and techniques. In particular new computational algorithms and new software regression packages have made it very easy to investigate the allequacy of conjectured models with many different techniques.

Bias in meta-analysis detected by a simple, graphical test

Abstract: Objective: Funnel plots (plots of effect estimates against sample size) may be useful to detect bias in meta-analyses that were later contradicted by large trials. We examined whether a simple test of asymmetry of funnel plots predicts discordance of results when meta-analyses are compared to large trials, and we assessed the prevalence of bias in published meta-analyses. Design: Medline search to identify pairs consisting of a meta-analysis and a single large trial (concordance of results was assumed if effects were in the same direction and the meta-analytic estimate was within 30% of the trial); analysis of funnel plots from 37 meta-analyses identified from a hand search of four leading general medicine journals 1993-6 and 38 meta-analyses from the second 1996 issue of the Cochrane Database of Systematic Reviews . Main outcome measure: Degree of funnel plot asymmetry as measured by the intercept from regression of standard normal deviates against precision. Results: In the eight pairs of meta-analysis and large trial that were identified (five from cardiovascular medicine, one from diabetic medicine, one from geriatric medicine, one from perinatal medicine) there were four concordant and four discordant pairs. In all cases discordance was due to meta-analyses showing larger effects. Funnel plot asymmetry was present in three out of four discordant pairs but in none of concordant pairs. In 14 (38%) journal meta-analyses and 5 (13%) Cochrane reviews, funnel plot asymmetry indicated that there was bias. Conclusions: A simple analysis of funnel plots provides a useful test for the likely presence of bias in meta-analyses, but as the capacity to detect bias will be limited when meta-analyses are based on a limited number of small trials the results from such analyses should be treated with considerable caution. Key messages Systematic reviews of randomised trials are the best strategy for appraising evidence; however, the findings of some meta-analyses were later contradicted by large trials Funnel plots, plots of the trials9 effect estimates against sample size, are skewed and asymmetrical in the presence of publication bias and other biases Funnel plot asymmetry, measured by regression analysis, predicts discordance of results when meta-analyses are compared with single large trials Funnel plot asymmetry was found in 38% of meta-analyses published in leading general medicine journals and in 13% of reviews from the Cochrane Database of Systematic Reviews Critical examination of systematic reviews for publication and related biases should be considered a routine procedure

Data clustering: a review

Abstract: Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Robust Locally Weighted Regression and Smoothing Scatterplots

Abstract: The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.