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Applied Regression Analysis
01 Jan 1966-
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
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.
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TL;DR: Funnel plots, plots of the trials' 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.
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
37,989 citations
TL;DR: An overview of pattern clustering methods from a statistical pattern recognition perspective is presented, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners.
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.
14,054 citations
TL;DR: Robust locally weighted regression as discussed by the authors is a method for smoothing a scatterplot, 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.
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.
10,225 citations
Cites background from "Applied Regression Analysis"
...…L S 3.2 Residuals vs. Fitted Values I t has long been argued that plotting residuals against fitted values from a regression analysis is useful for, among other things, detecting a dependence of the scale of the errors on the level of the fitted values (Daniel and Wood 1971; Draper and Smith 1966)....
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TL;DR: Efron and Tibshirani as discussed by the authors used bootstrap tests to assess mediation, finding that the sampling distribution of the mediated effect is skewed away from 0, and they argued that R. M. Kenny's (1986) recommendation of first testing the X --> Y association for statistical significance should not be a requirement when there is a priori belief that the effect size is small or suppression is a possibility.
Abstract: Mediation is said to occur when a causal effect of some variable X on an outcome Y is explained by some intervening variable M. The authors recommend that with small to moderate samples, bootstrap methods (B. Efron & R. Tibshirani, 1993) be used to assess mediation. Bootstrap tests are powerful because they detect that the sampling distribution of the mediated effect is skewed away from 0. They argue that R. M. Baron and D. A. Kenny's (1986) recommendation of first testing the X --> Y association for statistical significance should not be a requirement when there is a priori belief that the effect size is small or suppression is a possibility. Empirical examples and computer setups for bootstrap analyses are provided.
8,940 citations
TL;DR: The wrapper method searches for an optimal feature subset tailored to a particular algorithm and a domain and compares the wrapper approach to induction without feature subset selection and to Relief, a filter approach tofeature subset selection.
8,610 citations