Local regression

About: Local regression is a research topic. Over the lifetime, 2880 publications have been published within this topic receiving 221014 citations.

Applied multiple regression/correlation analysis for the behavioral sciences

Abstract: Contents: Preface. Introduction. Bivariate Correlation and Regression. Multiple Regression/Correlation With Two or More Independent Variables. Data Visualization, Exploration, and Assumption Checking: Diagnosing and Solving Regression Problems I. Data-Analytic Strategies Using Multiple Regression/Correlation. Quantitative Scales, Curvilinear Relationships, and Transformations. Interactions Among Continuous Variables. Categorical or Nominal Independent Variables. Interactions With Categorical Variables. Outliers and Multicollinearity: Diagnosing and Solving Regression Problems II. Missing Data. Multiple Regression/Correlation and Causal Models. Alternative Regression Models: Logistic, Poisson Regression, and the Generalized Linear Model. Random Coefficient Regression and Multilevel Models. Longitudinal Regression Methods. Multiple Dependent Variables: Set Correlation. Appendices: The Mathematical Basis for Multiple Regression/Correlation and Identification of the Inverse Matrix Elements. Determination of the Inverse Matrix and Applications Thereof.

Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

Abstract: G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

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.

Applied Regression Analysis and Other Multivariable Methods

Abstract: 1. CONCEPTS AND EXAMPLES OF RESEARCH. Concepts. Examples. Concluding Remarks. References. 2. CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS. Classification of Variables. Overlapping of Classification Schemes. Choice of Analysis. References. 3. BASIC STATISTICS: A REVIEW. Preview. Descriptive Statistics. Random Variables and Distributions. Sampling Distributions of t, ?O2, and F. Statistical Inference: Estimation. Statistical Inference: Hypothesis Testing. Error Rate, Power, and Sample Size. Problems. References. 4. INTRODUCTION TO REGRESSION ANALYSIS. Preview. Association versus Causality. Statistical versus Deterministic Models. Concluding Remarks. References. 5. STRAIGHT-LINE REGRESSION ANALYSIS. Preview. Regression with a Single Independent Variable. Mathematical Properties of a Straight Line. Statistical Assumptions for a Straight-line Model. Determining the Best-fitting Straight Line. Measure of the Quality of the Straight-line Fit and Estimate ?a2. Inferences About the Slope and Intercept. Interpretations of Tests for Slope and Intercept. Inferences About the Regression Line ?YY|X = ?O0 + ?O1X . Prediction of a New Value of Y at X0. Problems. References. 6. THE CORRELATION COEFFICIENT AND STRAIGHT-LINE REGRESSION ANALYSIS. Definition of r. r as a Measure of Association. The Bivariate Normal Distribution. r and the Strength of the Straight-line Relationship. What r Does Not Measure. Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient. Testing for the Equality of Two Correlations. Problems. References. 7. THE ANALYSIS-OF-VARIANCE TABLE. Preview. The ANOVA Table for Straight-line Regression. Problems. 8. MULTIPLE REGRESSION ANALYSIS: GENERAL CONSIDERATIONS. Preview. Multiple Regression Models. Graphical Look at the Problem. Assumptions of Multiple Regression. Determining the Best Estimate of the Multiple Regression Equation. The ANOVA Table for Multiple Regression. Numerical Examples. Problems. References. 9. TESTING HYPOTHESES IN MULTIPLE REGRESSION. Preview. Test for Significant Overall Regression. Partial F Test. Multiple Partial F Test. Strategies for Using Partial F Tests. Tests Involving the Intercept. Problems. References. 10. CORRELATIONS: MULTIPLE, PARTIAL, AND MULTIPLE PARTIAL. Preview. Correlation Matrix. Multiple Correlation Coefficient. Relationship of RY|X1, X2, !KXk to the Multivariate Normal Distribution. Partial Correlation Coefficient. Alternative Representation of the Regression Model. Multiple Partial Correlation. Concluding Remarks. Problems. References. 11. CONFOUNDING AND INTERACTION IN REGRESSION. Preview. Overview. Interaction in Regression. Confounding in Regression. Summary and Conclusions. Problems. References. 12. DUMMY VARIABLES IN REGRESSION. Preview. Definitions. Rule for Defining Dummy Variables. Comparing Two Straight-line Regression Equations: An Example. Questions for Comparing Two Straight Lines. Methods of Comparing Two Straight Lines. Method I: Using Separate Regression Fits to Compare Two Straight Lines. Method II: Using a Single Regression Equation to Compare Two Straight Lines. Comparison of Methods I and II. Testing Strategies and Interpretation: Comparing Two Straight Lines. Other Dummy Variable Models. Comparing Four Regression Equations. Comparing Several Regression Equations Involving Two Nominal Variables. Problems. References. 13. ANALYSIS OF COVARIANCE AND OTHER METHODS FOR ADJUSTING CONTINUOUS DATA. Preview. Adjustment Problem. Analysis of Covariance. Assumption of Parallelism: A Potential Drawback. Analysis of Covariance: Several Groups and Several Covariates. Comments and Cautions. Summary Problems. Reference. 14. REGRESSION DIAGNOSTICS. Preview. Simple Approaches to Diagnosing Problems in Data. Residual Analysis: Detecting Outliers and Violations of Model Assumptions. Strategies of Analysis. Collinearity. Scaling Problems. Diagnostics Example. An Important Caution. Problems. References. 15. POLYNOMIAL REGRESSION. Preview. Polynomial Models. Least-squares Procedure for Fitting a Parabola. ANOVA Table for Second-order Polynomial Regression. Inferences Associated with Second-order Polynomial Regression. Example Requiring a Second-order Model. Fitting and Testing Higher-order Model. Lack-of-fit Tests. Orthogonal Polynomials. Strategies for Choosing a Polynomial Model. Problems. 16. SELECTING THE BEST REGRESSION EQUATION. Preview. Steps in Selecting the Best Regression Equation. Step 1: Specifying the Maximum Model. Step 2: Specifying a Criterion for Selecting a Model. Step 3: Specifying a Strategy for Selecting Variables. Step 4: Conducting the Analysis. Step 5: Evaluating Reliability with Split Samples. Example Analysis of Actual Data. Issues in Selecting the Most Valid Model. Problems. References. 17. ONE-WAY ANALYSIS OF VARIANCE. Preview. One-way ANOVA: The Problem, Assumptions, and Data Configuration. for One-way Fixed-effects ANOVA. Regression Model for Fixed-effects One-way ANOVA Fixed-effects Model for One-way ANOVA. Random-effects Model for One-way ANOVA. -comparison Procedures for Fixed-effects One-way ANOVA. a Multiple-comparison Technique. Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares. Problems. References. 18. RANDOMIZED BLOCKS: SPECIAL CASE OF TWO-WAY ANOVA. Preview. Equivalent Analysis of a Matched-pairs Experiment. Principle of Blocking. Analysis of a Randomized-blocks Experiment. ANOVA Table for a Randomized-blocks Experiment. Models for a Randomized-blocks Experiment. Fixed-effects ANOVA Model for a Randomized-blocks Experiment. Problems. References. 19. TWO-WAY ANOVA WITH EQUAL CELL NUMBERS. Preview. Using a Table of Cell Means. General Methodology. F Tests for Two-way ANOVA. Regression Model for Fixed-effects Two-way ANOVA. Interactions in Two-way ANOVA. Random- and Mixed-effects Two-way ANOVA Models. Problems. References. 20. TWO-WAY ANOVA WITH UNEQUAL CELL NUMBERS. Preview. Problem with Unequal Cell Numbers: Nonorthogonality. Regression Approach for Unequal Cell Sample Sizes. Higher-way ANOVA. Problems. References. 21. THE METHOD OF MAXIMUM LIKELIHOOD. Preview. The Principle of Maximum Likelihood. Statistical Inference Using Maximum Likelihood. Summary. Problems. 22. LOGISTIC REGRESSION ANALYSIS. Preview. The Logistic Model. Estimating the Odds Ratio Using Logistic Regression. A Numerical Example of Logistic Regression. Theoretical Considerations. An Example of Conditional ML Estimation Involving Pair-matched Data with Unmatched Covariates. Summary. Problems. References. 23. POLYTOMOUS AND ORDINAL LOGISTIC REGRESSION. Preview. Why Not Use Binary Regression? An Example of Polytomous Logistic Regression: One Predictor, Three Outcome Categories. An Example: Extending the Polytomous Logistic Model to Several Predictors. Ordinal Logistic Regression: Overview. A "Simple" Hypothetical Example: Three Ordinal Categories and One Dichotomous Exposure Variable. Ordinal Logistic Regression Example Using Real Data with Four Ordinal Categories and Three Predictor Variables. Summary. Problems. References. 24. POISSON REGRESSION ANALYSIS. Preview. The Poisson Distribution. Example of Poisson Regression. Poisson Regression: General Considerations. Measures of Goodness of Fit. Continuation of Skin Cancer Data Example. A Second Illustration of Poisson Regression Analysis. Summary. Problems. References. 25. ANALYSIS OF CORRELATED DATA PART 1: THE GENERAL LINEAR MIXED MODEL. Preview. Examples. General Linear Mixed Model Approach. Example: Study of Effects of an Air Polluion Episode on FEV1 Levels. Summary!XAnalysis of Correlated Data: Part 1. Problems. References. 26. ANALYSIS OF CORRELATED DATA PART 2: RANDOM EFFECTS AND OTHER ISSUES. Preview. Random Effects Revisited. Results for Random Effects Models Applied to Air Pollution Study Data. Second Example!XAnalysis of Posture Measurement Data. Recommendations about Choice of Correlation Structure. Analysis of Data for Discrete Outcomes. Problems. References. 27. SAMPLE SIZE PLANNING FOR LINEAR AND LOGISTIC REGRESSION AND ANALYSIS OF VARIANCE. Preview. Review: Sample Size Calculations for Comparisons of Means and Proportions. Sample Size Planning for Linear Regression. Sample Size Planning for Logistic Regression. Power and Sample Size Determination for Linear Models: A General Approach. Sample Size Determination for Matched Case-control Studies with a Dichotomous Outcome. Practical Considerations and Cautions. Problems. References. Appendix A. Appendix B. Appendix C. Solutions to Exercises. Index.