Regression Analysis for Social Sciences

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ISBN: 9780127249551 | 0127249559
Cover: Paperback
Copyright: 6/25/1998

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Regression Analysis for Social Sciences presents methods of regression analysis in an accessible way, with each method having illustrations and examples. A broad spectrum of methods are included: multiple categorical predictors, methods for curvilinear regression, and methods for symmetric regression. This book can be used for courses in regression analysis at the advanced undergraduate and beginning graduate level in the social and behavioral sciences. Most of the techniques are explained step-by-step enabling students and researchers to analyze their own data. Examples include data from the social and behavioral sciences as well as biology, making the book useful for readers with biological and biometrical backgrounds. Sample command and result files for SYSTAT are included in the text. Key Features * Presents accessible methods of regression analysis * Includes a broad spectrum of methods * Techniques are explained step-by-step * Provides sample command and result files for SYSTAT

Preface

1 INTRODUCTION

(6)

2 SIMPLE LINEAR REGRESSION

(36)

2.1 Linear Functions and Estimation

(5)

2.2 Parameter Estimation

(14)

2.2.1 Criteria for Parameter Estimation

(5)

2.2.2 Least Squares Parameter Estimators

(8)

2.2.3 The Goodness of Fit of the Regression Model

(1)

2.3 Interpreting Regression Parameters

(2)

2.3.1 Interpreting the Intercept Parameter

(1)

2.3.2 Interpreting the Slope Parameter

(1)

2.4 Interpolation and Extrapolation

(1)

2.5 Testing Regression Hypotheses

(14)

2.5.1 Null Hypothesis: Slope Parameter Equals Zero

(2)

2.5.2 Data Example

(1)

2.5.3 Null Hypothesis: Slope Parameter Constant

(2)

2.5.4 Null Hypothesis 2: Two Slope Parameters are Equal

(2)

2.5.5 More Hypotheses for Slope Coefficients

(1)

2.5.6 Hypotheses Concerning Intercept Coefficients

(1)

2.5.7 Confidence Intervals

(3)

3 MULTIPLE LINEAR REGRESSION

(20)

3.1 Ordinary Least Squares Estimation

(6)

3.2 Data Example

(3)

3.3 Multiple Correlation and Determination

(5)

3.3.1 Expectancy of R(2) and Significance Testing

(3)

3.4 Significance Testing

(5)

4 CATEGORICAL PREDICTORS

(18)

4.1 Dummy and Effect Coding

(5)

4.2 More Than Two Categories

(7)

4.3 Multiple Categorical Predictors

(4)

5 OUTLIER ANALYSIS

(18)

5.1 Leverage Outliers

(8)

5.2 Remedial Measures

(10)

5.2.1 Scale Transformations

(4)

5.2.2 Weighted Least Squares

(5)

6 RESIDUAL ANALYSIS

(18)

6.1 Illustrations of Residual Analysis

100

(6)

6.2 Residuals and Variable Relationships

106

(11)

7 POLYNOMIAL REGRESSION

117

(16)

7.1 Basics

117

(7)

7.2 Orthogonal Polynomials

124

(4)

7.3 Example of Non-Equidistant Predictors

128

(5)

8 MULTICOLLINEARITY

133

(10)

8.1 Diagnosing Multicollinearity

136

(2)

8.2 Countermeasures to Multicollinearity

138

(5)

8.2.1 Data Example

139

(4)

9 MULTIPLE CURVILINEAR REGRESSION

143

(8)

10 INTERACTION TERMS IN REGRESSION

151

(24)

10.1 Definition and Illustrations

151

(3)

10.2 Multiplicative Terms

154

(8)

10.2.1 Predicting the Slope Parameter from a Second Predictor

155

(4)

10.2.2 Predicting Both Slope and Intercept

159

(3)

10.3 Variable Characteristics

162

(13)

10.3.1 Multicollinearity of Multiplicative Regression Terms

163

(1)

10.3.2 Leverage Points as Results of Multiplicative Regression Terms

164

(2)

10.3.3 Problems with ANOVA-Type Interactions

166

(4)

10.3.4 The Partial Interaction Strategy

170

(5)

11 ROBUST REGRESSION

175

(34)

11.1 The Concept of Robustness

175

(3)

11.2 Models of Robust Regression

178

(13)

11.2.1 Ridge Regression

178

(8)

11.2.2 Least Median of Squares Regression

186

(3)

11.2.3 Least Trimmed Squares

189

(1)

11.2.4 M-Estimators

190

(1)

11.3 Computational Issues

191

(18)

11.3.1 Ridge Regression

192

(11)

11.3.2 Least Median of Squares and Least Trimmed Squares Regression

203

(6)

12 SYMMETRIC REGRESSION

209

(28)

12.1 Pearson's Orthogonal Regression

210

(9)

12.1.1 Symmetry and Inverse Prediction

214

(2)

12.1.2 The Orthogonal Regression Solution

216

(1)

12.1.3 Inferences in Orthogonal Regression

217

(2)

12.1.4 Problems with Orthogonal Regression

219

(1)

12.2 Other Solutions

219

(6)

12.2.1 Choice of Method for Symmetric Regression

222

(3)

12.3 A General Model for OLS Regression

225

(5)

12.3.1 Discussion

229

(1)

12.4 Robust Symmetrical Regression

230

(1)

12.5 Computational Issues

230

(7)

12.5.1 Computing a Major Axis Regression

231

(2)

12.5.2 Computing Reduced Major Axis Solution

233

(4)

13 VARIABLE SELECTION TECHNIQUES

237

(22)

13.1 A Data Example

240

(4)

13.2 Best Subset Regression

244

(7)

13.2.1 Squared Multiple Correlation, R(2)

245

(2)

13.2.2 Adjusted Squared Multiple Correlation

247

(2)

13.2.3 Mallow's C(p)

249

(2)

13.3 Stepwise Regression

251

(6)

13.3.1 Forward Selection

252

(2)

13.3.2 Backward Elimination

254

(2)

13.3.3 Efroymson's Algorithm

256

(1)

13.4 Discussion

257

(2)

14 REGRESSION FOR LONGITUDINAL DATA

259

(18)

14.1 Within Subject Correlation

260

(6)

14.2 Robust Modeling of Longitudinal Data

266

(4)

14.3 A Data Example

270

(7)

15 PIECEWISE REGRESSION

277

(10)

15.1 Continuous Piecewise Regression

278

(3)

15.2 Discontinuous Piecewise Regression

281

(6)

16 DICHOTOMOUS CRITERION VARIABLES

287

(4)

17 COMPUTATIONAL ISSUES

291

(42)

17.1 Creating a SYSTAT System File

291

(4)

17.2 Simple Regression

295

(3)

17.3 Curvilinear Regression

298

(6)

17.4 Multiple Regression

304

(4)

17.5 Regression Interaction

308

(2)

17.6 Regression with Categorical Predictors

310

(5)

17.7 The Partial Interaction Strategy

315

(4)

17.8 Residual Analysis

319

(4)

17.9 Missing Data Estimation

323

(5)

17.10 Piecewise Regression

328

(5)

18 A ELEMENTS OF MATRIX ALGEBRA

333

(18)

A.1 Definition of a Matrix

333

(2)

A.2 Types of Matrices

335

(2)

A.3 Transposing Matrices

337

(1)

A.4 Adding Matrices

337

(1)

A.5 Multiplying Matrices

338

(4)

A.6 The Rank of a Matrix

342

(2)

A.7 The Inverse of a Matrix

344

(2)

A.8 The Determinant of a Matrix

346

(1)

A.9 Rules for Operations with Matrices

347

(2)

A.10 Exercises

349

(2)

B BASICS OF DIFFERENTIATION

351

(4)

C BASICS OF VECTOR DIFFERENTIATION

355

(4)

D POLYNOMIALS

359

(6)

D.1 Systems of Orthogonal Polynomials

361

(2)

D.2 Smoothing Series of Measures

363

(2)

E DATA SETS

365

(8)

E.1 Recall Performance Data

365

(5)

E.2 Examination and State Anxiety Data

370

(3)

References

373

(8)

Index

381

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Regression Analysis for Social Sciences

Summary

Table of Contents

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