Regression Analysis for Social Sciences

by von Eye; Schuster

• ISBN13: 9780127249551
• ISBN10: 0127249559
• eBook ISBN(s): 9780080550824, 9780127249551
• Edition: 1st
• Format: Paperback
• Copyright: 1998-06-25
• Publisher: Elsevier Science
• More Book Details
• Purchase Benefits

Summary

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

Table of Contents

Preface	xi
1 INTRODUCTION	1	(6)
2 SIMPLE LINEAR REGRESSION	7	(36)
2.1 Linear Functions and Estimation	7	(5)
2.2 Parameter Estimation	12	(14)
2.2.1 Criteria for Parameter Estimation	12	(5)
2.2.2 Least Squares Parameter Estimators	17	(8)
2.2.3 The Goodness of Fit of the Regression Model	25	(1)
2.3 Interpreting Regression Parameters	26	(2)
2.3.1 Interpreting the Intercept Parameter	27	(1)
2.3.2 Interpreting the Slope Parameter	27	(1)
2.4 Interpolation and Extrapolation	28	(1)
2.5 Testing Regression Hypotheses	29	(14)
2.5.1 Null Hypothesis: Slope Parameter Equals Zero	31	(2)
2.5.2 Data Example	33	(1)
2.5.3 Null Hypothesis: Slope Parameter Constant	34	(2)
2.5.4 Null Hypothesis 2: Two Slope Parameters are Equal	36	(2)
2.5.5 More Hypotheses for Slope Coefficients	38	(1)
2.5.6 Hypotheses Concerning Intercept Coefficients	39	(1)
2.5.7 Confidence Intervals	40	(3)
3 MULTIPLE LINEAR REGRESSION	43	(20)
3.1 Ordinary Least Squares Estimation	44	(6)
3.2 Data Example	50	(3)
3.3 Multiple Correlation and Determination	53	(5)
3.3.1 Expectancy of R(2) and Significance Testing	55	(3)
3.4 Significance Testing	58	(5)
4 CATEGORICAL PREDICTORS	63	(18)
4.1 Dummy and Effect Coding	65	(5)
4.2 More Than Two Categories	70	(7)
4.3 Multiple Categorical Predictors	77	(4)
5 OUTLIER ANALYSIS	81	(18)
5.1 Leverage Outliers	81	(8)
5.2 Remedial Measures	89	(10)
5.2.1 Scale Transformations	90	(4)
5.2.2 Weighted Least Squares	94	(5)
6 RESIDUAL ANALYSIS	99	(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