Statistical Analysis of Longitudinal

A comprehensive resource for analyzing a variety of categorical data, this book emphasizes the application of many recent advances of longitudinal categorical statistical methods. Each chapter provides basic methodology, helpful applications, examples using data from all fields of the social sciences, computer tutorials, and exercises. Written for social scientists and students, no advanced mathematical training is required. Step-by-step command files are given for both the CDAS and the SPSS software programs.

Preface

v

1. Describing Categorical Variables

1

(14)

1.1 Scale Levels and Categorical Variables

1

(2)

1.2 Graphic Representation of Categorical Data Information

3

(4)

1.3 Cross-Tabulation

7

(6)

Exercises

13

(2)

2 Log-Linear Modeling

15

(30)

2.1 Log-Linear Modeling: A Tutorial

15

(17)

2.1.1 Log-Linear Models and the Analogy to the General Linear Model

16

(4)

2.1.2 Design Matrices, Main Effects, and Interactions in Log-Linear Models

20

(6)

2.1.3 Fitting and Testing in Log-Linear Modeling

26

(6)

2.2 Log-Linear Modeling: A Data Example

32

(10)

2.2.1 Hierarchical and Nonstandard Log-Linear Models

39

(3)

Exercises

42

(3)

3 Log-Linear Models for Repeated Observations

45

(62)

3.1 Conditions for Valid Application of Log-Linear Modeling

45

(4)

3.2 Log-Linear Models for Repeated Observations I: Two Occasions

49

(17)

3.2.1 The Concepts of Persistence, Symmetry, and Association in 2 x 2 Tables

52

(4)

3.2.2 Axial Symmetry in I x I Tables

56

(3)

3.2.3 Axial Symmetry as a Nonstandard Log-Linear Model

59

(1)

3.2.4 Group Comparisons in Axial Symmetry

60

(5)

3.2.5 More Models and Options

65

(1)

3.3 Residual Analysis

66

(4)

3.4 A Special Case: Marginal Homogeneity in 2 x 2 Tables

70

(2)

3.5 Curve Fitting

72

(5)

3.6 Quasi-Independence

77

(2)

3.7 Marginal Homogeneity and Quasi-Symmetry

79

(9)

3.7.1 Marginal Homogeneity

80

(6)

3.7.2 Lehmacher's Simultaneous Marginal Homogeneity Sign Test

86

(2)

3.8 Computational Issues

88

(17)

3.8.1 Nonstandard Log-Linear Modeling Using CDAS

89

(8)

3.8.2 Nonstandard Log-Linear Modeling Using SPSS

97

(8)

Exercises

105

(2)

4 Chi-Square Partitioning Models

107

(18)

4.1 A Data Example

109

(1)

4.2 Decomposition Strategies

109

(1)

4.3 x^2 Partitioning by Joining

110

(9)

4.3.1 Helmert Contrasts and Hierarchical Contrasts

110

(4)

4.3.2 Application of Joining Methods in x^2 Partitioning

114

(5)

4.4 Splitting

119

(1)

4.5 More Repeated Measures Applications

120

(4)

Exercises

124

(1)

5 Prediction Analysis

125

(50)

5.1 An Introduction to Prediction Analysis of Cross-Classifications

127

(24)

5.1.1 Formulating Prediction Hypotheses: Making it Right

127

(7)

5.1.2 Identification of Hit Cells and Error Cells

134

(3)

5.1.3 Estimation of Expected Cell Frequencies

137

(4)

5.1.4 Running a Complete Prediction Analysis

141

(10)

5.2 Prediction Models for Longitudinal Data

151

(15)

5.2.1 Statement Calculus and Log-Linear Base Model

152

(1)

5.2.2 Composite Models for Longitudinal Data

153

(5)

5.2.3 Equifinality Models for Longitudinal Data

158

(3)

5.2.4 Equicausality Models for Longitudinal Data

161

(5)

5.3 Computational Issues

166

(6)

Exercises

172

(3)

6 Configural Frequency Analysis of Repeated Observations

175

(60)

6.1 Configural Frequency Analysis: A Tutorial

175

(26)

6.1.1 Types and Antitypes

176

(1)

6.1.2 Specification of a CFA Chance Model

177

(3)

6.1.3 Estimation of Expected Cell Frequencies

180

(3)

6.1.4 Testing for Types and Antitypes

183

(1)

6.1.4.1 Statistical Tests for Types and Antitypes

183

(2)

6.1.4.2 Alpha Adjustment in CFA testing

185

(4)

6.1.5 A Data Example: CFA of Drug Abuse Patterns

189

(8)

6.1.6 Computer Application

197

(4)

6.2 CFA of Longitudinal Data

201

(32)

6.2.1 CFA of First, Second, and Higher Differences

201

(8)

6.2.2 CFA of Trend and Level Information

209

(1)

6.2.2.1 CFA of Trend and Level Information: Level as a Covariate

209

(3)

6.2.2.2 CFA of Trend and Level Information: Level Cross-Classified

212

(5)

6.2.3 CFA of Treatment Effects

217

(3)

6.2.4 CFA of Differences Over Time

220

(5)

6.2.5 Prediction CFA

225

(2)

6.2.6 Computational Issues

227

(6)

Exercises

233

(2)

Selected Possible Solutions to Exercises

235

(8)

References

243

(10)

Author Index

253

(4)

Subject Index

257

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Statistical Analysis of Longitudinal Categorical Data in the Social and Behavioral Sciences: An introduction With Computer Illustrations

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Table of Contents

Supplemental Materials