The Multivariate Social Scientist; Introductory Statistics Using Generalized Linear Models

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ISBN: 9780761952008 | 0761952004
Cover: Hardcover
Copyright: 7/6/1999

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Starting from simple hypothesis testing and then moving towards model-building, this valuable book takes readers through the basics of multivariate analysis including: which tests to use on which data; how to run analyses in SPSS for Windows and GLIM4; how to interpret results; and how to report and present the reports appropriately.Using a unified conceptual framework (based around the Generalized Linear Model) the authors explain the commonalities and relationships between methods that include both the analysis of categorical and continuous data.

Preface

Introduction

(14)

Generalized Linear Models

(3)

The Random Component

(1)

The Systematic Component

(1)

The Link Function

(1)

Data Formats

(1)

Standard Statistical Analyses within the GLM Framework

(1)

Goodness-of-fit Measures and Model-Building

(2)

The Analysis of Deviance

(1)

Assumptions of GLMs

(3)

Properties of Scales and Corresponding Transformations

(1)

Overdispersion and the Variance Function

(1)

Non-linearity and the Link Function

(1)

Independent Measurement

(1)

Extrapolating Beyond the Measured Range of Variates

(1)

Summary

(2)

Data Screening

(40)

Levels of Measurement

(1)

Data Accuracy

(1)

Reliable Correlations

(1)

Missing Data

(1)

Outliers

(6)

On a Single Variable

(1)

Across Multiple Variables

(1)

Identifying Outliers

(1)

Leverage Values

(1)

Cook's Distance

(2)

Dealing with Outliers

(1)

Using Residuals to Check for Violations of Assumptions

(1)

Ordinary Residuals

(1)

Standardized Residuals

(1)

Studentized Residuals

(1)

Assumptions

(5)

Normality

(2)

Constant Variance

(1)

Linearity

(2)

Independence

(1)

Transformation and Curvilinear Models

(10)

Box--Cox Transformation with Skewed Errors

(3)

Fitting Models to Curvilinear Data Trends

(6)

Multicollinearity and Singularity

(1)

Diagnostics for Logistic Regression and Loglinear Models

(2)

Under and Overdispersion

(2)

Summary and Recommendations on the Order of Screening Practices

(1)

Statistical Software Commands

(10)

SPSS

(4)

GLIM

(6)

Ordinary Least-Squares Regression

(58)

Simple OLS Regression

(12)

The Regression Equation

(3)

Confidence Intervals for β

(3)

Confidence Intervals for Fitted y

(1)

Prediction Intervals

(2)

Goodness-of-fit Measures

(1)

The R2 Statistic

(1)

The F Statistic

(2)

A Worked Example of Simple Regression

(3)

Multiple OLS Regression

(27)

The Regression Equation

(1)

Interactions and Curvilinearity

(2)

Confidence Intervals for β

(1)

Confidence Intervals for Fitted y

(1)

Prediction Intervals

(1)

Goodness-of-fit Measures

(1)

The R2 and R2a Statistics

(1)

The F and Partial-F Statistics

(1)

Multicollinearity

(1)

Perfect Multicollinearity

(1)

High Multicollinearity

(2)

Identifying Instances of Multicollinearity

(2)

Dealing with Multicollinearity

(1)

Dummy Variable Coding Discontinuous Data

(1)

Indicator Coding

(4)

Deviation Coding

(3)

Dummy Coding Ordered Categorical Data

(1)

Model Selection

(1)

Criteria for Including and Removing Variables

(1)

Automated Model Selection

(1)

Forward Selection

(1)

Backward Elimination

(1)

Stepwise Selection

(1)

A Worked Example of Multiple Regression

(3)

Summary

101

(1)

Statistical Software Commands

102

(11)

SPSS

102

(4)

GLIM

106

(7)

Logistic Regression

113

(50)

Simple Logistic Regression

114

(16)

The Regression Equation

117

(4)

Calculating and Interpreting Model Parameters

121

(2)

Confidence Intervals for β

123

(1)

Confidence Intervals for Fitted y

124

(3)

Under and Overdispersion

127

(1)

Goodness-of-fit Measures

128

(1)

The Log-Likelihood Statistic

128

(1)

The Wald Statistic

129

(1)

Analysis of Classification Table Data

129

(1)

A Worked Example of Simple Logistic Regression

130

(4)

Multiple Logistic Regression

134

(13)

The Regression Equation

134

(1)

Interactions and Curvilinearity

135

(1)

Calculating and Interpreting Model Parameters

136

(1)

Confidence Intervals for β

137

(1)

Confidence Intervals for Fitted y

138

(1)

Goodness-of-fit Measures

139

(1)

The Log-Likelihood Statistic

139

(2)

Multicollinearity

141

(1)

Dummy Variable Coding Discontinuous Data

141

(2)

Indicator Coding

143

(1)

Deviation Coding

144

(1)

Model Selection

145

(1)

Criteria for Including and Removing Variables

146

(1)

A Worked Example of Multiple Logistic Regression

147

(5)

Summary

152

(1)

Statistical Software Commands

152

(11)

SPSS

152

(4)

GLIM

156

(7)

Loglinear Analysis

163

(54)

Traditional Bivariate Methods

164

(6)

Hypothesis Testing with Significance Tests

164

(1)

Goodness-of-fit Statistics

165

(1)

The Pearson X2 Statistic

165

(1)

The G2 Statistic

166

(1)

Adjusted Residuals

167

(1)

Modelling with Sample Odds Ratios

168

(1)

Confidence Intervals

169

(1)

Loglinear Models

170

(29)

The Loglinear Equation

171

(1)

A Bivariate Example

172

(3)

A Multivariate Example

175

(1)

Model Notation

175

(2)

Model Building

177

(2)

Goodness-of-fit Statistics and Residuals

179

(3)

Explanatory Variables with Ordered Categories

182

(1)

Scoring Ordered Categorical Variables

183

(1)

Bivariate Example with Explanatory Variables having Ordered Categories

184

(2)

Associations Between Nominal and Ordered Categorical Variables

186

(3)

Homogeneous Linear x Linear Associations

189

(2)

Logit Analysis --- Evaluating a Binary Response Variable

191

(1)

Multicategory Response Variables with Nominal and Ordered Categories

192

(1)

Nominal Response Variables: Baseline Category Logits

192

(1)

Ordered Response Variables

193

(6)

Summary

199

(1)

Statistical Software Commands

200

(17)

SPSS

200

(5)

GLIM

205

(12)

Factor Analysis

217

(36)

Overview

218

(2)

Factor Analysis Equations

220

(1)

Preliminary Analyses

221

(5)

Data Assumptions

222

(1)

Continuous and Ordered Categorical Data

222

(1)

Sample Size

222

(1)

Data Screening

222

(1)

Examining Correlations

223

(1)

Measures of Sampling Adequacy

224

(2)

Factor Extraction

226

(6)

Principal Components Analysis

226

(2)

Selecting the Number of Factors

228

(2)

Interpreting the Initial Factors

230

(2)

Factor Rotation

232

(5)

Interpreting the Rotated Factors

235

(2)

Including Factors in GLMs

237

(1)

A Worked Example of Factor Analysis

238

(10)

Summary

248

(1)

Statistical Software Commands

248

(5)

SPSS

249

(4)

Conclusion

253

(14)

Main Points of the GLM Framework

253

(1)

Sampling Assumptions and GLMs

254

(1)

Measurement Assumptions of Explanatory Variables in GLMs

255

(1)

Ordinal Variables

256

(1)

GLM Variants of ANOVA and ANCOVA

257

(1)

Repeated Measurements

258

(1)

Time Series Analysis

259

(1)

Gamma Errors and the Link Function: an Alternative to Data Transformation

260

(1)

Survival Analysis

261

(1)

Exact Sample and Sparse Data Methods

262

(1)

Cross Validation of Models

263

(1)

Software Recommendations

263

(4)

SPSS for Windows

263

(1)

GLIM

264

(1)

SAS

264

(1)

GENSTAT for Windows

264

(1)

Overall

265

(2)

References

267

(7)

Index

274

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The Multivariate Social Scientist; Introductory Statistics Using Generalized Linear Models

Summary

Table of Contents

Supplemental Materials