The Analysis of Cross-Classifications

Contents......Page f007.djvu
Preface......Page f013.djvu
1.1 Introduction......Page p001.djvu
1.1.1 The Nature of Categorical Variables......Page p003.djvu
1.1.2 Sampling Models......Page p004.djvu
1.1.3 Notation......Page p005.djvu
1.1.4 Marginal Tables......Page p006.djvu
1.2 A Short Review of the Chi Square Test for Independence......Page p007.djvu
1.2.1 Chi Square Tests Are Approximations......Page p009.djvu
1.2.2 Limitations of the Chi Square Test......Page p010.djvu
1.3 Examining Residuals......Page p011.djvu
1.4.1 A General Method of Partitioning......Page p013.djvu
1.4.2 Partitioning Into 2x2 Tables......Page p015.djvu
1.5 Quasi-Independence......Page p018.djvu
1.6.1 Symmetry......Page p024.djvu
1.6.2 Marginal Symmetry......Page p025.djvu
1.7 Summary......Page p026.djvu
2.1.1 The Interpretation of Measures of Association......Page p027.djvu
2.1.2 Confounding Factors......Page p030.djvu
2.1.3 Standardizing Tables......Page p031.djvu
2.2.1 Percents......Page p034.djvu
2.2.2 The Odds Ratio......Page p035.djvu
2.2.3 Yule\'s Q......Page p039.djvu
2.2.4 Yule\'s Y......Page p040.djvu
2.2.5 A Measure Based On Chi Square, Φ^2......Page p041.djvu
2.2.6 The Correlation Coefficient, ρ......Page p042.djvu
2.4.1 Definition......Page p043.djvu
2.4.2 Simultaneous Confidence Intervals......Page p044.djvu
2.5.2 The Contingency Coefficient......Page p046.djvu
2.6 Proportional-Reduction-in-Error Measures......Page p047.djvu
2.6.1 Goodman and Kruskal\'s Lambda......Page p048.djvu
2.6.2 Variance of Lambda......Page p050.djvu
2.6.3 Symmetric Version of Lambda......Page p051.djvu
2.6.4 Goodman and Kruskal\'s Tau......Page p052.djvu
2.6.5 An Alternative Interpretation of Tau......Page p054.djvu
2.6.6 Behavior of Measures of Association......Page p055.djvu
2.7.1 Unweighted κ......Page p058.djvu
2.7.2 Weighted κ......Page p059.djvu
2.7.3 The Variance of \\hat κ_w......Page p060.djvu
2.8.1 Prediction Logic Propositions......Page p061.djvu
2.8.2 An Index of Prediction Success......Page p062.djvu
2.8.3 The Variance of ∇......Page p063.djvu
2.8.4 Brief Discussion of Prediction Logic......Page p064.djvu
3.1 Introduction......Page p066.djvu
3.1.1 Definitions of Perfect Correlation......Page p067.djvu
3.1.2 The Concept of Pairs of Observations......Page p069.djvu
3.2.1 Kendall\'s τ_a......Page p072.djvu
3.2.2 Goodman and Kruskal\'s γ......Page p074.djvu
3.2.3 Asymmetric Measures, d_{AB} and d_{BA}......Page p075.djvu
3.2.4 Wilson\'s e......Page p076.djvu
3.2.6 τ_c......Page p078.djvu
3.2.7 Relationships Among the Measures......Page p079.djvu
3.3.1 A Parametric Interpretation of Ordinal Correlation......Page p081.djvu
3.3.2 Proportional-Reduction-in-Error Interpretations......Page p084.djvu
3.4 Standard Errors and Statistical Tests......Page p085.djvu
4.1 Introduction......Page p089.djvu
4.1.1 Interaction......Page p090.djvu
4.1.2 Partial Associations......Page p091.djvu
4.1.3 Zero Partial Association......Page p092.djvu
4.2 Test-Factor Stratification......Page p093.djvu
4.2.2 Test-Factor Standardization......Page p096.djvu
4.3.1 Treating Ordinal As Interval Scales......Page p098.djvu
4.3.2 Coefficients of Partial Association and Correlation......Page p100.djvu
4.3.3 A Shortcoming of Measures of Nominal and Ordinal Partial Association......Page p107.djvu
5.1 Introduction......Page p109.djvu
5.2 Log-Linear Models for Two-Way Tables......Page p111.djvu
5.2.1 No Effects Model......Page p112.djvu
5.2.2 Model Containing Only Row Effects......Page p113.djvu
5.2.3 Independence Model......Page p114.djvu
5.2.4 Saturated Model......Page p115.djvu
5.2.5 The Hierarchy Principle......Page p116.djvu
5.3.1 Mutual Independence Model......Page p117.djvu
5.3.2 Model with One Two-Factor Interaction......Page p118.djvu
5.3.3 A Note On Calculating Parameters......Page p120.djvu
5.3.5 Model with All Pairwise Interactions......Page p121.djvu
5.3.6 Saturated Model......Page p122.djvu
5.3.7 Independent Parameters......Page p124.djvu
5.4.1 Mutual Independence Model......Page p125.djvu
5.4.3 A Model with One Three-Factor Interaction......Page p126.djvu
5.4.4 A Model with Four Three-Factor Interactions......Page p128.djvu
5.4.6 Additional Models for Four or More Variables......Page p130.djvu
5.5 An Alternative View of Log-Linear Models......Page p131.djvu
5.5.1 Path Analysis and Diagrams......Page p133.djvu
5.5.2 Limitations of Path Models......Page p134.djvu
5.6 The Effects of Collapsing Variables......Page p135.djvu
5.6.1 An Algorithm for Determining Collapsibility......Page p136.djvu
5.6.2 Summary......Page p137.djvu
5.7.1 Saturated Models......Page p139.djvu
5.7.3 Variances of μ Terms......Page p140.djvu
6.1.1 Maximum Likelihood Estimation of Log-Linear Models......Page p142.djvu
6.1.2 Direct Versus Indirect Estimates......Page p144.djvu
6.1.3 How to Tell If Explicit Formulas for Expected Frequencies Exist......Page p145.djvu
6.2.1 Notation......Page p146.djvu
6.2.2 Goodman\'s Algorithm for Excluded Variables......Page p147.djvu
6.2.3 Goodman\'s Algorithm for Included Variables......Page p148.djvu
6.2.4 Examples......Page p149.djvu
6.3 Estimation by Iteration......Page p152.djvu
6.3.1 Iterative Proportional Fitting for Three Variables......Page p153.djvu
6.3.2 Iterative Proportional Fitting in General......Page p156.djvu
6.4 Test Statistics......Page p158.djvu
6.5 The Problem of Sampling Zeroes......Page p159.djvu
6.5.2 Testing Unsaturated Models......Page p160.djvu
6.5.3 Estimating Parameters in Unsaturated Models......Page p162.djvu
6.6 Partitioning Models......Page p163.djvu
6.6.1 Nested Models......Page p164.djvu
6.6.2 Tests On Marginal Tables......Page p166.djvu
6.6.3 A General Method of Partitioning......Page p167.djvu
6.6.4 Partitioning Two Common Models......Page p173.djvu
6.7.1 Problems in Defining Acceptance Criteria......Page p175.djvu
6.7.3 Simplicity......Page p176.djvu
6.7.4 Alternative Measures of Fit......Page p177.djvu
7.1 Introduction......Page p180.djvu
7.2 Multiple Regression with Categorical Variables......Page p181.djvu
7.2.1 Coding Categorical Independent Variables......Page p182.djvu
7.2.2 Dichotomous Dependent Variables......Page p185.djvu
7.2.3 Heteroscedasticity......Page p186.djvu
7.3.1 An Overview of GSK......Page p187.djvu
7.3.2 The Arrangement of the Data in GSK Analysis......Page p188.djvu
7.3.3 Defining the Dependent Variable: Response Functions......Page p193.djvu
7.3.4 Defining Models......Page p198.djvu
7.3.5 Interpretation of Model Parameters......Page p200.djvu
7.3.6 Significance Tests......Page p205.djvu
7.3.7 Examples......Page p207.djvu
7.3.8 Conclusion: A Test for Marginal Symmetry......Page p211.djvu
Appendix A: Vectors and Matrices......Page p214.djvu
Appendix B: Distribution of Chi Square......Page p218.djvu
Appendix C: Data Sources......Page p220.djvu
References......Page p221.djvu
Index......Page p231.djvu