| Foreword | 7 |
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| References | 9 |
| Preface | 10 |
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| References | 12 |
| Contents | 13 |
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| Acronyms | 18 |
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| List of Symbols | 20 |
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| 1 General Equating Theory Background | 24 |
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| 1.1 Introduction | 24 |
| 1.1.1 A Conceptual Description of Equating | 25 |
| 1.1.2 A Statistical Model View of Equating | 25 |
| 1.2 Statistical Models | 26 |
| 1.2.1 General Definition, Notation, and Examples | 26 |
| 1.2.2 Types of Statistical Models | 27 |
| 1.2.3 Mathematical Statistics Formulation of the Equating Problem | 29 |
| 1.2.4 Mathematical Form of the Equating Transformation | 30 |
| 1.2.5 Continuization | 31 |
| 1.2.6 Requirements for Comparability of Scores | 32 |
| 1.2.7 Assessing the Uncertainty of Equating Results | 32 |
| 1.3 Collecting Data in Equating | 33 |
| 1.3.1 Data Collection Designs in Equating | 34 |
| 1.3.1.1 Single Group Design | 34 |
| 1.3.1.2 Equivalent Groups Design | 34 |
| 1.3.1.3 Counterbalanced Design | 34 |
| 1.3.1.4 Non Equivalent Groups with Anchor Test Design | 35 |
| 1.3.1.5 Non Equivalent Groups with Covariates Design | 35 |
| 1.4 Some Examples of Equating Transformations | 36 |
| 1.4.1 The Equipercentile Equating Function | 36 |
| 1.4.2 The Linear Equating Function | 37 |
| 1.4.3 The Kernel Equating Function | 37 |
| 1.5 R Packages That Are Used in This Book | 38 |
| 1.6 Summary and Overview of the Book | 38 |
| References | 39 |
| 2 Preparing Score Distributions | 42 |
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| 2.1 Data | 42 |
| 2.1.1 Data from Ch2:kolenbrennan2014 | 42 |
| 2.1.2 Data from Ch2:vondavieretal2004 | 43 |
| 2.1.3 The ADM Admissions Test Data | 43 |
| 2.1.4 The SEPA Test Data | 44 |
| 2.2 Preparing the Score Data | 44 |
| 2.2.1 Functions to Create Score Frequency Distributions | 45 |
| 2.2.2 Score Data in the EG Design | 45 |
| 2.2.3 Score Data in the SG Design | 50 |
| 2.2.4 Score Data in the NEAT Design | 53 |
| 2.3 Presmoothing the Score Distributions | 56 |
| 2.3.1 Polynomial Log-Linear Models for Presmoothing | 56 |
| 2.3.2 Polynomial Log-Linear Smoothing in equate | 58 |
| 2.3.3 Examples | 59 |
| 2.3.3.1 Smoothing Univariate Distributions | 59 |
| 2.3.3.2 Smoothing a Bivariate Distribution | 60 |
| 2.3.4 Choosing the Best Log-Linear Model | 61 |
| 2.4 Using Other Arguments, Packages and Functions | 64 |
| 2.5 Summary | 65 |
| References | 65 |
| 3 Traditional Equating Methods | 66 |
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| 3.1 Equipercentile, Linear, and Mean Equating Transformations | 66 |
| 3.2 Assumptions in the Different Designs | 67 |
| 3.2.1 Assumptions in EG, SG, and CB Designs | 67 |
| 3.2.2 Assumptions in the NEAT Design | 68 |
| 3.3 Traditional Equating Methods for the EG, SG and CB Designs | 69 |
| 3.4 Traditional Equating Methods for the NEAT Design | 69 |
| 3.4.1 Linear Equating Methods for the NEAT Design | 70 |
| 3.4.1.1 Tucker Equating | 70 |
| 3.4.1.2 Nominal Weights Equating | 71 |
| 3.4.1.3 Levine Observed-Score Equating | 71 |
| 3.4.1.4 Levine True-Score Equating | 72 |
| 3.4.1.5 Chained Linear Equating | 73 |
| 3.4.2 Equipercentile Equating Methods for the NEAT Design | 73 |
| 3.4.2.1 Frequency Estimation | 73 |
| 3.4.2.2 Chained Equipercentile Equating | 74 |
| 3.4.2.3 Braun-Holland Equating | 74 |
| 3.5 Examples with the equate Function | 75 |
| 3.5.1 The equate Function | 75 |
| 3.5.2 Examples Under the EG and SG Designs | 76 |
| 3.5.3 Examples Under the NEAT Design | 83 |
| 3.5.3.1 Linear Methods | 83 |
| 3.5.3.2 Equipercentile Methods | 83 |
| 3.5.3.3 Comparison Between Linear and Equipercentile Methods | 84 |
| 3.5.4 Examples Using the ADM Data Under the NEAT Design | 86 |
| 3.6 Additional Features in equate | 86 |
| 3.7 Performing Traditional Equating Methods with SNSequate | 87 |
| 3.8 Comparing Traditional Test Equating Methods | 88 |
| 3.8.1 Bootstrap Standard Errors of Equating | 88 |
| 3.8.2 Bias and RMSE | 89 |
| 3.8.3 Examples Using equate | 90 |
| 3.8.4 Additional Example: A Comparison of Traditional Equating Methods | 91 |
| 3.9 Summary | 94 |
| References | 94 |
| 4 Kernel Equating | 96 |
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| 4.1 A Quick Overview of Kernel Equating | 96 |
| 4.2 Step 1: Presmoothing | 97 |
| 4.2.1 Presmoothing with SNSequate | 97 |
| 4.2.1.1 Presmoothing Under the EG Design | 98 |
| 4.2.1.2 Presmoothing Under the SG Design | 99 |
| 4.2.1.3 Presmoothing Under the CB Design | 101 |
| 4.2.1.4 Presmoothing Under the NEAT Design | 101 |
| 4.2.1.5 Modeling Complexities in the Data | 102 |
| 4.2.2 Presmoothing with kequate | 104 |
| 4.2.2.1 Presmoothing Under the EG Design | 104 |
| 4.2.2.2 Presmoothing Under the SG Design | 105 |
| 4.2.2.3 Presmoothing Under the CB Design | 106 |
