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Applying Test Equating Methods: Using R 1st ed. 2017 [Kõva köide]

  • Formaat: Hardback, 196 pages, kõrgus x laius x paksus: 235x155x18 mm, kaal: 5022 g, 57 Tables, color; 13 Illustrations, color; 20 Illustrations, black and white; XXVI, 196 p. 33 illus., 13 illus. in color., 1 Hardback
  • Sari: Methodology of Educational Measurement and Assessment
  • Ilmumisaeg: 13-Mar-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319518224
  • ISBN-13: 9783319518220
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  • Formaat: Hardback, 196 pages, kõrgus x laius x paksus: 235x155x18 mm, kaal: 5022 g, 57 Tables, color; 13 Illustrations, color; 20 Illustrations, black and white; XXVI, 196 p. 33 illus., 13 illus. in color., 1 Hardback
  • Sari: Methodology of Educational Measurement and Assessment
  • Ilmumisaeg: 13-Mar-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319518224
  • ISBN-13: 9783319518220
This book describes how to use test equating methods in practice. The non-commercial software R is used throughout the book to illustrate how to perform different equating methods when scores data are collected under different data collection designs, such as equivalent groups design, single group design, counterbalanced design and non equivalent groups with anchor test design. The R packages equate, kequate and SNSequate, among others, are used to practically illustrate the different methods, while simulated and real data sets illustrate how the methods are conducted with the program R. The book covers traditional equating methods including, mean and linear equating, frequency estimation equating and chain equating, as well as modern equating methods such as kernel equating, local equating and combinations of these. It also offers chapters on observed and true score item response theory equating and discusses recent developments within the equating field. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the Bayesian nonparametric estimation of equating functions. It also illustrates how to evaluate equating in practice using simulation and different equating specific measures such as the standard error of equating, percent relative error, different that matters and others.
1 General Equating Theory Background
1(18)
1.1 Introduction
1(2)
1.1.1 A Conceptual Description of Equating
2(1)
1.1.2 A Statistical Model View of Equating
2(1)
1.2 Statistical Models
3(7)
1.2.1 General Definition, Notation, and Examples
3(1)
1.2.2 Types of Statistical Models
4(2)
1.2.3 Mathematical Statistics Formulation of the Equating Problem
6(1)
1.2.4 Mathematical Form of the Equating Transformation
7(1)
1.2.5 Continuization
8(1)
1.2.6 Requirements for Comparability of Scores
9(1)
1.2.7 Assessing the Uncertainty of Equating Results
9(1)
1.3 Collecting Data in Equating
10(3)
1.3.1 Data Collection Designs in Equating
11(2)
1.4 Some Examples of Equating Transformations
13(2)
1.4.1 The Equipercentile Equating Function
13(1)
1.4.2 The Linear Equating Function
14(1)
1.4.3 The Kernel Equating Function
14(1)
1.5 R Packages That Are Used in This Book
15(1)
1.6 Summary and Overview of the Book
15(4)
References
16(3)
2 Preparing Score Distributions
19(24)
2.1 Data
19(2)
2.1.1 Data from Kolen and Brennan (2014)
19(1)
2.1.2 Data from von Davier et al. (2004)
20(1)
2.1.3 The ADM Admissions Test Data
20(1)
2.1.4 The SEPA Test Data
21(1)
2.2 Preparing the Score Data
21(12)
2.2.1 Functions to Create Score Frequency Distributions
22(1)
2.2.2 Score Data in the EG Design
22(5)
2.2.3 Score Data in the SG Design
27(3)
2.2.4 Score Data in the NEAT Design
30(3)
2.3 Presmoothing the Score Distributions
33(8)
2.3.1 Polynomial Log-Linear Models for Presmoothing
33(2)
2.3.2 Polynomial Log-Linear Smoothing in equate
35(1)
2.3.3 Examples
36(2)
2.3.4 Choosing the Best Log-Linear Model
38(3)
2.4 Using Other Arguments, Packages and Functions
41(1)
2.5 Summary
42(1)
References
42(1)
3 Traditional Equating Methods
43(30)
3.1 Equipercentile, Linear, and Mean Equating Transformations
43(1)
3.2 Assumptions in the Different Designs
44(2)
3.2.1 Assumptions in EG, SG, and CB Designs
44(1)
3.2.2 Assumptions in the NEAT Design
45(1)
3.3 Traditional Equating Methods for the EG, SG and CB Designs
46(1)
3.4 Traditional Equating Methods for the NEAT Design
46(6)
3.4.1 Linear Equating Methods for the NEAT Design
47(3)
3.4.2 Equipercentile Equating Methods for the NEAT Design
50(2)
3.5 Examples with the equate Function
52(11)
3.5.1 The equate Function
52(1)
3.5.2 Examples Under the EG and SG Designs
53(7)
3.5.3 Examples Under the NEAT Design
60(3)
3.5.4 Examples Using the ADM Data Under the NEAT Design
63(1)
3.6 Additional Features in equate
63(1)
3.7 Performing Traditional Equating Methods with SNSequate
64(1)
3.8 Comparing Traditional Test Equating Methods
65(6)
3.8.1 Bootstrap Standard Errors of Equating
65(1)
3.8.2 Bias and RMSE
66(1)
3.8.3 Examples Using equate
67(1)
3.8.4 Additional Example: A Comparison of Traditional Equating Methods
68(3)
3.9 Summary
71(2)
References
71(2)
4 Kernel Equating
73(38)
4.1 A Quick Overview of Kernel Equating
73(1)
4.2 Step 1: Presmoothing
74(16)
4.2.1 Presmoothing with SNSequate
74(7)
4.2.2 Presmoothing with kequate
81(5)
4.2.3 Assessing Log-Linear Model Fit
86(4)
4.3 Step 2: Estimation of Score Probabilities
90(2)
4.3.1 Estimation of Score Probabilities with SNSequate
90(1)
4.3.2 Estimation of Score Probabilities with kequate
91(1)
4.4 Step 3: Continuization
92(3)
4.4.1 Bandwidth Selection
93(1)
4.4.2 Choosing the Kernel
93(1)
4.4.3 Continuization Choices in SNSequate
94(1)
4.4.4 Continuization Choices in kequate
94(1)
4.5 Step 4: Equating
95(7)
4.5.1 Equating in SNSequate
95(4)
4.5.2 Equating in kequate
99(3)
4.6 Step 5: Computation of Accuracy Measures
102(7)
4.6.1 Calculating the Standard Error of Equating
103(1)
4.6.2 Standard Error of Equating Difference
103(1)
4.6.3 Percent Relative Error
103(1)
4.6.4 Obtaining SEE, SEED, and PRE in SNSequate
104(2)
4.6.5 Obtaining SEE, SEED, and PRE in kequate
106(3)
4.7 Different Features in kequate and SNSequate
109(1)
4.8 Summary
109(2)
References
109(2)
5 Item Response Theory Equating
111(26)
5.1 IRT Models
111(2)
5.1.1 Scoring Using IRT Models
112(1)
5.2 Equating IRT Scores
113(6)
5.2.1 Parameter Linking
113(6)
5.3 Equating Observed Scores Under the IRT Framework
119(9)
5.3.1 IRT True-Score Equating
120(1)
5.3.2 IRT Observed-Score Equating
120(1)
5.3.3 IRT True-Score and Observed-Score Equating Using SNSequate
121(5)
5.3.4 IRT True-Score and Observed-Score Equating Using equateIRT
126(2)
5.4 Other Equating Methods for IRT Scores
128(5)
5.4.1 Concurrent Calibration
128(3)
5.4.2 Fixed Item Parameter Calibration
131(2)
5.5 Other R Packages for IRT Analysis
133(1)
5.6 Summary
134(3)
References
134(3)
6 Local Equating
137(20)
6.1 The Concept of Local Equating
137(2)
6.1.1 True Equating Transformation
138(1)
6.2 Performing Local Equating
139(1)
6.3 Local Linear Equating Transformations
139(5)
6.3.1 Local Linear Equating Conditioning on Anchor Test Scores: NEAT Design
140(1)
6.3.2 Local Linear Equating Method of Conditional Means: SG Design
140(1)
6.3.3 Local Linear Equating Examples in R
140(4)
6.4 Local Equipercentile Equating Transformations
144(10)
6.4.1 Local IRT Observed-Score Equating
145(1)
6.4.2 Local Observed-Score Kernel Equating Conditioning on Anchor Test Scores
146(1)
6.4.3 Local IRT Observed-Score Kernel Equating
146(1)
6.4.4 Local Equipercentile Equating Examples in R
147(7)
6.5 Other Local Equating Methods
154(1)
6.6 Summary
154(3)
References
154(3)
7 Recent Developments in Equating
157(22)
7.1 Alternative Kernel Equating Transformations
157(4)
7.1.1 Epanechnikov Kernel
157(1)
7.1.2 Adaptive Kernels
158(1)
7.1.3 Examples of Epanechnikov and Adaptive Kernel Equating in SNSequate
159(2)
7.2 Bandwidth Selection in Kernel Equating
161(2)
7.2.1 Rule-Based Bandwidth Selection
161(1)
7.2.2 Bandwidth Selection with Double Smoothing
162(1)
7.2.3 Examples of the Rule-Based and Double Smoothing Bandwidth Selection Methods Using kequate
162(1)
7.3 Item Response Theory Kernel Equating
163(5)
7.3.1 Two Polytomous IRT Models
163(1)
7.3.2 Performing IRT Kernel Equating with kequate
164(1)
7.3.3 Examples of IRT Kernel Equating for Binary Scored Items Using kequate
165(2)
7.3.4 Examples of IRT Kernel Equating for Poly tomous Scored Items Using kequate
167(1)
7.4 Bayesian Nonparametric Approach to Equating
168(4)
7.4.1 Bayesian Nonparametric Modeling
168(1)
7.4.2 BNP Model for Equating
169(1)
7.4.3 An Illustration of the BNP Model for Equating in SNSequate
170(2)
7.5 Assessing the Equating Transformation
172(5)
7.5.1 An Illustration of Assessing φ(x) in Kernel Equating Using SNSequate
174(3)
7.6 Summary
177(2)
References
177(2)
Appendix A Installing and Reading Data in R
179(4)
A.1 Installing R
179(1)
A.1.1 R Studio
179(1)
A.2 Installing and Loading R Packages
180(1)
A.3 Working Directory and Accessing Data
180(1)
A.4 Loading Data of Different File Formats
181(2)
Reference
182(1)
Appendix B Additional Material
183(12)
B.1 Design Functions
183(2)
B.2 C Matrices
185(1)
B.3 Calculation of the SEE
185(1)
B.4 Score Distributions Under the NEAT Design
186(1)
B.5 The Lord-Wingersky Algorithm
187(1)
B.6 Other Justifications for Local Equating
188(1)
B.7 Epanechnikov Kernel Density Estimate and Derivatives
189(1)
B.8 The Double Smoothing Bandwidth Selection Method in Kernel Equating
190(1)
B.9 The DBPP Model
191(1)
B.10 Measures of Statistical Assessment When Equating Test Scores
191(4)
References
192(3)
Index 195

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