Linear models for optimal test design:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2005
|
| Schriftenreihe: | Statistics for social and behavioral sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 408 S. graph. Darst. |
| ISBN: | 0387202722 9780387202723 |
Internformat
MARC
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| 100 | 1 | |a Linden, Wim J. van der |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear models for optimal test design |c Wim J. van der Linden |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2005 | |
| 300 | |a XXIII, 408 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics for social and behavioral sciences | |
| 650 | 7 | |a Experimenteel ontwerp |2 gtt | |
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| 650 | 7 | |a Testconstructie |2 gtt | |
| 650 | 7 | |a Tests |2 gtt | |
| 650 | 4 | |a Educational tests and measurements |x Design and construction | |
| 650 | 4 | |a Examinations |x Design and construction | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018879151 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804141008127000576 |
|---|---|
| adam_text | Contents
Foreword
vii
Preface
xi
1
Brief History of Test Theory and Design
1
1.1
Classical Test Design
..................... 2
1.1.1
Standardized Testing in Psychology
........ 2
1.1.2
Classical Test Theory
................ 4
1.1.3
Discussion
....................... 8
1.2
Modern Test Design
...................... 9
1.2.1
New Notion of Standardization
........... 9
1.2.2
Item-Response Theory
................ 11
1.2.3
Item Calibration and Ability Measurement
.... 14
1.2.4
Test and Item Information Functions
........ 16
1.2.5
Test Characteristic Function
............
IT
1.2.6
Comparison Between Classical
and
IRT
Parameters
................. 19
1.2.7
Ability Scale and Item Mapping
.......... 19
1.2.8 Birnbaum
Approach to Test Design
........ 21
1.3
Test Design in This Book
.................... 23
1.3.1
Four Modes of Test Assembly
............ 24
1.3.2
Choice of Test Assembly Modes
........... 26
1.4
An Application of lateger Programming
to Test Assembly
....................... 26
xviii Contents
1.5
Literature
........................... 28
1.6
Summary
............................
ЗО
1.7
Exercises
............................ 31
2
Formulating Test Specifications
33
2.1
Examples of Test Specifications
............... 34
2.2
Classification of Attributes
.................. 36
2.2.1
Type of Attribute
.................. 36
2.2.2
Level of Attribute
.................. 37
2.3
Constraints and Objectives
.................. 38
2.4
Standard Form of the Set of Test Specifications
...... 40
2.4.1
Number of Objective Functions
........... 40
2.4.2
Number of Constraints
................ 41
2.5
Literature
........................... 42
2.6
Summary
............................ 43
2.7
Exercises
............................ 44
3
Modeling Test-Assembly Problems
47
3.1
Identifying Decision Variables
................ 48
3.2
Modeling Constraints
..................... 51
3.2.1
Quantitative Constraints
............... 51
3.2.2
Categorical Constraints
............... 55
3.2.3
Logical Constraints
.................. 59
3.2.4
Checking Constraints
................ 61
3.3
Formulating Objective Functions
.............. 64
3.3.1
Quantitative Objective Functions
.......... 64
3.3.2
Categorical Objective Functions
.......... 66
3.3.3
Objective Functions with Goal Values
....... 67
3.3.4
Multiobjective Test Assembly
............ 68
3.3.5
Nonlinear Objectives
................. 72
3.4
Literature
........................... 72
3.5
Summary
............................ 72
3.6
Exercises
............................ 74
4
Solving Test-Assembly Problems
77
4.1
Standard -Model
for a
Single Test
.............. 78
4.1.1
Cheeking Interactions Between
the Objective Function and Constraints
...... 80
4.2
Branch-and-Bound Search
.................. 81
4.2.1
Tree Search
...................... 82
4.2.2
Implementation Decisions
.............. 84
4.2.3
Problem Size and Solution Time
.......... 85
4.2.4
A Useful Approximation
............... 86
4.2.5
Software
........................ 87
4.3
Network-Flow Approximation
................ 87
Contents
xix
4.4
Constructive Heuristics
.................... 89
4.4.1
Greedy Heuristics
................... 89
4.4.2
Luecht Heuristic
................... 91
4.4.3
Swanson-Stocking Heuristic
............. 91
4.5
Local Search Heuristics
.................... 92
4.5.1
Genetic Algorithms
.................. 93
4.5.2
Simulated Annealing
................. 94
4.6
Simultaneous and Sequential Optimization
......... 96
4.7
Optimal Design Approach
.................. 98
4.8
Literature
........................... 101
4.9
Summary
............................ 102
Models for Assembling Single Tests
105
5.1
IRT-Based Test Assembly
.................. 106
5.1.1
Absolute and Relative Targets
........... 107
5.1.2
Methods for Specifying Targets
for Information Functions
.............. 108
5.1.3
Assembling Tests for Absolute Targets
....... 110
5.1.4
Assembling Tests for Relative Targets
....... 113
5.1.5
Cutoff Scores
..................... 114
5.1.6
Empirical Examples
................. 114
5.2
Classical Test Assembly
.................... 115
5.2.1
Maximizing Test Reliability
............. 117
5.2.2
Maximizing Predictive Validity
........... 138
5.2.3
Constraining Test Reliability
............ 119
5.2.4
Empirical Example
.................. 120
5.3
Matching Observed-Score Distributions
........... 121
5.3.1
Conditions on the Response Functions
....... 122
5.3.2
Constraints in the Test-Assembly Model
...... 123
5.3.3
Discussion
....................... 124
5.3.4
Empirical Examples
................. 124
5.4
Item Matching
......................... 125
5.4.1
Matching Items in a Reference Test
........ 129
5.4.2
Test Splitting
..................... 131
5.4.3
Discussion
....................... 133
5.4.4
Empirical Example
.................. 133
5.5
Literat
lire
........................... 135
5.6
Summary
............................ 136
5.7
Exercises
............................ 137
Models for Assembling Multiple Tests
139
6.1
Sequential Assembly
..................... 141
6.1.І
Heuristic Correction
................. 142
6.2
Simultaneous Assembly
....................
І42
6.2.1
Item Overlap
..................... 144
Contents
6.2.2 Controlling Targets
Through Constraints.....
145
6.3
Big-Shadow-Test Method
................... 146
6.3.1
Discussion
....................... 150
6.4
Alternative Backup Methods
................. 151
6.5
Optimizing BIB Designs
................... 152
6.6
Empirical Examples
...................... 155
6.7
Literature
........................... 159
6.8
Summary
............................ 161
6.9
Exercises
............................ 162
Models for Assembling Tests with Item Sets
165
7.1
Simultaneous Selection of Items and Stimuli
........ 166
7.2
Power-Set Method
....................... 170
7.3
Edited-Set Method
...................... 174
7.4
Pivot-Item Method
...................... 174
7.5
Two-Stage Method
...................... 175
7.5.1
Stage
1:
Selection of Stimuli
............. 175
7.5.2
Stage
2:
Selection of Items from Sets
........ 178
7.5.3
Alternative Version
.................. 179
7.6
Empirical Example
...................... 179
7.7
Literature
........................... 185
7.8
Summary
............................ 185
7.9
Exercises
............................ 186
Models for Assembling Tests
Measuring Multiple Abilities
189
8.1
Différent
Cases of Multidimensional Testing
........ 190
8.1.1
Both Abilities Intentional
.............. 190
8.1.2
One Nuisance Ability
................ 191
8.1.3
Composite Ability
.................. 191
8.1.4
Simple Structure of Multidimensional Abilities
. . 192
8.1.5
Simple Structure of
Unidimensional
Abilities
. . . 192
8.2
Variance Functions
...................... 192
8.3
Linearization of the Problem
................. 194
8.3.1
Linear Decomposition
................ 194
8.3.2
Linear Approximation
................ 197
8.4
Main Models
.......................... 197
8.4.1
Model for Relative Targets
............. 198
8.4.2
Model for Absolute Targets
............. 200
8.4.3
Applications to Different Cases
........... 200
8.5
Alternative Objectives
for Multidimensional Test Assembly
............. 203
8-5.1
Matching Observed-Score Distributions
...... 203
8.5.2
Item Matching
.................... 204
8.5.3
Other Generalizations of
Unidimensional
Problems
204
Contents xxi
8.6
Empirical Example
...................... 204
8.7
Literature
........................... 207
8.8
Summary
............................ 207
8.9
Exercises
............................ 209
9
Models for Adaptive Test Assembly
211
9.1
Shadow-Test Approach
.................... 213
9.1.1
Random Test Length
................. 214
9.1.2
Fixed Test Length
.................. 214
9.1.3
Definition of Shadow Tests
............. 216
9.1.4
Standard Model for a Shadow Test
......... 217
9.1.5
Calculating Shadow Tests
.............. 218
9.1.6
Empirical Example
.................. 219
9.1.7
Discussion
....................... 221
9.2
Alternative Objective Functions
............... 222
9.2.1
Kullback-Leibler Information
........... . 223
9.2.2
Bayesian Item-Selection Criteria
.......... 223
9.3
Adaptive Testing with Item Sets
............... 224
9.4
Controlling Item Exposure
.................. 225
9.4.1
Alpha Stratification
................. 225
9.4.2
Sympson-Hetter Method
............... 229
9.4.3
Multiple-Shadow-Test Approach
.......... 230
9.4.4
Method with Ineligibility Constraints
........ 233
9.5
Controlling the Speededness of the Test
........... 235
9.5.1
Response-Time Model
................ 237
9.5.2
Ability and Speed as Intentional Factors
...... 238
9.5.3
Speed as a Nuisance Factor
............. 239
9.6
Reporting Scores on a Reference Test
............ 241
9.7
Multidimensional Adaptive Test Assembly
......... 248
9.7.1
Minimizing Error Variances
............. 248
9.7.2
Computational Aspects
............... 251
9.7.3
Maximizing Kullback-Leibler Information
..... 251
9.7.4
Empirical Examples
................ . 252
9.8
Final Comments
........................ 253
9.9
Literature
........................... 257
9.10
Summary
............................ 259
9.11
Exercises
............................ 261
10
Designing Item Pools for Programs with Fixed Tests
265
10.1
Definition of Design Space
.................. 266
10.2
Programs with Parallel Forms of a Single Test
....... 268
10.2.1
Standard Desiga Model
............... 268
10.3
Programs with Parallel Forms of Multiple Tests
...... 270
10.3.1
Simultaneous Model
................. 271
10.3.2
Item Overlap
.....................
2T2
xxii Contents
10.3.3 Model
with Aggregated Bounds
........... 275
10.3.4
Discussion
....................... 276
10.4
Cost Function
......................... 276
10.4.1
Smoothing Cost Functions
.............. 277
10.5
Item Sets
............................ 278
10.5.1
Simultaneous Model
................. 278
10.5.2
Three-Stage Approach
................ 281
10.6
Calculating Solutions
..................... 282
10.7
Dynamic Versions of Design Models
............. 284
10.7.1
Dynamic Models
................... 284
10.7.2
Item Author as Attribute
.............. 286
10.7.3
Empirical Example
.................. 287
10.8
Assembling an Operational Item Pool
............ 290
10.9
Final Comment
........................ 291
10.10
Literature
........................... 292
10.11
Summary
............................ 293
10.12
Exercises
............................ 294
11
Designing Item Pools for Programs with Adaptive Tests
297
11.1
Programs with a Single Adaptive Test
........... 298
11.1.1
Design Model for Shadow Tests
........... 298
11.1.2
Blueprint without Item-Exposure Control
..... 301
11.1.3
Blueprint with Marginal Item-Exposure Control
. 302
11.1.4
Blueprint with Conditional Item-Exposure Control
302
11.1.5
Empirical Example
.................. 303
11.2
Programs with Multiple Adaptive Tests
........... 304
11.2.1
Different Tests from the Same Item Pool
...... 304
11.2.2
Same Test from Different Item Pools
........ 305
11.3
Item Sets
............................ 305
11.3.1
Design Model
..................... 305
11.3.2
Calculating the Blueprint
.............. 308
11.4
Calculating Shadow Tests
................... 309
11.5
Some Remaining Topics
.................... 309
11.5.1
Stratifying an Item Pool
............... 309
11.5.2
Empirical Example
.................. 310
11.5.3
Assembling an Item Pool a« a Set
of Fixed Test Forms
................. 311
11.5.4
Empirical Example
.................. 313
11.5.5
Assembling a System of Rotating Item Pools
. . . 314
11.5.6
Empirical Example
.................. 320
11.6
Literature
........................... 323
11.7
Summary
............................ 324
11.8
Exercises
............................ 325
12
Epilogue
327
Contents xxiii
Appendix 1: Basic
Concepts
in Linear Programming 333
Al.l
Mathematical
Programming................. 333
AI.1.1 Linear Programming................. 334
AI.1.2
Nonlinear
Programming............... 335
AI. 1.3
Other Forms of Mathematical Programming
.... 335
Al.
1.4
Constraints on Variables
............... 336
Al.
2
Graphical Example
...................... 337
Al.2.1 Problem
........................ 337
Al.
2.2
Graphical Representation
.............. 338
Al.2.3 Number of Solutions
................. 340
A1.3 Simplex Method
........................ 341
A1.4 Network-Flow Problems
................... 342
A1.5 Solving Integer Problems
................... 344
Al.
6
Literature
........................... 346
Appendix
2:
Example of a Test-Assembly Problem
in OPL Studio
347
Answers to Exercises
353
Bibliography
389
Index
403
|
| any_adam_object | 1 |
| author | Linden, Wim J. van der |
| author_facet | Linden, Wim J. van der |
| author_role | aut |
| author_sort | Linden, Wim J. van der |
| author_variant | w j v d l wjvd wjvdl |
| building | Verbundindex |
| bvnumber | BV035986346 |
| callnumber-first | L - Education |
| callnumber-label | LB3060 |
| callnumber-raw | LB3060.65 |
| callnumber-search | LB3060.65 |
| callnumber-sort | LB 43060.65 |
| callnumber-subject | LB - Theory and Practice of Education |
| classification_rvk | CM 3000 |
| ctrlnum | (OCoLC)62409235 (DE-599)BVBBV035986346 |
| dewey-full | 150.28/7 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 150 - Psychology |
| dewey-raw | 150.28/7 |
| dewey-search | 150.28/7 |
| dewey-sort | 3150.28 17 |
| dewey-tens | 150 - Psychology |
| discipline | Psychologie |
| format | Book |
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| id | DE-604.BV035986346 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:09:02Z |
| institution | BVB |
| isbn | 0387202722 9780387202723 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018879151 |
| oclc_num | 62409235 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG |
| owner_facet | DE-473 DE-BY-UBG |
| physical | XXIII, 408 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics for social and behavioral sciences |
| spelling | Linden, Wim J. van der Verfasser aut Linear models for optimal test design Wim J. van der Linden New York [u.a.] Springer 2005 XXIII, 408 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics for social and behavioral sciences Experimenteel ontwerp gtt Lineaire modellen gtt Multicriteria evaluatieanalyse gtt Testconstructie gtt Tests gtt Educational tests and measurements Design and construction Examinations Design and construction Psychometrie (DE-588)4176236-8 gnd rswk-swf Testtheorie (DE-588)4131939-4 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Psychometrie (DE-588)4176236-8 s Testtheorie (DE-588)4131939-4 s DE-604 Lineares Modell (DE-588)4134827-8 s 1\p DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018879151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Linden, Wim J. van der Linear models for optimal test design Experimenteel ontwerp gtt Lineaire modellen gtt Multicriteria evaluatieanalyse gtt Testconstructie gtt Tests gtt Educational tests and measurements Design and construction Examinations Design and construction Psychometrie (DE-588)4176236-8 gnd Testtheorie (DE-588)4131939-4 gnd Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4176236-8 (DE-588)4131939-4 (DE-588)4134827-8 |
| title | Linear models for optimal test design |
| title_auth | Linear models for optimal test design |
| title_exact_search | Linear models for optimal test design |
| title_full | Linear models for optimal test design Wim J. van der Linden |
| title_fullStr | Linear models for optimal test design Wim J. van der Linden |
| title_full_unstemmed | Linear models for optimal test design Wim J. van der Linden |
| title_short | Linear models for optimal test design |
| title_sort | linear models for optimal test design |
| topic | Experimenteel ontwerp gtt Lineaire modellen gtt Multicriteria evaluatieanalyse gtt Testconstructie gtt Tests gtt Educational tests and measurements Design and construction Examinations Design and construction Psychometrie (DE-588)4176236-8 gnd Testtheorie (DE-588)4131939-4 gnd Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Experimenteel ontwerp Lineaire modellen Multicriteria evaluatieanalyse Testconstructie Tests Educational tests and measurements Design and construction Examinations Design and construction Psychometrie Testtheorie Lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018879151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lindenwimjvander linearmodelsforoptimaltestdesign |