Symbols and Acronyms |
|
xxi | |
|
1 Introduction to Measurement |
|
|
1 | (11) |
|
|
1 | (2) |
|
|
3 | (2) |
|
|
5 | (1) |
|
|
5 | (3) |
|
|
8 | (1) |
|
|
9 | (3) |
|
2 The One-Parameter Model |
|
|
12 | (30) |
|
Conceptual Development of the Rasch Model |
|
|
12 | (5) |
|
|
17 | (3) |
|
The One-Parameter Logistic Model and the Rasch Model |
|
|
20 | (1) |
|
Assumptions Underlying the Model |
|
|
21 | (2) |
|
An Empirical Data Set: The Mathematics Data Set |
|
|
23 | (1) |
|
Conceptually Estimating an Individual's Location |
|
|
23 | (5) |
|
Some Pragmatic Characteristics of Maximum Likelihood Estimates |
|
|
28 | (1) |
|
The Standard Error of Estimate and Information |
|
|
29 | (3) |
|
An Instrument's Estimation Capacity |
|
|
32 | (3) |
|
|
35 | (7) |
|
3 Joint Maximum Likelihood Parameter Estimation |
|
|
42 | (44) |
|
Joint Maximum Likelihood Estimation |
|
|
42 | (2) |
|
Indeterminacy of Parameter Estimates |
|
|
44 | (1) |
|
How Large a Calibration Sample? |
|
|
45 | (1) |
|
Example: Application of the Rasch Model to the Mathematics Data, JMLE, BIGSTEPS |
|
|
46 | (22) |
|
Example: Application of the Rasch Model to the Mathematics Data, JMLE, mixRasch |
|
|
68 | (7) |
|
|
75 | (1) |
|
Summary of the Application of the Rasch Model |
|
|
76 | (1) |
|
|
77 | (9) |
|
4 Marginal Maximum Likelihood Parameter Estimation |
|
|
86 | (49) |
|
Marginal Maximum Likelihood Estimation |
|
|
86 | (7) |
|
Estimating an Individual's Location: Expected A Posteriori |
|
|
93 | (5) |
|
Example: Application of the Rasch Model to the Mathematics Data, MMLE, BILOG-MG |
|
|
98 | (13) |
|
Metric Transformation and the Total Characteristic Function |
|
|
111 | (4) |
|
Example: Application of the Rasch Model to the Mathematics Data, MMLE, mirt |
|
|
115 | (10) |
|
|
125 | (10) |
|
5 The Two-Parameter Model |
|
|
135 | (44) |
|
Conceptual Development of the Two-Parameter Model |
|
|
135 | (2) |
|
Information for the Two-Parameter Model |
|
|
137 | (2) |
|
Conceptual Parameter Estimation for the 2PL Model |
|
|
139 | (1) |
|
How Large a Calibration Sample? |
|
|
140 | (2) |
|
Metric Transformation, 2PL Model |
|
|
142 | (1) |
|
Example: Application of the 2PL Model to the Mathematics Data, MMLE, BILOG-MG I |
|
|
143 | (3) |
|
Fit Assessment: An Alternative Approach for Assessing Invariance |
|
|
146 | (6) |
|
Example: Application of the 2PL Model to the Mathematics Data, MMLE, mirt |
|
|
152 | (10) |
|
Information and Relative Efficiency |
|
|
162 | (3) |
|
|
165 | (14) |
|
6 The Three-Parameter Model |
|
|
179 | (58) |
|
Conceptual Development of the Three-Parameter Model |
|
|
179 | (3) |
|
Additional Comments about the Pseudo-Guessing Parameter, %j I |
|
|
182 | (1) |
|
Conceptual Parameter Estimation for the 3PL Model |
|
|
183 | (4) |
|
How Large a Calibration Sample? |
|
|
187 | (1) |
|
Assessing Conditional Independence |
|
|
188 | (4) |
|
Example: Application of the 3PL Model to the Mathematics Data, MMLE, BILOG-MG I |
|
|
192 | (3) |
|
Fit Assessment: Conditional Independence Assessment |
|
|
195 | (3) |
|
Fit Assessment: Model Comparison |
|
|
198 | (2) |
|
Example: Application of the 3PL Model to the Mathematics Data, MMLE, mirt |
|
|
200 | (9) |
|
Assessing Person Fit: Appropriateness Measurement |
|
|
209 | (7) |
|
Information for the Three-Parameter Model |
|
|
216 | (4) |
|
Metric Transformation, 3PL Model |
|
|
220 | (1) |
|
Handling Missing Responses |
|
|
220 | (4) |
|
Issues to Consider in Selecting among the 1PL, 2PL, and 3PL Models |
|
|
224 | (2) |
|
|
226 | (11) |
|
7 Rasch Models for Ordered Polytomous Data |
|
|
237 | (76) |
|
Conceptual Development of the Partial Credit Model |
|
|
238 | (5) |
|
Conceptual Parameter Estimation of the PC Model |
|
|
243 | (1) |
|
Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE, flexMIRT I |
|
|
244 | (12) |
|
Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE, mirt |
|
|
256 | (11) |
|
|
267 | (5) |
|
Conceptual Parameter Estimation of the RS Model |
|
|
272 | (1) |
|
Example: Application of the RS Model to an Attitudes Toward Condoms Scale, JMLE, BIGSTEPS I |
|
|
272 | (15) |
|
Example: Application of the PC Model to an Attitudes Toward Condoms Scale, JMLE, mixRasch |
|
|
287 | (5) |
|
How Large a Calibration Sample? |
|
|
292 | (2) |
|
Information for the PC and RS Models |
|
|
294 | (2) |
|
Metric Transformation, PC and RS Models |
|
|
296 | (1) |
|
|
296 | (17) |
|
8 Non-Rasch Models for Ordered Polytomous Data |
|
|
313 | (43) |
|
The Generalized Partial Credit Model |
|
|
313 | (5) |
|
Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE, flexMIRT |
|
|
318 | (3) |
|
Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE, mirt |
|
|
321 | (3) |
|
Conceptual Development of the Graded Response Model |
|
|
324 | (9) |
|
How Large a Calibration Sample? |
|
|
333 | (1) |
|
Information for Graded Data |
|
|
334 | (2) |
|
Metric Transformation, GPC and GR Models |
|
|
336 | (1) |
|
Example: Application of the GR Model to an Attitudes Toward Condoms Scale, MMLE, flexMIRT I |
|
|
337 | (3) |
|
Example: Application of the GR Model to an Attitudes Toward Condoms Scale, MMLE, mirt |
|
|
340 | (3) |
|
Conceptual Development of the Continuous Response Model |
|
|
343 | (8) |
|
|
351 | (5) |
|
9 Models for Nominal Polytomous Data |
|
|
356 | (35) |
|
Conceptual Development of the Nominal Response Model |
|
|
357 | (8) |
|
Information for the NR Model |
|
|
365 | (1) |
|
Metric Transformation, NR Model |
|
|
366 | (1) |
|
Conceptual Development of the Multiple-Choice Model |
|
|
366 | (2) |
|
How Large a Calibration Sample? |
|
|
368 | (2) |
|
Example: Application of the NR Model to a General Science Test, MMLE, mirt |
|
|
370 | (13) |
|
|
383 | (8) |
|
10 Models for Multidimensional Data |
|
|
391 | (52) |
|
Conceptual Development of a Multidimensional IRT Model |
|
|
391 | (6) |
|
Multidimensional Item Location and Discrimination |
|
|
397 | (4) |
|
Item Vectors and Vector Graphs |
|
|
401 | (3) |
|
The Multidimensional Three-Parameter Logistic Model |
|
|
404 | (1) |
|
Assumptions of the MIRT Model |
|
|
404 | (1) |
|
Estimation of the M2PL Model |
|
|
405 | (1) |
|
Information for the M2PL Model |
|
|
406 | (2) |
|
|
408 | (2) |
|
Metric Transformation, M2PL Model |
|
|
410 | (1) |
|
Example: Calibration of Interpersonal Engagement Instrument, M2PL Model, sirt.noharm |
|
|
411 | (10) |
|
Obtaining Person Location Estimates |
|
|
421 | (1) |
|
Example: Calibration of Interpersonal Engagement Instrument, M2PL Model, mirt |
|
|
422 | (7) |
|
Example: Calibration of Interpersonal Engagement Instrument, M2PL Model, flexMIRT I |
|
|
429 | (2) |
|
|
431 | (12) |
|
|
443 | (35) |
|
|
443 | (2) |
|
Equating: Data Collection Phase |
|
|
445 | (1) |
|
Equating: Transformation Phase |
|
|
446 | (8) |
|
Example: Application of the Total Characteristic Function Equating Method, EQUATE |
|
|
454 | (9) |
|
Example: Application of the Total Characteristic Function Equating Method, SNSequate |
|
|
463 | (2) |
|
Example: Fixed-Item and Concurrent Calibration Equating |
|
|
465 | (6) |
|
|
471 | (7) |
|
12 Differential Item Functioning |
|
|
478 | (47) |
|
Differential Item Functioning and Item Bias |
|
|
479 | (4) |
|
Mantel-Haenszel Chi-Square |
|
|
483 | (3) |
|
The TSW Likelihood Ratio Test |
|
|
486 | (1) |
|
|
487 | (4) |
|
Example: DIF Analysis of Vocabulary Test, SAS CMH |
|
|
491 | (3) |
|
Example: DIF Analysis of Vocabulary Test, mantelhaen. test and difR |
|
|
494 | (7) |
|
Example: DIF Analysis of Vocabulary Test, SAS proc logistic |
|
|
501 | (7) |
|
Example: DIF Analysis of Vocabulary Test, glm and difR |
|
|
508 | (10) |
|
|
518 | (7) |
|
|
525 | (72) |
|
Multilevel IRT---Two Levels |
|
|
525 | (5) |
|
Example: Estimating the Rasch Model from a Multilevel Perspective, proc glimmix |
|
|
530 | (11) |
|
Example: Rasch Model Estimation, lme4 |
|
|
541 | (4) |
|
Person-Level Predictors for Items |
|
|
545 | (2) |
|
Example: Person-Level Predictors for Items---DIF Analysis, proc glimmix |
|
|
547 | (4) |
|
Example: Person-Level Predictors for Items---DJF Analysis, lme4 |
|
|
551 | (5) |
|
Person-Level Predictors for Respondents |
|
|
556 | (2) |
|
Example: Person-Level Predictors for Respondents---Nutrition Literacy, proc glimmix |
|
|
558 | (4) |
|
Example: Person-Level Predictors for Respondents, lme4 |
|
|
562 | (5) |
|
Item-Level Predictors for Items |
|
|
567 | (2) |
|
Example: Item-Level Predictors for Items---Nutrition Literacy, proc glimmix |
|
|
569 | (2) |
|
Example: Item-Level Predictors for Items---Nutrition Literacy, lme4 |
|
|
571 | (3) |
|
Multilevel IRT---Three Levels |
|
|
574 | (5) |
|
Example: Three-Level Model Analysis---Nutrition Literacy, proc glimmix |
|
|
579 | (3) |
|
Example: Three-Level Analysis of Nutrition Literacy Data, lme4 |
|
|
582 | (5) |
|
|
587 | (10) |
|
Appendices A-G Can be accessed online at the book's companion website (www. guilford.com/deayala-materials), which also provides links to data, syntax, and output files in different software packages for the book's examples |
|
|
|
Appendix A Maximum Likelihood Estimation of Person Locations |
|
|
|
Estimating an Individual's Location: Empirical Maximum Likelihood |
|
|
|
|
|
Estimating an Individual's Location: Newton's Method for MLE |
|
|
|
R Function for MLE of with the Rasch Model |
|
|
|
Revisiting Zero Variance Binary Response Patterns |
|
|
|
Appendix B Maximum Likelihood Estimation of Item Locations |
|
|
|
R function for MLE of 5 with the Rasch Model |
|
|
|
Appendix C The Normal Ogive Models |
|
|
|
Conceptual Development of the Normal Ogive Model |
|
|
|
The Relationship between IRT Statistics and Traditional Item Analysis |
|
|
|
|
|
Relationship of the Two-Parameter Normal Ogive and Logistic Models |
|
|
|
Extending the Two-Parameter Normal Ogive Model to a Multidimensional |
|
|
|
|
|
Appendix D Computerized Adaptive Testing |
|
|
|
|
|
Fixed-Branching Techniques |
|
|
|
Variable-Branching Techniques |
|
|
|
Advantages of Variable-Branching over Fixed-Branching Methods |
|
|
|
IRT-Based Variable-Branching Adaptive Testing Algorithm |
|
|
|
Appendix E. Linear Logistic Test Model (LLTM) |
|
|
|
Example of LLTM Calibration Using eRm |
|
|
|
Appendix F Mixture Models |
|
|
|
|
|
|
|
Example: Application of the Mixture Rasch Model to Writing Problem Data, CMLE, WINMIRA |
|
|
|
Example: Application of the Mixture Rasch Model to Writing Problem Data, CMLE, psychomix |
|
|
|
|
|
Using Principal Axis for Estimating Item Discrimination |
|
|
|
Infinite Item Discrimination Parameter Estimates |
|
|
|
Example: NOFIARM Unidimensional Calibration |
|
|
|
An Approximate Chi-Square Statistic for NOHARM |
|
|
|
Relative Efficiency, Monotonicity, and Information |
|
|
|
|
|
Odds, Odds Ratios, and Logits |
|
|
|
The Person Response Function |
|
|
|
Linking: A Temperature Analogy Example |
|
|
|
Should DIF Analyses Be Based on Latent Classes? |
|
|
|
The Separation and Reliability Indices |
|
|
|
Dependency in Traditional Item Statistics and Observed Scores |
|
|
|
Conditional Independence Using 3 |
|
|
|
Standalone NOHARM Calibration of Interpersonal Engagement Instrument, M2PL Model |
|
|
|
CFI, GFI, M2, RMSEA, TLI, and SRMR |
|
|
|
An Introduction to Kernel Equating |
|
|
|
Correspondence between the Rasch Model and a Loglinear Model |
|
|
|
|
References |
|
597 | (28) |
Author Index |
|
625 | (6) |
Subject Index |
|
631 | (12) |
About the Author |
|
643 | |