Chapter
2.1. The Spearman–Brown formula for a test of double length
2.2. Which split half? Cronbach’s coefficient Alpha
2.3. Estimating true score
3.1. An obiter dictum on P
3.2. Returning to the 1-PL
3.3. Estimating proficiency
3.4. Example of how ICCs multiply to yield the likelihood of proficiency
3.5. On the accuracy of the proficiency estimate
3.6. Estimating item parameters
3.6.1. Notation and general principles
3.6.2. Maximum marginal likelihood estimation
4 What’s a testlet and why do we need them?
What is a context effect?
4.2.2. Item difficulty ordering
4.2.3. Summary of context effect problems
4.2.4. An issue of robustness
4.3. Traditional solutions
4.3.3. Item difficulty ordering
4.4. Testlets – an alternative solution
4.5. An initial summing up
5 The origins of testlet response theory – three alternatives
5.2. Summary and conclusions
6 Fitting testlets with polytomous IRT models
6.2.2. An IRT model for testlets
6.3.1. Matching the model to the test
6.3.3. Increased sensitivity of detection
6.4.1. Testlet DIF detection
6.5.1. Overall performance
6.5.3. Differential performance
6.5.4. A testlet examination of White–African-American performance on Reading Comprehension: a brief case study
6.5.5. Standardized total impact
PART II Bayesian testlet response theory
Recapitulation and introduction
7 A brief history and the basic ideas of modern testlet response theory
7.1. Introduction. Testlets as a multidimensional structure
7.2. Advances in estimation and computing: essential developments to allow us to include items as part of the testlets
7.4. Modeling testlets: introducing the testlet parameter…
8 The 2-PL Bayesian testlet model
8.2. The model specification
8.3. Computation under the Bayesian 2-PL TRT model
8.3.1. The JML and MML estimation approaches
8.3.2. Maximum a posteriori estimation
8.3.3. Bayesian estimation using Markov chain Monte Carlo methods
8.4. A demonstration of the efficacy of the Bayesian 2-PL testlet model
8.5. A roadmap for the remaining computational chapters
9 The 3-PL Bayesian testlet model
9.1. The 3-PL Bayesian testlet model
9.2. Varying local dependence within testlets
9.3. Simulation results for the Bayesian 3-PL testlet model
9.4. An application of the Bayesian 3-PL testlet model to GRE data
10 A Bayesian testlet model for a mixture of binary and polytomous data
10.1. Bayesian testlet model for binary and polytomous data
10.2. Simulation results for the Bayesian mixed testlet model
10.3. The application of the Bayesian mixed testlet model to the North Carolina Test of Computer Skills
11 A Bayesian testlet model with covariates
11.1. An extended Bayesian TRT model
11.2. Example 1: USMLE data
11.2.1. Modeling the data
11.2.2. The results of the covariate augmented analysis
11.3. Example 2: Using testlet response theory to understand a survey of patients with breast cancer
11.3.3. Using covariates to understand why
Using regression analysis
11.3.4. Using the posterior distributions of the covariate coefficients
11.3.5. What was the effect of local dependence?
12 Testlet nonresponse theory: dealing with missing data
12.1. Missing at random and missing completely at random
12.2. Ignorable nonresponse
12.2.1. An illustrative example
12.3. Nonignorable nonresponse – omitted and not reached items
PART III Two applications and a tutorial
13 Using posterior distributions to evaluate passing scores: the PPoP curve
13.3. Example: the integrated clinical encounter score of Clinical Skills Assessment
13.4. Discussion and conclusion
14 A Bayesian method for studying DIF: cautionary tale filled with surprises and delights
14.2. A Bayesian procedure for measuring DIF
14.4. A practical procedure and some results
14.5.1. Small-scale study
14.5.2. Large simulation study
14.5.3. Interpretation of the simulations
15.1. General Bayesian inference problem
15.2. Bayesian inference for IRT models
15.3. Computation for the Bayesian IRT model
15.4. Some advice for those using Bayesian IRT models
Testlet Response Theory and Its Applications
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