Preface; Contents; Continuation Ratio Model in Item Response Theory and Selection of Models for Polytomous Items; 1 Introduction; 2 The Continuation Ratio Model and Parameter Estimation; 3 An Illustration; 4 Comparisons of Polytomous Models; 5 Discussion; Appendix; References; Using the Asymmetry of Item Characteristic Curves (ICCs) to Learn About Underlying Item Response Processes; 1 Introduction; 1.1 Other Implications of Ignoring Asymmetry in ICCs; 1.2 Item Response Processes and Asymmetric ICCs; 2 Molenaar's Normal Ogive RH Model

2.1 Bayesian Estimation of Heteroscedastic Two-Parameter and Three-Parameter Normal Ogive Models3 Simulation Study; 3.1 Low Complexity Disjunctive Items: A Two Subprocess Model; 3.2 Moderate Complexity Items: One Subprocess Model; 3.3 Moderately High Complexity Conjunctive Items: A Two Subprocess Model; 3.4 High Complexity Conjunctive Items: A Five Subprocess Model; 4 Simulation Results; 5 Discussion; References; A Three-Parameter Speeded Item Response Model: Estimation and Application; 1 Introduction; 2 Leave-the-Harder-till-Later Speeded Three-Parameter Logistic Item Response Model

3 Simulation Study4 Application; 5 Concluding Remarks; References; An Application of a Random Mixture Nominal Item Response Model for Investigating Instruction Effects; 1 Introduction; 2 A Random Item Mixture Nominal Response Model; 3 Simulation Study; 3.1 Simulation Design; 3.2 Simulation Study Results; 4 Empirical Study: Instruction Effects on Students' Fractions Computation; 4.1 Data Description; 4.2 Model Estimation; 4.3 Results; 4.3.1 Characteristics of Latent Classes; 4.3.2 Instruction Effects; 5 Conclusion and Discussions; References

Item Response Theory Models for Multidimensional Ranking Items1 The Rasch Ipsative Model for Multidimensional Pairwise-Comparison Items; 2 Item Response Models for Multidimensional Ranking Items; 2.1 The Exploded Logit IRT; 2.2 The Generalized Logit IRT; 3 Simulations; 4 An Empirical Example; 5 Summary and Discussion; References; Different Growth Measures on Different Vertical Scales; 1 Properties of Vertical Scales; 2 A Few Growth Measures and Their Relationships; 2.1 Simple Gain and Residual Gain Scores; 2.2 Three CSPR Measures; 2.3 Scale Dependency of the Growth Measures

3 Vertical Scales and the Relationships Among the Growth Measures3.1 Two Vertical Scaling Examples; 3.2 Empirical Data Comparison; 4 Conclusion and Discussion; References; Investigation of Constraint-Weighted Item Selection Procedures in Polytomous CAT; 1 Introduction; 1.1 The Maximum Priority Index (MPI) Method; 2 Method; 2.1 Simulation Study; 2.2 Evaluation Criteria; 3 Results; 4 Discussion; References; Estimating Classification Accuracy and Consistency Indices for Multidimensional Latent Ability; 1 Introduction; 2 Model and Methods; 2.1 A Multidimensional Graded Response Model