Cognitive Assessment/ Kikumi K.Tatsuoka

1 Dimensionality of Test Data and Aberrant
Response Patterns
1.1 General Overview of Cognitively Diagnostic Methodologies
1.2 Dimensionality of Tests
1.3 Detection of Aberrant Response Patterns and Their Effect
on Dimensionality
1.4 Nonparametric Rule Space: Spotting Erroneous Rules
of Operations
2 Parametric Person-Fit Statistics, Zeta (Q, and Generalized
Zetas (^1/ • • •/
2.1 History of Person-Fit Statistics
2.2 Using Person-Fit Statistics and IRT 6 for Representing
Response Patterns
2.3 The Zeta (Q Index
2.4 Semantic Meaning of ^
2.5 Generalized ^
3 Cognitive Modeling by Developing an Incidence Q Matrix
3.1 Preparation of the Q-Matrix Theory
3.2 Analysis of Knowledge States and Their Partially
Ordered Structure
3.3 A Q Matrix as a Cognitive Model
3.4 Stable Attributes as Knowledge and Cognitive
Processing Skills
3.5 Relationship Among Attributes From the Graph
Theory Approach
3.6 Partial-Order Relations Embedded in a Q Matrix:
Boolean Algebra
3.7 Attribute Space and Item Response Space
3.8 Universal Set of Knowledge States and Ideal
Item Score Patterns
4 Knowledge Space Generated From a Q Matrix
4.1 More About Attribute Space and Item Response Space
4.2 Boolean Description Function (BDF): Determination of Ideal
Response Patterns as Error-Free States of Knowledge and
Capabilities
4.3 Prerequisite Relationships in a Q Matrix
4.4 Equivalent Classes of Attribute Patterns
4.5 Item Construction
5 A Classification Space: Rule Space as a Cartesian Product
of the Person Parameter 0 in Item Response Theory, C,
and Generalized
5.1 Cognitive Sensitivity for Item Response Curves
5.2 Clustering Item Response Functions Into Homogeneous
Categories and the Relationship Among Categories
5.3 Representing Items in a Tree Based on the Underlying Tasks
5.4 Rule Space as the Cartesian Product of Two Variables, IRT
0 and ^
5.5 Variability of Response Errors and a Cluster of Response
Patterns Around a Knowledge State (or, Equivalently, Ideal
Item Score Patterns)
5.6 Bug Distributions; Distribution of Responses Around an
Ideal Item Score Pattern
5.7 Expanding the Rule Space to a Multidimensional Space
5.8 Conceptual Framework of the Rule Space Methodology
6 Classification Rules
6.1 Intuitive Classification Using Generalized Distance
6.2 Conditional Density Function of Group
6.3 Conditional Probabilities and the Bayes Theorem
6.4 Classification Into One of Two Groups (Knowledge States)
6.5 Classification Into One of Several Groups,
6.6 Error Probabilities or Misclassification Probabilities
6.7 Distribution of D^
7 Rule Space Decision Rules and Attribute Mastery
Probabilities
7.1 Classification Rule for Two Groups in Two Dimensional
Rule Space
7.2 Probabilities of Misclassifications.
7.3 Classification of Observed Response X Into One of Many
Predetermined Knowledge States
7.4 Attribute Mastery Probabilities
7.5 Reduction of Irrelevant Knowledge States
8 Posterior Probabilities With Different Prior Probabilities
and Their Effect on the Attribute Mastery Probabilities
8.1 Two or More Higher Dimensional Rule Space and Density
Functions of Knowledge States
8.2 Classification Criterion: Cutoff and Errors
8.3 Prior Probabilities: Gamma Function, Uniform Function,
and Observed Frequencies
8.4 Attribute Mastery Probabilities and the Effects
From Different Priors as the Classification Criterion
a Becomes Larger
8.5 Slippage Probabilities
8.6 The Length of Tests, the Size of Sets of Attributes,
and a Sample Size
8.7 Latent Class Models, the Hybrid Model, the Mixture
Distribution Diagnostic Model, and the POSET Model
9 Reliabilities of Item Score, Person's Score, Attribute
Mastery Probability, and Their Relationship
to the Classical Test Theory
9.1 Summary List of the Information Obtainable from a Rule
Space Analysis
9.2 True Score and Pseudotrue Score of Item j for Person i
and the Reliability of Observed Item Score X; and Attribute
Mastery Probability for an Individual
9.3 True Scores of Item j for Person i
9.4 Relationship Between the RS True Scores Estimated From a
Set of Ideal Item Score Patterns and Those From Attribute
Mastery Probabilities.
9.5 Nonparametric Attribute Characteristic Curves (ACCs)
9.6 Nonparametric Item Response Curves
9.7 Test-Retest Reliability
10 Validation of Attributes, a Q Matrix Coded by the
Involvement of Attributes to Items, and a Test
10.1 Selection of Attributes
10.2 Validation of a Q Matrix
10.3 Selection of a Smaller Number of Attributes
From a Larger Number of Attributes
10.4 Validation of the Rule Space Analysis Results
10.5 Controlled Remediation: Cognitively Diagnostic
Computerized Adaptive Testing and Remediation
10.6 An RSM Analysis as a Hypothesis Testing Method
10.7 Using RSM in Examining the Construct Validity of a Test