Test Data Engineering : Latent Rank Analysis, Biclustering, and Bayesian Network.
Kojiro. Shojima
Bok Engelsk 2022 · Electronic books.
| Omfang | 1 online resource (596 pages)
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| Opplysninger | Intro -- Contents -- Abbreviations, Symbols, and Notations -- Abbreviations -- Symbols -- Notations -- 1 Concept of Test Data Engineering -- 1.1 Measurement as Projection -- 1.2 Testing as Projection -- 1.3 Artimage Morphing -- 1.4 Test Data Engineer -- 1.5 What Is ``Good'' Testing? -- 1.5.1 Context of Measurement -- 1.5.2 Context of Explanation -- 1.5.3 Context of Presence -- 1.6 Book Overview -- 2 Test Data and Item Analysis -- 2.1 Data Matrix -- 2.2 Mathematical Expressions of Data -- 2.2.1 Mathematical Expression of Data Matrix -- 2.2.2 Mathematical Expression of Item Data Vector -- 2.2.3 Mathematical Expression of Student Data Vector -- 2.3 Student Analysis -- 2.3.1 Total Score -- 2.3.2 Passage Rate -- 2.3.3 Standardized Score -- 2.3.4 Percentile Rank -- 2.3.5 Stanine -- 2.4 Single-Item Analysis -- 2.4.1 Correct Response Rate -- 2.4.2 Item Odds -- 2.4.3 Item Threshold -- 2.4.4 Item Entropy -- 2.5 Interitem Correct Response Rate Analysis -- 2.5.1 Joint Correct Response Rate -- 2.5.2 Conditional Correct Response Rate -- 2.5.3 Item Lift -- 2.5.4 Mutual Information -- 2.6 Interitem Correlation Analysis -- 2.6.1 Phi Coefficient -- 2.6.2 Tetrachoric Correlation -- 2.6.3 Item-Total Correlation -- 2.6.4 Item-Total Biserial Correlation -- 2.7 Test Analysis -- 2.7.1 Simple Statistics of Total Score -- 2.7.2 Distribution of Total Score -- 2.8 Dimensionality Analysis -- 2.8.1 Dimensionality of Correlation Matrix -- 2.8.2 Multivariate Standard Normal Distribution -- 2.8.3 Eigenvalue Decomposition -- 2.8.4 Scree Plot -- 2.8.5 Eigenvector -- 2.8.6 Eigenspace -- 3 Classical Test Theory -- 3.1 Measurement Model -- 3.2 Reliability -- 3.3 Parallel Measurement -- 3.4 Tau-Equivalent Measurement -- 3.5 Tau-Congeneric Measurement -- 3.6 Chapter Summary -- 4 Item Response Theory -- 4.1 Theta (θ): Ability Scale -- 4.2 Item Response Function.. - 11.2.8 Estimation of Parameter Set.. - 4.2.1 Two-Parameter Logistic Model -- 4.2.2 Three-Parameter Logistic Model -- 4.2.3 Four-Parameter Logistic Model -- 4.2.4 Required Sample Size -- 4.2.5 Test Response Function -- 4.3 Ability Parameter Estimation -- 4.3.1 Assumption of Local Independence -- 4.3.2 Likelihood of Ability Parameter -- 4.3.3 Maximum Likelihood Estimate -- 4.3.4 Maximum a Posteriori Estimate -- 4.3.5 Expected a Posteriori Estimate -- 4.3.6 Posterior Standard Deviation -- 4.4 Information Function -- 4.4.1 Test Information Function -- 4.4.2 Item Information Function of 2PLM -- 4.4.3 Item Information Function of 3PLM -- 4.4.4 Item Information Function of the 4PLM -- 4.4.5 Derivation of TIF -- 4.5 Item Parameter Estimation -- 4.5.1 EM Algorithm -- 4.5.2 Expected Log-Posterior Density -- 4.5.3 Prior Density of Item Parameter -- 4.5.4 Expected Log-Likelihood -- 4.5.5 Quadrature Approximation -- 4.5.6 Maximization Step -- 4.5.7 Convergence Criterion of EM Cycles -- 4.5.8 Posterior Standard Deviation -- 4.6 Model Fit -- 4.6.1 Analysis Model -- 4.6.2 Null and Benchmark Models -- 4.6.3 Chi-Square Statistics -- 4.6.4 Goodness-of-Fit Indices -- 4.6.5 Information Criteria -- 4.7 Chapter Summary -- 5 Latent Class Analysis -- 5.1 Class Membership Matrix -- 5.2 Class Reference Matrix -- 5.3 The EM Algorithm -- 5.3.1 Expected Log-Likelihood -- 5.3.2 Expected Log-Posterior Density -- 5.3.3 Maximization Step -- 5.3.4 Convergence Criterion of EM Cycles -- 5.4 Main Outputs of LCA -- 5.4.1 Test Reference Profile -- 5.4.2 Item Reference Profile -- 5.4.3 Class Membership Profile -- 5.4.4 Latent Class Distribution -- 5.5 Model Fit -- 5.5.1 Analysis Model -- 5.5.2 Null Model and Benchmark Model -- 5.5.3 Chi-Square Statistics -- 5.5.4 Model-Fit Indices and Information Criteria -- 5.6 Estimating the Number of Latent Classes -- 5.7 Chapter Summary -- 6 Latent Rank Analysis -- 6.1 Latent Rank Scale.. - 6.1.1 Test Accuracy -- 6.1.2 Test Discrimination -- 6.1.3 Test Resolution -- 6.1.4 Selection and Diagnostic Tests -- 6.1.5 Accountability and Qualification Test -- 6.1.6 Rank Reference Matrix -- 6.2 Estimation by Self-organizing Map -- 6.2.1 Winner Rank Selection -- 6.2.2 Data Learning by Rank Reference Matrix -- 6.2.3 Prior Probability in Winner Rank Selection -- 6.2.4 Results Under SOM Learning -- 6.3 Estimation by Generative Topographic Mapping -- 6.3.1 Update of Rank Membership Matrix -- 6.3.2 Rank Membership Profile Smoothing -- 6.3.3 Update of Rank Reference Matrix -- 6.3.4 Convergence Criterion -- 6.3.5 Results Under GTM Learning -- 6.4 IRP Indices -- 6.4.1 Item Location Index -- 6.4.2 Item Slope Index -- 6.4.3 Item Monotonicity Index -- 6.4.4 Section Summary -- 6.5 Can-Do Chart -- 6.6 Test Reference Profile -- 6.6.1 Ordinal Alignment Condition -- 6.7 Latent Rank Estimation -- 6.7.1 Estimation of Rank Membership Profile -- 6.7.2 Rank-Up and Rank-Down Odds -- 6.7.3 Latent Rank Distribution -- 6.8 Model Fit -- 6.8.1 Benchmark Model and Null Model -- 6.8.2 Chi-square Statistics -- 6.8.3 DF and Effective DF -- 6.8.4 Model-Fit Indices and Information Criteria -- 6.9 Estimating the Number of Latent Ranks -- 6.10 Chapter Summary and Supplement -- 6.10.1 LRA-SOM Vs LRA-GTM -- 6.10.2 Equating Under LRA -- 6.10.3 Differences Between IRT, LCA, and LRA -- 7 Biclustering -- 7.1 Biclustering Parameters -- 7.1.1 Class Membership Matrix -- 7.1.2 Field Membership Matrix -- 7.1.3 Bicluster Reference Matrix -- 7.2 Parameter Estimation -- 7.2.1 Likelihood and Log-Likelihood -- 7.2.2 Estimation Framework Using EM Algorithm -- 7.2.3 Expected Log-Likelihood -- 7.2.4 Expected Log-Posterior Density -- 7.2.5 Maximization Step -- 7.2.6 Convergence Criterion of EM Cycles -- 7.3 Ranklustering -- 7.3.1 Parameter Estimation Procedure.. - 7.3.2 Class Membership Profile Smoothing -- 7.3.3 Other Different Points -- 7.4 Main Outputs -- 7.4.1 Bicluster Reference Matrix -- 7.4.2 Field Reference Profile -- 7.4.3 Test Reference Profile -- 7.4.4 Field Membership Profile -- 7.4.5 Field Analysis -- 7.4.6 Rank Membership Profile -- 7.4.7 Latent Rank Distribution -- 7.4.8 Rank Analysis -- 7.5 Model Fit -- 7.5.1 Benchmark Model -- 7.5.2 Null Model -- 7.5.3 Analysis Model -- 7.5.4 Effective Degrees of Freedom of Analysis Model -- 7.5.5 Section Summary Thus Far -- 7.5.6 Model-Fit Indices -- 7.5.7 Information Criteria -- 7.6 Optimal Number of Fields and Ranks -- 7.7 Confirmatory Ranklustering -- 7.8 Infinite Relational Model -- 7.8.1 Binary Class Membership Matrix and Latent Class Vector -- 7.8.2 Binary Field Membership Matrix and Latent Field Vector -- 7.8.3 Estimation Process -- 7.8.4 Gibbs Sampling for Latent Class -- 7.8.5 Gibbs Sampling for Latent Field -- 7.8.6 Convergence and Parameter Estimation -- 7.8.7 Section Summary -- 7.9 Chapter Summary -- 8 Bayesian Network Model -- 8.1 Graph -- 8.1.1 Terminology -- 8.1.2 Adjacency Matrix -- 8.1.3 Reachability -- 8.1.4 Distance and Diameter -- 8.1.5 Connected Graph -- 8.1.6 Simple Graph -- 8.1.7 Acyclic Graph -- 8.1.8 Section Summary and Directed Acyclic Graph -- 8.2 D-Separation -- 8.2.1 Chain Rule -- 8.2.2 Serial Connection -- 8.2.3 Diverging Connection -- 8.2.4 Converging Connection -- 8.2.5 Section Summary -- 8.3 Parameter Learning -- 8.3.1 Parameter Set -- 8.3.2 Parent Item Response Pattern -- 8.3.3 Likelihood -- 8.3.4 Posterior Density -- 8.3.5 Maximum a Posteriori Estimate -- 8.4 Model Fit -- 8.4.1 Analysis Model -- 8.4.2 Null Model -- 8.4.3 Benchmark Model -- 8.4.4 Chi-Square Statistic and Degrees of Freedom -- 8.4.5 Section Summary -- 8.5 Structure Learning -- 8.5.1 Genetic Algorithm -- 8.5.2 Population-Based Incremental Learning.. - 8.5.3 PBIL Structure Learning -- 8.6 Chapter Summary -- 9 Local Dependence Latent Rank Analysis -- 9.1 Local Independence and Dependence -- 9.1.1 Local Independence -- 9.1.2 Global Independence -- 9.1.3 Global Dependence -- 9.1.4 Local Dependence -- 9.1.5 Local Dependence Structure (Latent Rank DAG) -- 9.2 Parameter Learning -- 9.2.1 Rank Membership Matrix -- 9.2.2 Temporary Estimate of Smoothed Membership -- 9.2.3 Local Dependence Parameter Set -- 9.2.4 Likelihood -- 9.2.5 Posterior Distribution -- 9.2.6 Estimation of Parameter Set -- 9.2.7 Estimation of Rank Membership Matrix -- 9.2.8 Marginal Item Reference Profile -- 9.2.9 Test Reference Profile -- 9.3 Model Fit -- 9.3.1 Benchmark Model -- 9.3.2 Null Model -- 9.3.3 Analysis Model -- 9.3.4 Section Summary -- 9.4 Structure Learning -- 9.4.1 Adjacency Array -- 9.4.2 Number of DAGs and Topological Sorting -- 9.4.3 Population-Based Incremental Learning -- 9.4.4 Structure Learning by PBIL -- 9.5 Chapter Summary -- 10 Local Dependence Biclustering -- 10.1 Parameter Learning -- 10.1.1 Results of Ranklustering -- 10.1.2 Dichotomized Field Membership Matrix -- 10.1.3 Local Dependence Parameter Set -- 10.1.4 PIRP Array -- 10.1.5 Likelihood -- 10.1.6 Posterior Density -- 10.1.7 Estimation of Parameter Set -- 10.2 Outputs -- 10.2.1 Field PIRP Profile -- 10.2.2 Rank Membership Matrix Estimate -- 10.2.3 Marginal Field Reference Profile -- 10.2.4 Test Reference Profile -- 10.2.5 Model Fit -- 10.3 Structure Learning -- 10.4 Chapter Summary -- 11 Bicluster Network Model -- 11.1 Difference Between BINET and LDB -- 11.2 Parameter Learning -- 11.2.1 Binary Field Membership Matrix -- 11.2.2 Class Membership Matrix -- 11.2.3 Parent Student Response Pattern -- 11.2.4 Local Dependence Parameter Set -- 11.2.5 Parameter Selection Array -- 11.2.6 Likelihood -- 11.2.7 Posterior Distribution.
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| Dewey | |
| ISBN | 9789811699863
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