Doubly Classified Model with R (eBook)

Dr Tan works as a research fellow in the Department of Research & Innovation Division, Institute for Adult Learning, Singapore. Teck Kiang completed his Ph.D. at the Nanyang Technological University, Singapore. He received a Bachelor of Accountancy degree, a Master of Science (Statistics) degree at the National University of Singapore and a Master of Accountancy degree at the Auckland University, New Zealand. He is currently a member of psychometric society. His research interests include school compositions and student’s performance, education mismatch, skills utilization, employment vulnerability, and job satisfaction. He shared his research and statistical interests through workshops conducted at conferences, at local universities with faculty members and graduate students, to adult learners, educators and researchers. He also conducted yearly workshop series to adult learners. The workshop topics he had covered include Introduction to R, R Programming, R Graphics, Doubly Classified Models, Multilevel Analysis, Propensity Score Analysis, Decision Trees, Sampling, Inter-rater Reliability and Item Response Theory. Teck Kiang has published numerous papers related to school and adult education. His recent useR! Conference 2015 presentation titled “Extending the quasi-symmetry model: Quasi symmetry with n degree” shared a series of newly derived quasi-symmetry models that generalize the quasi-symmetry model to explain the association of generic skills using doubly classified models. A recent written chapter on “The determinants of training participation, A multilevel approach: Evidence from PIAAC” examined the heterogeneity of covariates across 24 countries using multilevel random slope models. 

Table of ContentsPrefaceSymbolsChapter 1 Introduction to R1.1 What is R?1.2 Libraries in R1.3 Installing R1.4 Running R1.5 Installing Adds-On Packages and Libraries1.6 Basic Data Types1.6.1 Numeric1.6.2 Integer1.6.3 Logical1.6.4 Character1.7 Data Structure1.7.1 VectorVector AssignmentCombining VectorsVector ArithmeticRecycling RuleVector IndexDuplicate IndexesOut-of-Order Indexes1.7.2 Matrix1.7.3 Data Frame1.7.4 List1.7.5 Factor1.8 Read File into RChapter 1 ExercisesChapter 2 Basic Concepts2.1 Contingency and Square Table2.2 Generating Frequency Tables2.2.1 Tables from Vector2.2.1 Tables from Data Frame2.2.2 Margin Total and Proportion2.2.3 xtab Function2.2.4 Package gmodels, CrossTable Function2.2.5 Package descr, CrossTable Function2.3 Graphics for Tabulation2.3.1 Bar Plot – Base2.3.2 Package ggplot22.3.3 Package lattice2.4 Odds, Odds Ratios, Local Odds Ratios, and MarginOddsProperties and Interpretation of OddsOdds RatioProperties of Odds RatiosLocal Odds RatiosLog Odds RatiosMargin Total2.5 Applications of Doubly Classified2.5.1 Studies on pairs of matched individuals2.5.2 Association between two essentially similar variables2.5.3 Two point longitudinal study for a common variable2.5.4 Inter-rater Agreement2.5.5 Two Indicators from a ScaleChapter 2 ExercisesChapter 3 Examining Symmetry of Doubly Classified Table3.1 McNemar’s Test of Symmetry3.2 Variations of McNemar Test3.2.1 Exact Binomial Test3.2.2 Mid-p McNemar Test3.2.3 Which Test to Use?3.3 Bower’s Test of Symmetry3.4 Marginal Symmetry / Homogeneity ModelChapter 3 ExercisesChapter 4 Symmetry and Asymmetry Models4.1 Complete Symmetry ModelSymbolic TableNon-Standard Log-linear Approach in Generating ModelComplete Symmetry Model – Non-Standard Log-Linear SpecificationProperties of Complete Symmetry ModelFunction model.summaryA Detailed Illustration - the Dummy Specification4.2 Conditional Symmetry Model4.3 Odds Symmetry ModelRelationships of Complete Symmetry, Conditional Symmetry, Odds Symmetry I and II4.4 Diagonal Parameters Symmetry ModelRelationships of Complete Symmetry, Conditional Symmetry and Diagonal Parameters Symmetry Model4.5 Linear Diagonal Parameters Symmetry Model4.6 Quasi Symmetry ModelRelationship of QS, S, and CS4.7 Quasi Diagonal Parameters Symmetry ModelRelationships of S, CS, QS, DPS, and QDPS4.8 The 2-Ratios Parameter Symmetry ModelRelationships of Conditional Symmetry, Linear Diagonal Parameters Symmetry, and 2 Ratios Parameters Symmetry Models4.9 Quasi Conditional Symmetry Model4.10 Quasi Odds Symmetry ModelRelationships of QS, QCS and QOSRelationships of Odds Symmetry I, Odds Symmetry II, and Quasi Odds Symmetry ModelChapter 4 ExercisesChapter 5 Point-Symmetry Models5.1 Complete Point Symmetry Model5.2 Inclined Point Symmetry ModelRelationship of Complete Point Symmetry and Inclined Point Symmetry5.3 Quasi Point Symmetry Model5.4 Quasi Inclined Point Symmetry ModelRelationship between Quasi Point Symmetry and Quasi Inclined Point Symmetry5.5 Proportional Point Symmetry Model5.5.1 Comparison of Proportional and Inclined Point Symmetry Model5.5.2 Relationship of Completed Point Symmetry Model, Inclined Point Symmetry Model and Proportional Point Symmetry Model5.6 Local Point Symmetry ModelReversal Point-Symmetry Models5.7 Reverse Local Point Symmetry Model5.8 Reverse Proportional Point Symmetry Model5.9 Reverse Inclined Point Symmetry Model5.10 Quasi Reverse Inclined Point Symmetry Model5.11 Reverse Conditional Symmetry5.12 Quasi Reverse Conditional Symmetry ModelChapter 5 ExercisesChapter 6 Non-independence Models6.1 Independence and Non-Independence ModelNon-Independence Model6.2 Principal Diagonal Models6.2.1 Fixed Distance Model6.2.2 Variable Distance Model6.3 Diagonal Band Models6.3.1 Uniform Loyalty Model6.3.2 Quasi Independence Model6.3.3 Triangle Parameters Model6.4 Full diagonal Models6.4.1 Diagonal Absolute Model6.4.2 Uniform Association Model6.4.3 Uniform Fixed Distance Association Model6.4.4 Uniform Variable Distance Association ModelChapter 6 ExercisesChapter 7 Symmetry + Independence Models7.1 Non-symmetry + Independence Model7.2 Non-symmetry + Independence Triangle Model7.3 Non-symmetry + Independence Diagonals Model7.4 Non-symmetry + Independence Diagonals Absolute7.5 Non-symmetry + Independence Diagonals Absolute Triangle7.6 Non-symmetry + Independence Models – Without Diagonal CellsChapter 7 ExercisesChapter 8 Modeling Strategy8.1 Fit Statistics8.2 Graphical Approach8.2.1 Heat Map Square Table8.2.2 Three dimensional Bar Heat Map Bar Plot8.2.3 Local Odds Ratio Square Table Heat Map Plot8.2.4 Local Odds Ratio Square Table 3D Bar Chart Heat Map Plot8.2.5 Package gplots Square Table Balloon Plot8.2.6 Mosaic PlotChapter 8 ExercisesChapter 9 Creating Square models9.1 Reversed Complete Symmetry Model9.2 Parallel Diagonal Symmetry Model9.3 Quasi-Symmetry with n Degree ModelsChapter 9 ExerciseChapter 10 Summary10.1 Symbolic Table Summary10.2 R Syntax Summary10.3 Hierarchical Tree10.3.1 Hierarchical Tree – Asymmetry Models10.3.2 Hierarchical Tree – Point Symmetry Models10.4 Nested Models – Chi-Square Difference TestChapter 10 ExerciseAcknowledgementsReferences