Doubly Classified Model with R

ISBN-13: 9789811349812 / Angielski / Miękka / 2018 / 264 str.

Teck Kiang Tan

Spis treści

Table of Contents

Preface

Symbols

Chapter 1 Introduction to R

1.1 What is R?

1.2 Libraries in R

1.3 Installing R

1.4 Running R

1.5 Installing Adds-On Packages and Libraries

1.6 Basic Data Types

1.6.1 Numeric

1.6.2 Integer

1.6.3 Logical

1.6.4 Character

1.7 Data Structure

1.7.1 Vector

Vector Assignment

Combining Vectors

Vector Arithmetic

Recycling Rule

Vector Index

Duplicate Indexes

Out-of-Order Indexes

1.7.2 Matrix

1.7.3 Data Frame

1.7.4 List

1.7.5 Factor

1.8 Read File into R

Chapter 1 Exercises

Chapter 2 Basic Concepts

2.1 Contingency and Square Table

2.2 Generating Frequency Tables

2.2.1 Tables from Vector

2.2.1 Tables from Data Frame

2.2.2 Margin Total and Proportion

2.2.3 xtab Function

2.2.4 Package gmodels, CrossTable Function

2.2.5 Package descr, CrossTable Function

2.3 Graphics for Tabulation

2.3.1 Bar Plot – Base

2.3.2 Package ggplot2

2.3.3 Package lattice

2.4 Odds, Odds Ratios, Local Odds Ratios, and Margin

Odds

Properties and Interpretation of Odds

Odds Ratio

Properties of Odds Ratios

Local Odds Ratios

Log Odds Ratios

Margin Total

2.5 Applications of Doubly Classified

2.5.1 Studies on pairs of matched individuals

2.5.2 Association between two essentially similar variables

2.5.3 Two point longitudinal study for a common variable

2.5.4 Inter-rater Agreement

2.5.5 Two Indicators from a Scale

Chapter 2 Exercises

Chapter 3 Examining Symmetry of Doubly Classified Table

3.1 McNemar’s Test of Symmetry

3.2 Variations of McNemar Test

3.2.1 Exact Binomial Test

3.2.2 Mid-p McNemar Test

3.2.3 Which Test to Use?

3.3 Bower’s Test of Symmetry

3.4 Marginal Symmetry / Homogeneity Model

Chapter 3 Exercises

Chapter 4 Symmetry and Asymmetry Models

4.1 Complete Symmetry Model

Symbolic Table

Non-Standard Log-linear Approach in Generating Model

Complete Symmetry Model – Non-Standard Log-Linear Specification

Properties of Complete Symmetry Model

Function model.summary

A Detailed Illustration - the Dummy Specification

4.2 Conditional Symmetry Model

4.3 Odds Symmetry Model

Relationships of Complete Symmetry, Conditional Symmetry, Odds Symmetry I and II

4.4 Diagonal Parameters Symmetry Model

Relationships of Complete Symmetry, Conditional Symmetry and Diagonal Parameters Symmetry Model

4.5 Linear Diagonal Parameters Symmetry Model

4.6 Quasi Symmetry Model

Relationship of QS, S, and CS

4.7 Quasi Diagonal Parameters Symmetry Model

Relationships of S, CS, QS, DPS, and QDPS

4.8 The 2-Ratios Parameter Symmetry Model

Relationships of Conditional Symmetry, Linear Diagonal Parameters Symmetry, and 2 Ratios Parameters Symmetry Models

4.9 Quasi Conditional Symmetry Model

4.10 Quasi Odds Symmetry Model

Relationships of QS, QCS and QOS

Relationships of Odds Symmetry I, Odds Symmetry II, and Quasi Odds Symmetry Model

Chapter 4 Exercises

Chapter 5 Point-Symmetry Models

5.1 Complete Point Symmetry Model

5.2 Inclined Point Symmetry Model

Relationship of Complete Point Symmetry and Inclined Point Symmetry

5.3 Quasi Point Symmetry Model

5.4 Quasi Inclined Point Symmetry Model

Relationship between Quasi Point Symmetry and Quasi Inclined Point Symmetry

5.5 Proportional Point Symmetry Model

5.5.1 Comparison of Proportional and Inclined Point Symmetry Model

5.5.2 Relationship of Completed Point Symmetry Model, Inclined Point Symmetry Model and Proportional Point Symmetry Model

5.6 Local Point Symmetry Model

Reversal Point-Symmetry Models

5.7 Reverse Local Point Symmetry Model

5.8 Reverse Proportional Point Symmetry Model

5.9 Reverse Inclined Point Symmetry Model

5.10 Quasi Reverse Inclined Point Symmetry Model

5.11 Reverse Conditional Symmetry

5.12 Quasi Reverse Conditional Symmetry Model

Chapter 5 Exercises

Chapter 6 Non-independence Models

6.1 Independence and Non-Independence Model

Non-Independence Model

6.2 Principal Diagonal Models

6.2.1 Fixed Distance Model

6.2.2 Variable Distance Model

6.3 Diagonal Band Models

6.3.1 Uniform Loyalty Model

6.3.2 Quasi Independence Model

6.3.3 Triangle Parameters Model

6.4 Full diagonal Models

6.4.1 Diagonal Absolute Model

6.4.2 Uniform Association Model

6.4.3 Uniform Fixed Distance Association Model

6.4.4 Uniform Variable Distance Association Model

Chapter 6 Exercises

Chapter 7 Symmetry + Independence Models

7.1 Non-symmetry + Independence Model

7.2 Non-symmetry + Independence Triangle Model

7.3 Non-symmetry + Independence Diagonals Model

7.4 Non-symmetry + Independence Diagonals Absolute

7.5 Non-symmetry + Independence Diagonals Absolute Triangle

7.6 Non-symmetry + Independence Models – Without Diagonal Cells

Chapter 7 Exercises

Chapter 8 Modeling Strategy

8.1 Fit Statistics

8.2 Graphical Approach

8.2.1 Heat Map Square Table

8.2.2 Three dimensional Bar Heat Map Bar Plot

8.2.3 Local Odds Ratio Square Table Heat Map Plot

8.2.4 Local Odds Ratio Square Table 3D Bar Chart Heat Map Plot

8.2.5 Package gplots Square Table Balloon Plot

8.2.6 Mosaic Plot

Chapter 8 Exercises

Chapter 9 Creating Square models

9.1 Reversed Complete Symmetry Model

9.2 Parallel Diagonal Symmetry Model

9.3 Quasi-Symmetry with n Degree Models

Chapter 9 Exercise

Chapter 10 Summary

10.1 Symbolic Table Summary

10.2 R Syntax Summary

10.3 Hierarchical Tree

10.3.1 Hierarchical Tree – Asymmetry Models

10.3.2 Hierarchical Tree – Point Symmetry Models

10.4 Nested Models – Chi-Square Difference Test

Chapter 10 Exercise

Acknowledgements

References

O autorze

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. 

Blurb

This book provides practical applications of doubly classified models by using R syntax to generate the models. It also presents these models in symbolic tables so as to cater to those who are not mathematically inclined, while numerous examples throughout the book illustrate the concepts and their applications. For those who are not aware of this modeling approach, it serves as a good starting point to acquire a basic understanding of doubly classified models. It is also a valuable resource for academics, postgraduate students, undergraduates, data analysts and researchers who are interested in examining square contingency tables.​