Categorical Variables in Developmental Research - Methods of Analysis

Front Cover

Categorical Variables in Developmental Research: Methods of Analysis

Copyright Page

Contents

Contributors

Preface

Acknowledgments

In Memoriam

Part 1: Measurement and Repeated Observations of Categorical Data

Chapter 1. Measurement Criteria for Choosing among Models with Graded Responses

1. Introduction

2. Measurement Criteria for a Model for Graded Responses

3. Models for Graded Responses

4. Examples

5. Summary and Discussion

References

Chapter 2. Growth Modeling with Binary Responses

1. Introduction

2. Conventional Modeling and Estimation with Binary Longitudinal Data

3. More General Binary Growth Modeling

4. Analyses

5. Conclusions

References

Chapter 3. Probit Models for the Analysis of Limited Dependent Panel Data

1. Introduction

2. Model Specification

3. Estimation Method

4. Analysis of Production Output from German Business Test Data

5. Conclusion

References

Part 2: Catastrophe Theory

Chapter 4. Catastrophe Analysis of Discontinuous Development

1. Introduction

2. Catastrophe Theory

3. Issues in Conservation

4. The Cusp Model

5. Empirical Studies

6. Discussion

References

Chapter 5. Catastrophe Theory of Stage Transitions in Metrical and Discrete Stochastic Systems

1. Introduction

2. Elementary Catastrophe Theory

3. Catastrophe Theory for Metrical Stochastic Systems

4. Catastrophe Theory for Discrete Stochastic Systems

5. General Discussion and Conclusion 128 References

Part 3: Latent Class and Log-Linear Models

Chapter 6. Some Practical Issues Related to the Estimation of Latent Class and Latent Transition Parameters

1. Introduction

2. Methods

3. Discussion

References

Chapter 7. Contingency Tables and Between- Subject Variability

1. Introduction

2. Association Variability

3. The Simulation Procedure

4. Tests Based on Multinomial Variability

5. Tests Based on Between-Subject Variability

6. Procedures with Two Types of Variability

7. Discussion

References

Chapter 8. Assessing Reliability of Categorical Measurements Using Latent Class Models

1. Introduction

2. The Latent Class Model: A Nonparametric Method of Assessing Reliability

3. Reliability of Dichotomous Measurements in a Prototypical Case

4. Assessment of Reliability by Group or by Time

5. Conclusion

References

Chapter 9. Partitioning Chi-Square: Something Old, Something New, Something Borrowed, but Nothing BLUE (Just ML)

1. Introduction

2. Partitioning Independence Models

3. Analyzing Change and Stability

4. How to Partition Chi-Square

5. Discussion

References

Chapter 10. Nonstandard Log-Linear Models for Measuring Change in Categorical Variables

1. Introduction

2. Bowker's Test

3. Log-Linear Models for Axial Symmetry

4. Axial Symmetry in Terms of a Nonstandard Log-Linear Model

5. Group Comparisons

6. Quasi-Symmetry

7. Discussion

References

Chapter 11. Application of the Multigraph Representation of Hierarchical Log-Linear Models

1, Introduction

2. Notation and Review

3. The Generator Multigraph

4. Maximum Likelihood Estimation and Fundamental Conditional Independencies

5. Examples

6. Summary

References

Part 4: Applications

Chapter 12. Correlation and Categorization under a Matching Hypothesis

1. Introduction

2. An Interesting Plot

3. The Binomial Effect Size Display

4. An Organizing Principle for Interval-Level Variables

5. Definition of the Matching Hypothesis

6. A Data Example

7. Correlation as a Count of Matches

8. Correlation as a Count of How Many Fall within a Set Range

9. Data Simulation

10. Building Uncertainties from Rounding Error into the Interpretation of a Correlation

11. Discussion

References

Chapter 13. Residualized Categorical Phenotypes and Behavioral Genetic Modeling

1. The Problem

2. Weighted Least-Squares Estimation

3. Proportional Effects Genotype–Environment Correlation Model

4. Method

5. Results

6. Conclusions

References

Index